$$561204 imes58 = ? imes 55555$$ implies ? = $$561204 imes58 div 55555$$ = 586

The series involves one over 9x9, 9x6, 6x6, 6x4, 4x4, etc

L is the 12th alphabet and M is the 13th alphabet. Likewise, U is the 21 st and W 23rd alphabet.

True Because m is even ie divisible by 2. n is divisible by 3 So, their product is divisible by 2 x 3 ie 6. 

In the figure, $$ riangle AQR sim riangle APS$$ => $$frac{AQ}{AP} = frac{QR}{PS} = frac{AR}{AS} = k$$ --------Eqn(I) Statement I : PQ = 3 cm , RS = 4 cm , $$angle$$ QPS = 60° In right $$ riangle$$ PQM => $$sin 60^{circ} = frac{QM}{QP}$$ => $$frac{sqrt{3}}{2} = frac{QM}{3}$$ => $$QM = frac{3 sqrt{3}}{2} = RN$$ Similarly, $$sin (angle RSN) = frac{3 sqrt{3}}{8}$$ => $$angle RSN = sin^{-1} (frac{3 sqrt{3}}{8})$$ $$ herefore$$ In $$ riangle$$ APS => $$angle PAS = 180^{circ} - angle APS - angle PSA$$ => $$angle PAS = 120^{circ} - sin^{-1} (frac{3 sqrt{3}}{8})$$ Thus, statement I alone is sufficient. Statement II : PS = 10, QR = 5 From eqn(I), $$k = frac{1}{2}$$ But, we do not know anything regarding the measures of the remaining sides or any of the angles. So, statement II is not sufficient.

$$(α^2 +β^2)$$ can be reduced to $$(α+β)^2 - 2(αβ)$$
Now as we can see, we need both values of (α+β) and (αβ) to solve the equation.
Hence answer will be D.

Both x = 4 and x = 16 satisfy the condition in statement A. Using only statement B, we cannot find the unique value of x. Using both A and B, we can infer that x = 4 Hence, option C is the answer.

The length of FI is twice the length of IG. So, the sides of the triangle FIG are in the ratio 2:1:$$sqrt5$$. So, angle FGO = angle FGI, which is definitely not equal to 30 or 45 or 60. Hence, option D is the answer.

The pattern followed is = $$n+sqrt{n^3}$$ Eg :- 6 + $$sqrt{216};7 + sqrt{343};8 + sqrt{512};9 + sqrt{729};$$ Now, $$10^3=1000$$ Thus, the next term = $$10+sqrt{1000}$$ => Ans - (D)

Expression = $$frac{1}{4} : frac{1}{8} :: frac{2}{3} :$$[u]?[/u] The pattern followed is = $$n:frac{n}{2}$$ Eg :- $$frac{1}{4}:frac{1}{4} imesfrac{1}{2}=frac{1}{4}:frac{1}{8}$$ Similarly, $$frac{2}{3} imesfrac{1}{2}=frac{1}{3}$$ => Ans - (D)

Expression : $$10+10div10-10 imes10=10$$ (A) : $$10-10div10+10 imes10$$ = $$10-1+100=109
eq10$$ (B) : $$10div10+10-10 imes10=10$$ = $$1+10-100=-89
eq10$$ (C) : $$10 imes10div10-10+10=10$$ = $$10-10+10=10$$ (D) : $$10div10+10-10 imes10=10$$ = $$1+10-100=-89
eq10$$
=> Ans - (C)

Expression = $$frac{2}{3}:frac{19}{29}::frac{8}{7}:?$$ The pattern followed is = $$frac{a}{b}:frac{10a-1}{10b-1}$$ Eg = $$frac{2}{3}:frac{10(2)-1}{10(3)-1}=frac{19}{29}$$ Similarly, $$frac{8}{7}:frac{10(8)-1}{10(7)-1}=frac{79}{69}$$ => Ans - (C)

$$frac{1}{8}:frac{1}{64}$$ = 8 let the missing number be y $$frac{1}{16}:frac{1}{y}$$ = 8
y = 128

If we assign numbers to the alphabets such as A = 1 , B = 2 , C = 3 and so on, we get : $$sqrt{AFI}=sqrt{1+6+9}=sqrt{16}=4=1+3equiv13=M$$
and $$sqrt{ADD}=sqrt{1+4+4}=sqrt{9}=3=1+2equiv12=L$$ Similarly, $$sqrt{ABA}=sqrt{1+2+1}=sqrt{4}=2=1+1equiv11=K$$ => Ans - (D)

Expression : $$frac{34}{49} imes frac{147}{272} div frac{27}{32}= ?$$ = $$frac{3}{8} imes frac{32}{27}$$
= $$frac{4}{9}$$

Expression : 477 $$div$$  53 + 64 $$ imes$$ 3 = ? = $$(frac{477}{53}) + 192$$ = $$9 + 192 = 201$$

Expression : (53 $$ imes$$ 18) + (85 $$ imes$$  7) = ? = 954 + 595 = 1549

Expression : $$(5)^{3}+(12)^{2}-(26 div 2) =(?)^{2}$$ => $$125 + 144 - (frac{26}{2}) = (x)^2$$ => $$(x)^2 = 269 - 13 = 256$$ => $$x = sqrt{256} = 16$$

Expression : $$1frac{5}{14}+3frac{4}{7}+4frac{9}{28}=?$$ = $$(1 + 3 + 4) + (frac{5}{14} + frac{4}{7} + frac{9}{28})$$ = $$8 + (frac{10 + 16 + 9}{28})$$ = $$8 + frac{35}{28} = 8 + frac{5}{4}$$ = $$frac{37}{4} = 9 frac{1}{4}$$

Expression : $$sqrt{9280 div16 imes 4 -16}=?$$ = $$sqrt{frac{9280}{16} imes 4 - 16}$$ = $$sqrt{(580 imes 4) - 16}$$ = $$sqrt{2320 - 16} = sqrt{2304}$$ = $$48$$

Expression : $$frac{7702}{43.96}+25.11 imes45.88=? imes15$$ => $$frac{7700}{44} + 25 imes 46 = x imes 15$$ => $$175 + 1150 = 15x$$ => $$x = frac{1325}{15} = 88.33$$ => $$x approx 88$$

Expression : $$24.98^{2} imesfrac{16.02^{2}}{(7.98 imes15.04)} imes38.93=130 imes?^{2}$$ => $$25^2 imes frac{16^2}{8 imes 16} imes 39 = 130 imes x^2$$ => $$625 imes 2 imes 39 = 130 imes x^2$$ => $$x^2 = 125 imes 3 = 375$$ => $$x = sqrt{375} = 19.5 approx 20$$

Expression : $$2775 imesfrac{160}{sqrt{(?)}}=5550$$ => $$frac{160}{sqrt{(x)}} = frac{5550}{2775} = 2$$ => $$sqrt{x} = frac{160}{2} = 80$$ => $$x = (80)^2 = 6400$$

Expression : $$frac{1810}{24.05} imes7.95+11.02 imes18.88=?-306$$ => $$(frac{1800}{24} imes 8) + (11 imes 19) = (x - 306)$$ => $$600 + 209 = x - 306$$ => $$x = 809+ 306 = 1115$$

Expression : $$?\%of(frac{5224}{5.001} imesfrac{3}{11})=375.05$$ => $$frac{x}{100} imes frac{5225}{5} imes frac{3}{11} = 375$$ => $$frac{x}{100} imes 95 imes 3 = 375$$ => $$x = frac{375 imes 100}{285} approx 132$$

Expression : $$15.99 imes9.89-sqrt{624.89}-17.001 imes1.99=?^{2}$$ => $$(x)^2 = (16 imes 10) - (sqrt{625}) - (17 imes 2)$$ => $$(x)^2 = 160 - 25 - 34 = 101$$ => $$x approx sqrt{100} = 10$$

Expression : $$frac{9601}{11.98} imessqrt{(531)}+95.88=?$$ = $$frac{9600}{12} imes sqrt{529} + 96$$ = $$800 imes 23 + 96$$ = $$18400 + 96 = 18496$$

Expression : $$frac{2430}{16}-16.97+sqrt{(?)}=164$$ => $$frac{2432}{16} - 17 + sqrt{x} = 164$$ => $$152 - 17 + sqrt{x} = 164$$ => $$sqrt{x} = 164 - 135 = 29$$ => $$x = 29^2 = 841$$

Expression : $$sqrt{(576)}+sqrt{(1764)}=sqrt{(?)}$$ => $$sqrt{x} = 24 + 42 = 66$$ => $$x = (66)^2 = 4356$$

Expression : $$(2frac{2}{5}+3frac{1}{4}-2frac{7}{8}) imes?=222$$ => $$[(2 + 3 - 2) + (frac{2}{5} + frac{1}{4} - frac{7}{8}) imes x] = 222$$ => $$(3 + frac{2}{5} - frac{5}{8}) imes x = 222$$ => $$(3 - frac{9}{40}) imes x = 222$$ => $$frac{111}{40} x = 222$$ => $$x = 222 imes frac{40}{111}$$ => $$x = 2 imes 40 = 80$$

Expression : $$42 imes4-sqrt{(625)}-132=frac{143}{?}$$ => $$168 - 25 - 132 = frac{143}{x}$$ => $$168 - 157 = frac{143}{x}$$ => $$x = frac{143}{11} = 13$$

Expression : $$frac{frac{126}{14} imes?-7 imes3}{8^{2}-7 imes6+20}=1$$ => $$frac{9x - 21}{64 - 42 + 20} = 1$$ => $$9x - 21 = 42$$ => $$9x = 42 + 21 = 63$$ => $$x = frac{63}{9} = 7$$

Expression : $$frac{125^{2} imessqrt{(15)} imes5^{3}}{sqrt{(375)}}=5^{11-?}$$ => $$frac{(5)^6 imes sqrt{15} imes (5)^3}{5 sqrt{15}} = 5^{11-?}$$ => $$5^{6 + 3 - 1} = 5^{11-?}$$ => $$11 - x = 8$$ => $$x = 11 - 8 = 3$$

Expression : $$(0.8)^{2.5} imesfrac{(0.8)^{1.5}}{(0.8)^{0.5}}=(0.2)^{3.5} imes2^{?}$$ => $$(0.8)^{2.5 + 1.5 - 0.5} = (0.2)^{3.5} imes 2^{x}$$ => $$(0.8)^{3.5} = (0.2)^{3.5} imes 2^{x}$$ => $$2^x = frac{(0.8)^{3.5}}{(0.2)^{3.5}}$$ => $$2^x = (4)^{3.5} = 2^7$$ => $$x = 7$$

Expression : $$(frac{42.25}{0.5}+frac{16.2}{0.2}) imes?=1986$$ => $$(84.5 + 81) imes x = 1986$$ => $$165.5 imes x = 1986$$ => $$x = frac{1986}{165.5} = 12$$

Expression : $$(frac{1frac{7}{60}}{1frac{27}{40}}) imes(1frac{29}{34}) imes? = 231$$ => $$frac{frac{67}{60}}{frac{67}{40}} imes (frac{63}{34}) imes x = 231$$ => $$frac{40}{60} imes (frac{63}{34}) imes x = 231$$ => $$frac{2}{3} imes (frac{63}{34}) imes x = 231$$ => $$frac{21}{17} imes x = 231$$ => $$x = 231 imes frac{17}{21}$$ => $$x = 11 imes 17 = 187$$

Expression : $$29^{2} - 435 + ?= 1652 imes 0.5$$ => $$841 - 435 + x = 826$$ => $$x = 826 - 406$$ => $$x = 420$$

Expression : $$frac{1.12 imes 2.24 - 0.78 imes 1.56}{4 imes (1.12 - 0.78)} = ?$$ = $$frac{2 (1.12)^2 - 2 (0.78)^2}{4 (1.12 - 0.78)}$$ = $$frac{2 (1.12 - 0.78) (1.12 + 0.78)}{4 (1.12 - 0.78)}$$     [Using, $$a^2 - b^2 = (a - b) (a + b)$$] = $$frac{1.12 + 0.78}{2}$$ = $$frac{1.9}{2} = 0.95$$

The given expression is of the form $$frac{(a+b)^2-(a-b)^2}{a*b}$$
$$(a+b)^2-(a-b)^2 = a^2+b^2+2ab - (a^2-2ab+b^2) = 4ab$$
Hence, the given expression equals $$frac{(a+b)^2-(a-b)^2}{a*b} = frac{4ab}{ab}=4$$ So, the correct option is option (a)

Note that $$37*37=1369$$
and, $$28*28=784$$ Hence, the given expression equals $$sqrt{1369} imessqrt{784}=37*28$$
$$37*28=1036$$ So, the correct answer is 1036 which is option (d)

4004 = 4*1001 = 4*7*11*13 So, the given equation equals $$frac{4}{7}$$ of $$frac{6}{11}$$ of $$frac{5}{13}$$ of $$4004$$ which equals  $$frac{4}{7}$$ of $$frac{6}{11}$$ of $$frac{5}{13}$$ of $$4*7*11*13$$ which equals $$4*6*5*4=480$$

Expression : $$117.95 imes 8.017 imes 4.98$$ $$approx 118 imes 8 imes 5$$ = $$118 imes 40 = 4720$$

Expression : $$3745 div 24.05 imes 17.98 = ?$$ $$approx frac{3745}{24} imes 18$$ = $$frac{3745}{4} imes 3 = 2808.75$$ $$approx 2800$$

Expression : $$(0.0729 div 0.1)^{3}div (0.081 imes 10)^{5}$$ $$ imes (0.3 imes 3)^{5}=(0.9)^{?+3}$$ => $$(frac{0.0729}{0.1})^3 div (0.81)^5 imes (0.9)^5 = (0.9)^{x + 3}$$ => $$(0.729)^3 imes frac{1}{(0.9^2)^5} imes (0.9)^5 = (0.9)^{x + 3}$$ => $$(0.9^3)^3 imes (0.9)^{5 - 10} = (0.9)^{x + 3}$$ => $$(0.9)^{9 - 5} = (0.9)^{x + 3}$$ Comparing powers on both sides => $$x + 3 = 4$$ => $$x = 4 - 3 = 1$$

Expression : $$[(3024 div 189)^{frac{1}{2}} + (684 div 19)^{2}] = (?)^{2}+ 459$$ => $$(frac{3024}{189})^{frac{1}{2}} + (frac{684}{19})^2 = (x)^2 + 459$$ => $$(16){frac{1}{2}} + (36)^2 = (x)^2 + 459$$ => $$4 + 1296 = (x)^2 + 459$$ => $$(x)^2 = 1300 - 459 = 841$$ => $$x = sqrt{841} = pm 29$$

Expression : $$(13+2sqrt{5})^{2}=? imessqrt{5}+189$$ Using : $$(a + b)^2 = a^2 + b^2 + 2ab$$ => $$(13)^2 + (2sqrt{5})^2 + (2.13.2sqrt{5}) = (x imes sqrt{5}) + 189$$ => $$169 + 20 + 52sqrt{5} = xsqrt{5} + 189$$ => $$189 + 52sqrt{5} = xsqrt{5} + 189$$ Comparing both sides, we get : => $$x = 52$$

Expression : $$1478.4 div 56 + 66.8 imes 57$$ = $$(? imes 3) + (34 imes 34.5)$$ => $$(frac{1478.4}{56}) + (66.8 imes 57)$$ = $$(x imes 3) + (34 imes 34.5)$$ => $$26.4 + 3807.6 = 3x + 1173$$ => $$3834 = 3x + 1173$$ => $$3x = 3834 - 1173 = 2661$$ => $$x = frac{2661}{3} = 887$$

Expression : $$(562.5 imes 6)^{6}div(135 div 9)^{10}$$ $$div(37.5 imes 6)^{7}=(3.75 imes 4)^{?-6}$$ => $$(3375)^6 div (15)^{10} div (225)^7 = (15)^{x - 6}$$ => $$((15)^3)^6 div (15)^{10} div ((15)^2)^7 = (15)^{x - 6}$$ => $$(15)^{18} imes frac{1}{(15)^{10}} imes frac{1}{(15)^{14}} = (15)^{x - 6}$$ => $$(15)^{18 - 10 - 14} = (15)^{x - 6}$$ => $$(15)^{-6} = (15)^{x - 6}$$ Comparing both sides, we get : => $$x - 6 = -6$$ => $$x = 6 - 6 = 0$$

Expression : $$7072 div (16\% of 884) = 30 imes1frac{1}{2}of(? div 39)$$ => $$7072 div (frac{16}{100} imes 884) = 30 imes frac{3}{2} imes frac{x}{39}$$ => $$8 imes frac{100}{16} = frac{15x}{13}$$ => $$50 = frac{15x}{13}$$ => $$x = frac{50 imes 13}{15}$$ => $$x = 43.33 approx 43$$

Expression : $${8^{1.1}} imes {4^2}^{.7} imes {2^{3.3}} = {2^?}$$ => $$(2)^{3 imes 1.1} imes (2)^{2 imes 0.7} imes (2)^{3.3} = (2)^x$$ => $$(2)^{3.3} imes (2)^{1.4} imes (2)^{3.3} = (2)^x$$ => $$(2)^{3.3 + 1.4 + 3.3} = (2)^x$$ Comparing both sides, we get : => $$x = 3.3 + 1.4 + 3.3 = 8$$

Expression : $$1{1 over 8} + 1{6 over 7} + 3{3 over 5}$$ = ? = $$(1 + 1 + 3) + (frac{1}{8} + frac{6}{7} + frac{3}{5})$$ = $$5 + (frac{35 + 240 + 168}{280})$$ = $$5 + frac{443}{280} = 5 + frac{280 + 163}{280}$$ = $$5 + (1 + frac{163}{280}) = 6{{163} over {280}}$$

Expression : $${2^{0.2}} imes 64 imes {8^{1.3}} imes {4^{0.2}} = {8^?}$$ => $$(2)^{0.2} imes (2)^6 imes (2)^{3 imes 1.3} imes (2)^{2 imes 0.2} = (2)^{3 imes x}$$ => $$(2)^{0.2 + 6 + 3.9 + 0.4} = (2)^{3 x}$$ => $$(2)^{10.5} = (2)^{3 x}$$ Comparing powers of 2, we get : => $$3x = 10.5$$ => $$x = frac{10.5}{3} = 3.5$$

Expression : $$12.95 imes7.05+(85.01)^{2} imes10.99=?$$ = $$(13 imes 7) + (85^2 imes 11)$$ = $$91 + (7225 imes 11)$$ = $$91 + 79475 = 79566$$

Expression : 13.999% of 134.999 + $$sqrt {7.999 imes 8.0001}$$  = 20 % of ? $$approx 14 \%$$ of $$135 + sqrt{8 imes 8} = frac{20}{100} imes x$$ => $$18.9 + 8 = frac{x}{5}$$ => $$x approx 5 imes (19 + 8) = 5 imes 27$$ => $$x = 135$$

$$frac{5}{8}$$ x 4011.33 = 2507.08
$$frac{7}{10}$$ of 3411.22 = 2387.854
2507.08 + 2387.854 = 4894.934 ≈ 4890

8787 ÷ 343 = 25.61
$$sqrt{50}$$ = 7.07
25.61 x 7.07 = 181.06 ≈ 180

5$$frac{17}{37}$$ = $$frac{202}{37}$$

4$$frac{51}{52}$$ = $$frac{259}{52}$$

11$$frac{1}{7}$$ = $$frac{78}{7}$$

2$$frac{3}{4}$$ = $$frac{11}{4}$$

$$frac{202}{37}$$ x $$frac{259}{52}$$ x $$frac{78}{7}$$ = 303

303 + $$frac{11}{4}$$ = 305.75

[(5$$sqrt{7}$$ + $$sqrt{7}$$ ) × (4$$sqrt{7}$$ + 8$$sqrt{7}$$ )] - (19)2
= [6$$sqrt{7}$$ x 12$$sqrt{7}$$] - 192
= [72 x 7] - 192
= 143

The given statement can be written as $$frac{1575}{45} + 24 *sqrt{256}$$ =$$35+24*16$$ =$$35+384$$ = 419 ( Approximately 420)
Option B is the right answer.

The given statement can be written as $$frac{160}{4} + 1960 - 120 = 1960-80 = 1880$$. Option D is the right answer.

The given equation can be written as $$frac{160}{40} + frac{4}{5}* 180 - 120$$ $$4+144-120= 28$$ Option A is the right answer.

I : $$x^{2} + 11x + 18 = 0$$ => $$x^{2} + 2x + 9x = 18 = 0$$ => $$x (x + 2) + 9 (x + 2) = 0$$ => $$x$$ = -2, -9 II : $$y^{2} - sqrt{81} = 0$$ => $$y^{2} = sqrt{81}$$ => $$y^{2} = 9$$ => $$y$$ = 3, -3 Since, 3 > -2 > -3 Hence, no relation can be established.

The given statement can be written as $$frac{116}{4} - frac{15}{3} - 40 = -x$$ $$45 - 29 = x$$ => $$x = 16$$ ( Approx. 17 - since we have reduced both the values in the question slightly) Option D is the right answer.

14.08 ~ 14 3.01 ~ 13 104.11 ~ 104 4.02 ~ 4 Now , (14.08² x 3.01 × 104.11 ÷ 4.02) is equivalent to ( 14² x 3 × (104 ÷ 4)) = (196 x 3 x 26) = 15288

The given question can be written as $$frac{sqrt{225}*12}{20}$$ = $$frac{15*12}{20}$$ =$$9$$ Option C is the right answer.

$$R igstar K$$ which means R is smaller than K
K % D which means K is greater than D
D @ V which means D is equal to V
$$V delta M$$ which means V is smaller than or equal to D.
We can conclude that M is greater than or equal to D.
Either III or IV is correct conclusion.

0.0004 / 0.0001 = 4 4 * 36 = 144 The option that is closest to this is option c).

As we need to find the approximate value of the given equation, we can make some small approximations. $$(15.01)^{2} imessqrt{730} approx 15^2 imes sqrt{729}$$ This equals $$225*27 = 6075$$ Hence, the correct option is option (d)

As we are finding the approximate value of the given equation, let us slightly increase one of the terms and decrease the other time slightly. Hence, $$25.05 imes123.95+388.999 imes15.001 approx 25 imes 124 + 389 imes 15$$ This equals $$3100 + 5835 = 8935$$ So, the correct option is option (c)

We need to find the approximate value of $$frac{1}{8}$$ of $$ frac{2}{3}$$ of $$frac{3}{5}$$ of 1715 $$frac{1}{8}$$ of $$frac{2}{3}$$ of $$frac{3}{5}$$ = $$frac{1}{20}$$
Hence, the approximate value equals $$frac{1}{20} imes 1715 = 85.75 approx 85$$ Hence, the correct answer is option (b)

[u][/u]Expression : $$(10008.99)^{2}/(10009.001) imessqrt{3589} imes0.4987=?$$ $$approx frac{(10009)^2}{10009} imes sqrt{3600} imes 0.5$$ = $$1009 imes 60 imes 0.5$$ = $$1009 imes 30 = 30270$$ $$approx 30,000$$ => Ans - (A)

Expression : $$frac{2}{5}+frac{7}{8} imesfrac{17}{19}divfrac{6}{5}=?$$ = $$frac{2}{5} + (frac{7}{8} imes frac{17}{19} imes frac{5}{6})$$ = $$frac{2}{5} + frac{595}{912}$$  $$approx 0.4+0.6=1$$ => Ans - (A)

Original sequence: P % R 1 5 ⋆" id="MathJax-Element-1-Frame" role="presentation" tabindex="0">⋆ M T E 3 B $ V N 4 K A 8 W I 6 2 G # U H 7 Ö J Q 9 L Y
Question Sequence: 1 $$star$$ T 3 $ N K 8 I ? Ö Q L
The pattern here is simple, alternate terms have been written down in the question sequence.
So after I we should have 2 followed by #, followed by H
This is there in the first option, so the correct answer is option A

We know that $$x^a + x^b = x^{a+b}$$ In this case, the expression becomes $$left{10^{3.7} imes10^{1.3} ight}^2=left{10^{3.7+1.3} ight}^2 = left{10^5 ight}^2 = 10^{10} $$ As the option is not available, the correct answer is option (e)

Let the number to replace the question mark be $$X$$ So, $$3978+112 imes2 = X div2$$
Or, $$3978 + 224 = X div 2$$
Or, $$4202 = X div 2$$
Or, $$X = 4202 imes 2 = 8404$$ Hence, the correct option is option (d)

$$3frac{1}{3} div 6frac{3}{7} imes 1frac{1}{2} imes frac{22}{7}$$ This equals $$frac{10}{3} div frac{45}{7} imes frac{3}{2} imes frac{22}{7}$$ This equals $$frac{10}{3} imes frac{7}{45} imes frac{3}{2} imes frac{22}{7} = frac{22}{9}$$
As this is not given in any of the options, the correct answer is option (e)

$$40.83 imes1.20 imes1.2= 40.83 imes 1.44$$ This equals $$40.83 imes 1.44 = 58.7952$$ Hence, the correct answer is option (c)

In order to find the approximate value of $$1010div36+187 imes20.05$$, let us approximate the values first. Let us replace $$1010$$ with $$1008$$ as it is a multiple of 36 and $$20.05 approx 20$$ So, the expression looks like this $$1008 div 36 + 187 imes 20 = 28 + 3740 = 3768$$ The closest option to this is option (b)

In order to find the approximation value of $$127.001 imes 7.998 + 6.05 imes 4.001$$, let us approximate the values first. $$6.05 approx 6$$ and $$4.001 approx 4$$ and $$127.001 approx 127$$ and $$7.998 approx 8$$ So, the approximate value looks $$127 imes 8 + 6 imes 4 = 1016 + 24 = 1040$$ Hence, the correct option is option(d)

In order to find the approximate value of $$125\% of 4875 + 88.005 imes 14.995$$, let us approximate the values. $$88.005 approx 88$$ and $$14.995 approx 15$$ So, the expression looks like $$125\% imes 4875 + 88 imes 15 = 6093 + 1320 = 7413$$ The closest option to this is option (e)

Using (b), 20 # 10 * 2 = $$frac{20-10}{2}$$ = 5 => m = 5 Using (d), m • 6 $$lambda$$ 4 = (6 * 4) - 5 = 24 - 5 = 19

The statements are : M > T , T $$geq$$ K , K = D Combining above inequalities, we get : M > T $$geq$$ K = D The conclusions : D < M [true] M > K [true] Thus, both conclusions are true.

$$p=pm100$$ $$q=(10000)^frac{1}{2}$$ =$$pm100$$ Hence p = q.

|a| * |b| = |ab| For this to be -ab, it has to be multiplied by -1. So, option a) is the correct answer.

Let the number required be equal to $$X$$ Hence, $$(15)^{2}+(18)^{2}-20=sqrt{X}$$ 225 + 324 -20 = $$sqrt{X}$$ So, X = $$ 529^2$$ =279841

$$9frac{3}{4}+7frac{2}{17}-9frac{1}{15}$$ This equals $$frac{39}{4} + frac{121}{17} - frac{136}{15}$$
The LCM of $$4, 15, 17 = 1020$$ Hence, the required expression equals $$frac{9945}{1020} + frac{7260}{1020} - frac{9248}{1020}$$ This equals $$frac{7957}{1020} = 7frac{817}{1020}$$

We need to find the approximate value of (421% of 738) $$div$$ 517
This is approximately equal to $$(4.2 imes 7.4) div 5.2 approx 31.08 div 5.2 approx 6$$ Hence, the correct option is option (a)

Let the number to be found out be equal to $$X$$ Hence, $$sqrt[3]{X}=(36 imes24)div9$$
So, $$sqrt[3]{X} = 4 imes 24 = 96$$ So, the value of X is $$96 imes 96 imes 96 = 884736$$ So, the correct option is option (a)

$$9\% of 386 = 34.74$$
$$6.5\% of 144 = 9.36$$ Hence, the required product is $$34.74 imes 9.36 = 325.1664$$

We need to find the value of $$(35423+7164+41720) -(317 imes89)$$ $$35423+7164+41720 = 84307$$
$$317 imes 89 = 28213$$ So, the required value is $$84307 - 28213 = 56094$$
As, this is not given in the options, the correct answer is option (e)

We need to find the value of $$(800div64) imes(1296div36)$$=? $$800 div 64 = 100 div 8 = 25 div 2 = 12.5$$
$$1296 div 36 = 216 div 6 = 36$$ So, $$(800div64) imes(1296div36) = 12.5 imes 36 = 450$$ As this is not given in any of the options, the correct answer is option (e)

First, we convert mixed fractions into proper fractions:
$$5frac{1}{4}=frac{21}{4}$$
$$6frac{2}{3}=frac{20}{3}$$
$$7frac{1}{6}=frac{43}{6}$$
Now, $$5frac{1}{4}+6frac{2}{3}+7frac{1}{6}=frac{21}{4}+frac{20}{3}+frac{43}{6}$$ = $$frac{229}{12}$$ In mixed fraction form 229/12 = $$19frac{1}{12}$$
Option C is correct.

Lets assume the unknown number to be x.
Now, we will solve in a stepwise manner going by BODMAS rule.
144^2=20736,
20736/48=432
432*18=7776
7776/36=216
Now x=216^2 = 46656 which is option D.

The problem can be solved quickly by rounding of as option values are quite far away from each other.
Now, 755~750, 777~800 and 523~500.
We are asked to evaluate (755 $$\%$$ of 777) $$div$$ 523=? i.e (750*500)/ (800 * 100) = 4.68 = 5 (approx).
Therefore, correct option is A.

L $$igstar$$P i.e L is smaller than or equal to P.
P % V i.e P is smaller than V.
V # D i.e V is equal to D.
Now, L $$igstar$$ V cannot be true as V is greater than P and hence L.
Even, L $ D i.e L is equal to D cannot be said with surety.
Both, conclusion I and II do not follow.
Option D is correct answer.

The given statement can be written as $$RD=Vleq M$$ The conclusions are (i) $$ R D $$ From the statement, no relationship can be established between R and D or V and R. Hence, both these conclusions are false. Since,D is equal to V and V is less than or equal to M, D must be less than or equal to M. Hence, either conclusion III or IV must be true ( Collectively exhaustive). Hence, option D is the right answer.

The question can be reframed as, $$15^{2}$$*$$sqrt(729)$$=$$225 imes27$$=607

By approximating 561~560, 19.99~20 and 35.05~ 35 for easier calculation,  the question can be written as,  560*(20/35)=320

Here we are approximating 25.05~25, 123.95~124, 388.99~389, 15.001~15.  The question can be rewritten as, 25*123+388*15=8935
Hence the correct option is 8935.

Now, $$frac{1}{8} of frac{2}{3} $$= (1/8)*(2/3)=1/12 Also, ( $$frac{1}{8} of frac{2}{3}$$ ) of $$frac{3}{5}$$ = (1/12) * (3/5) = 1/20
Now, (1/20) 0f 1715= (1/20)*1715 = 85

__ $$leq$$ __ < P > __ , P cannot be at this position, as at this position P would be greater than A in every possible combination. Hence Option E.

B_L_O_N_D
Since B has to be greater than N, "

P >L ? A $$geq$$ N = T Now, P > L and A $$geq$$ T For P to be greater than A, A should be $$leq$$ L. For T to be $$leq$$ L, L has to be $$geq$$ A.
Hence for the given statements to be definitely true, L can either be =, or > or $$geq$$ A. Thus, A.

Rounding off the decimals to the nearest whole number and calculating the result would give an answer close to the actual answer.
$$12^2 = 144$$
$$16^2 = 256$$
$$12^2 + 16^2 = 144 + 256 = 390 $$
Let the unknown term be x.
$$x^2 imes 4^2 = 390$$
$$x^2 = frac{390}{16}$$
$$ x^2 approx 24$$
$$x approx 5$$
Hence Option D is the correct answer.

$$sqrt{288}$$ lies between 16 and 17.
While calculating , other numbers can be rounded of to the nearest multiple of 10 or the whole number.
Hence 1440 divided by 16 is 90 and 90 times 15 is 1350.
1350+ $$sqrt{288} approx $$ 1367. The nearest value in the option is Option B.

Expression : ( 52.02^{2} - 34.01^{2}) $$div$$ 17.99 $$ imes$$ $$sqrt{?}$$ = 1720 = $$(52^2 - 34^2) div 18 imes sqrt{?} = 1720$$ = $$frac{(52 - 34) (52 + 34)}{18} imes sqrt{?} = 1720$$ = $$sqrt{?} = frac{1720}{86} = 20$$ $$ herefore$$ ? = 20 * 20 = 400

Expression : ( 1800 $$div sqrt{?}$$ $$ imes$$ 29.99 ) $$div$$ 15.02 = 144 = $$frac{1800}{sqrt{?}} imes frac{30}{15} = 144$$
= $$sqrt{?} = frac{1800 imes 2}{144} = 25$$ $$ herefore$$ ? = 25 * 25 = 625

Expression : $$349.98 imes 19.99 + ?^2 imes 180.16 = 11500$$ = $$(350 imes 20) + (?^2 imes 180) = 11500$$ = $$?^2 imes 180 = 11500 - 7000 = 4500$$ = $$?^2 = frac{4500}{180} = 25$$ = $$? = sqrt{25} = 5$$

Since approximate values are sufficient we can round off the values to the nearest whole number.
$$25$$%of $$460 + 65 div 5$$
$$ 25 $$%of $$460 = 115$$
$$ 65 div 5 = 13$$
$$115+13= 128$$
Option B is the correct answer

Since approximate values are sufficient we can round off the values to the nearest whole number.
$$359 div 15 approx 24$$
$$359 div 15 + 450 div 9 + 56 =24 + 50 +56 = 130$$
Hence Option E is the correct answer.

Let the unknown power be a.
$$3^{a} imes sqrt{170} = 183.998div8.001 + 328.02$$
Round off the values to the nearest whole number.
$$3^{a} imes sqrt{170} = 184 div 8 + 328$$
$$ sqrt{170} approx 13 ( 13^2 =169 )$$
$$3^{a} imes 13 = 23+ 328=351$$
$$3^a = frac{351}{13}$$
$$3^a= 27$$
$$3^a= 3^3$$
$$a=3$$
Option E is the correct answer.

Expression : $$124.001 imes 14.001 div 3.4999 + 2^2 = ?$$ = $$124 imes frac{14}{3.5} + 2^2$$ = $$124 imes 4 + 2^2$$ = $$500$$

Expression : $$frac{3}{5}offrac{4}{7}offrac{7}{9}of425=?$$ = $$frac{3 imes 4 imes 7}{5 imes 7 imes 9} imes425$$ = $$frac{4}{15} * 425$$ = $$frac{1700}{15} = 113$$

Since it is sufficient to find the approximate value, round off the values.
42.11 $$ imes$$ 5.006 = 42 $$ imes$$ 5 $$approx$$ 210
$$sqrt{7} $$ lies between 2 and 3.The actual value of $$sqrt{7}$$ = 2.645.
$$sqrt{7} imes$$ 15.008 = $$sqrt{7} imes$$ 15 $$approx$$ 39.
210-39 = 171
The nearest Option is Option B.
Hence Option B is the correct answer.

Since approximate values are sufficient, round off the values to the nearest whole number.
97 + 33 + 15 $$ imes$$ 8 = 130 + 120 = 250
Option C is the correct answer.

$$sqrt{11449}$$ x $$sqrt{6241}$$ - (54)2 - (74)2 = $$sqrt{?}$$
$$sqrt{?}$$ = [107 x 79] - 2916 - 5476
= 8453 - 2916 - 5476 = 61
$$sqrt{?}$$= (61)2 = 3721

[ $$sqrt{8}$$ (3 +1) x $$sqrt{8}$$(8 + 7)] - 98
= [4$$sqrt{8}$$ x 15 x $$sqrt{8}$$ ] - 98
= [60 x $$sqrt{8}$$] - 98
= 480 - 98 = 382

We solve the problem as per BODMAS rule
$$frac{195}{308}$$ ÷ $$frac{39}{44}$$ = $$frac{5}{7}$$
$$frac{28}{65}$$ x $$frac{5}{7}$$ = $$frac{4}{13}$$
$$frac{4}{13}$$ + $$frac{5}{26}$$ = $$frac{13}{26}$$ = $$frac{1}{2}$$

Expression = $$2375.85 div 18.01 - 4.525 imes 8.05 = ?$$ $$approx frac{2376}{18} - (5 imes 8)$$ = $$132 - 40 = 92$$ $$approx 90$$

Expression : $$2508 div 15.02 + ? imes 11 = 200$$ => $$(frac{2505}{15}) + (? imes 11) = 200$$ => $$167 + (? imes 11) = 200$$ => $$? imes 11 = 200 - 167 = 33$$ => $$? = frac{33}{11} = 3$$

Expression : $$3.2 imes 8.1 + 3185 div 4.95 = ?$$ = $$(3 imes 8) + (frac{3185}{5})$$ = $$24 + 637 = 661$$ $$approx 660$$

Expression : $$3frac{3}{2} imesfrac{8}{45}+1frac{2}{3} imesfrac{2}{15}=?$$ = $$(frac{9}{2} imesfrac{8}{45})+(frac{5}{3} imesfrac{2}{15})$$ = $$frac{4}{5}+frac{2}{9}$$ = $$frac{(36+10)}{45}$$ = $$frac{46}{45}=1frac{1}{45}$$ => Ans - (B)

Expression : $$frac{3}{8}offrac{4}{7}offrac{7}{9}of738=?$$ = $$frac{3}{8} imes frac{4}{7} imes frac{7}{9} imes 738$$
= $$frac{1}{6} imes 738 = 123$$

In each group of words, the group is formed by taking alternate words in the series.
Only in 9DF, this pattern has not been followed.
Hence, the correct option is B.

Only 9 is immediately followed by %. Only one such pattern exists for the entire series.
Hence, option B signifying 1 pattern is correct.

Let the number in the question mark be equal to $$X$$. So, $$X = 814296 imes 36 div 96324 = 304.33 approx 304$$

The numerator in the given fraction equals 9795+7621+938 = 18354 The denominator in the given fraction equals 541+831+496 = 1868 So, the given ratio becomes 18354/1868 = 9.82 ~ 9

By BODMAS rule, we will first solve brackets. 739% of 383 = 2830.37 Now, we go for division, 2830.37 $$div$$ 628 = 4.50 Hence, the correct option is B.

By applying BODMAS rule, first we do multiplication,
$$6.1325 imes 44.0268= 269.9944$$ Now, we subsequently do addition. $$628.306+ 269.9944 = 898.3004 approx 900$$ Hence, the correct option is E.

By rule of indices, ab    x    ac  = ab+c          Hence, by this rule, we can solve as, $$(10)^{24} imes (10)^{-21}= (10)^{24-21} =10^3 = 1000$$ Therefore, correct option is D.

Let the number which should be used in place of the question mark equals X. Hence, $$205 imes$$ X$$ imes 13 = 33625 + 25005 = 58630$$ So, $$205 imes$$ X $$= 4510$$ So, X$$= 22$$

Let them number in the question mark be X. So, $$2172 div $$ X $$=1832 - 956 - 514 = 362$$ So, $$2172 div$$ X = $$362$$ Or, X $$=2172 div 362 = 6$$

The number in the place of the question mark equals $$frac{135^2 div 15 imes 32}{45 imes 24} = frac{135 imes 135 div 15 imes 32}{45 imes 24}$$ $$frac{135 imes135div15 imes32}{45 imes 24}=frac{9 imes 9 imes 32}{3 imes24}=36$$

Expression : $$814296 imes 36 = ? imes 96324$$ => $$? = frac{814296 imes 36}{96324}$$ => $$? = 304.33 approx 304$$

Expression : $$(739\% of 383) div 628 = ?$$ = $$(frac{739}{100} imes 383) div 628$$ = $$(frac{740}{100} imes 380) div 630$$ = $$frac{2812}{630}$$ = $$4.46 approx 4.50$$

Expression : $$628.306 + 6.1325 imes 44.0268 = ?$$ = $$628 + (6 imes 44)$$
= $$628 + 264$$ = $$892 approx 900$$

Expression : $$[(135)^{2} div 15 imes 32] div ? = 45 imes 24$$ => $$[frac{135 imes 135 imes 32}{15}] div ? = 45 imes 24$$ => $$38880 div ? = 45 imes 24$$ => $$? = frac{38880}{45 imes 24}$$ => $$? = 36$$

Expression : 0.0004 $$div$$ 0.0001 $$ imes$$ 36.000009 = ? = $$frac{0.0004}{0.0001} * 36$$ = 4 * 36 = 144 $$approx$$ 145

Expression : $$4^{7} div 16^{4} imes sqrt{16}=?$$ = $$frac{4^7}{(4^2)^4} * 4$$ = $$frac{4^8}{4^8} = 1$$

Expression : 18800 $$div$$  470 $$div$$   20 = ? = $$frac{18800}{470} div 20$$ = $$40 div 20$$ = $$2$$

Expression : $$8frac{1}{4} + 60\% of frac{6}{5} = 15 - ?$$
=> $$15 - ? = frac{33}{4} + (frac{60}{100} imes frac{6}{5})$$ => $$15 - ? = frac{33}{4} + frac{18}{25}$$ => $$? = 15 - frac{33}{4} - frac{18}{25}$$ => $$? = frac{27}{4} - frac{18}{25}$$ => $$? = frac{675 - 72}{100} = 6.03$$

Expression : $$frac{18 imes14+46}{16 imes10-23}=?$$ = $$frac{252 + 46}{160 - 23}$$ = $$frac{298}{137}$$ = $$2frac{24}{137}$$

Expression : $$65\% of 400 + sqrt{?} = 40\% of 800 - 12\% of 400$$ => $$(frac{65}{100} imes 400) + (sqrt{?}) = (frac{40}{100} imes 800) - (frac{12}{100} imes 400)$$ => $$260 + sqrt{?} = 320 - 48$$ => $$sqrt{?} = 272 - 260 = 12$$ => $$? = 12^2 = 144$$

Expression : $$638 + 254 div 8 imes 4 = ?$$ = $$638 + frac{254 imes 4}{8}$$ = $$638 + 127 = 765$$

Expression : $$90780divsqrt{?}=85 imes12$$ => $$frac{90780}{sqrt{?}} = 85 imes 12$$ => $$sqrt{?} = frac{90780}{85 imes 12} = 89$$ => $$? = 89^2 = 7921$$

Expression : $$3frac{1}{6}+4frac{2}{3}-1frac{1}{4}=?$$ = $$(3 + 4 - 1) + (frac{1}{6} + frac{2}{3} - frac{1}{4})$$ = $$6 + frac{5}{6} - frac{1}{4}$$ = $$6 + frac{7}{12} = 6frac{7}{12}$$

Expression : $$14.8 imes 12.3 imes 8.6 = ?$$ = $$15 imes 12 imes 8.7$$ = $$180 imes 8.7 = 1566$$ $$approx 1565.544$$

Expression : $$41.25 + 11.085 imes 2.75 = ?$$ = $$41.25 + 12 imes 2.5$$ = $$41.25 + 30 = 71.25$$ $$approx 72$$

Expression : $$(3986 + 2416 + 3897) div 754 = ?$$ = $$frac{4000 + 2400 + 3900}{750}$$ = $$frac{10300}{750} = 13.73$$ $$approx 14$$

Expression : $$[(1.3)^{2} imes (4.2)^{2}] div 2.7 = ?$$ = $$frac{1.69 imes 17.64}{2.7}$$ = $$frac{1.7 imes 17.5}{2.7} approx$$ 11

Expression : $$[(1.5)^{2} imes (3.2)^{2}] div 2.3 = ?$$ = $$frac{2.25 imes 10.24}{2.3}$$ = $$frac{23.04}{2.3}$$ $$approx 10$$

Expression : $$(4863 + 1174 + 2829) div 756 = ?$$ = $$frac{8866}{756} = 11.72$$ $$approx 12$$

Expression : $$37.35 + 13.064 imes 3.46 = ?$$ $$approx 37 + 13 imes 3.5$$ = $$37 + 45.5 = 82.5$$ $$approx 83$$

Expression : $$sqrt{964} imessqrt{348}=?$$ $$approx 31 imes 18.65$$ = $$578.15 approx 579$$

Expression : $$(2640 div 48) imes (2240 div 35) = ?$$ = $$55 imes 64 = (50 + 5) imes 64$$ = $$3200 + 320 = 3520$$

Expression : $$(91)^{2} + (41)^{2} - sqrt{?} = 9858$$ => $$sqrt{?} = (91)^2 + (41)^2 - 9858$$ => $$sqrt{?} = 8281 + 1641 - 9858 = 104$$ => $$? = (104)^2 = 10816$$

Expression : $$(98360 + 25845 - 36540) div 2500 = ?$$ = $$87665 imes frac{1}{2500}$$ = $$35.066$$

Expression : $$196 imes 948 div 158 = ?$$
= $$196 imes 948 imes frac{1}{158}$$ = $$196 imes 6 = 1176$$

Expression : $$sqrt[3]{13824} imessqrt{?}=864$$
=> $$sqrt[3]{2^3 imes 2^3 imes 2^3 imes 3^3} imes sqrt{?} = 864$$ => $$2 imes 2 imes 2 imes 3 imes sqrt{?} = 864$$ => $$sqrt{?} = frac{864}{24} = 36$$ => $$? = 36^2 = 1296$$

Expression : $$(786 imes 64) div 48 =?$$
= $$786 imes 64 imes frac{1}{48}$$ = $$131 imes 8 = 1048$$

Let x be the unknown quantity, then x = $$frac{4900}{28} imesfrac{444}{12}$$ = 175 x 37 = 6475

Let x be the unknown quantity, then x = $$frac{6425}{125} imes8$$ = 51.4 x 8 = 411.2

Let x be the unknown quantity, then x = $$frac{95}{7} + frac{37}{7} imes frac{5}{2} = frac{95}{7} + frac{185}{14} = frac{375}{14}$$

Let x be the unknown quantity, then x = $$frac{140 - 90}{49 +16 + 169} = frac{50}{234} = frac{25}{117}$$

Let x be the unknown quantity, then x =$$ frac{61}{5} - (frac{23}{9} imesfrac{19}{5}) = 2frac{22}{45}$$. So the correct option is none of these.

Let x be the unknown quantity, then x = $$frac{3}{7} imesfrac{4}{5} imesfrac{5}{8} imes490 = frac{3}{7} imesfrac{1}{2} imes490$$ = 105

Let x be the unknown quantity, then x = 33.2 - 15.6 = 17.6

Let the number to replace the question mark be equal to $$X$$ So, $$8frac{2}{5} imes 5frac{2}{3}+X=50frac{1}{5}$$
Or, $$frac{42}{5} imes frac{17}{3} + X = frac{251}{5}$$
So, $$X = frac{251}{5} - frac{714}{15} = frac{753 - 714}{15} = frac{39}{15}$$ This equals $$frac{13}{5} = 2 frac{3}{5}$$

We need to find the value of the expression $$frac{17 imes 4+4^{2} imes 2}{90div5 imes 12}$$ This equals $$frac{68 + 16 imes 2}{18 imes 12}$$
Which is $$frac{68 + 32} {216} = frac{100}{216} = frac{25}{54}$$ Hence, the correct answer is option (a)

We need to find the value of the expression $$8frac{5}{9} imes 4frac{3}{5}-6frac{1}{3}$$ This equals $$frac{77}{9} imes frac{23}{5} - frac{19}{3}$$
Which is $$frac{1771}{45} - frac{19}{3} = frac{1771}{45} - frac{285}{45} = frac{1486}{45} = 33 frac{1}{45}$$ Hence, the correct answer is option (d)

We need to find the value of the expression $$1740div 12 imes 4070div110$$ This equals $$145 imes 37$$
Which is equal to $$5365$$

In order to find the value of $$16.45 imes 2.8+4.5 imes 1.6$$, let us find the value of the individual elements first $$16.45 imes 2.8 = 46.06$$
$$4.5 imes 1.6 = 7.2$$ Hence, the sum equals $$46.06 + 7.2 = 53.26$$ which is option (c)

The required expression is $$frac{4}{9} imes frac{3}{8} imes frac{2}{7} imes 294$$ This equals $$frac{1}{3} imes frac{1}{2} imes 2 imes 42 = 14$$ Hence, the correct answer is option (b)

Statements : B > N , N $$geq$$ R , F $$leq$$ R => B > N $$geq$$ R $$geq$$ F Conclusions : B > R [true] F $$leq$$ N [true] R < B [true] Thus, all three conclusions are true.

We need to find the value of $$3960 div 24 imes 392 div 14$$ $$3960 div 24 = 165$$
$$392 div 14 = 28$$ Hence, the product equals $$165 imes 28 = 4620$$

We need to find the value of $$frac{34 imes 4-12 imes 8}{6^{2}+sqrt{196}+(11)^{2}}$$ Let us first calculate the numerator, $$34 imes 4 - 12 imes 8 = 136 - 96 = 40$$
The denominator equals $$6^2 + sqrt{196} +11^2 = 36 +14 +121 = 171$$ Hence, the fraction equals $$frac{40}{171}$$

Let the number to replace the question mark be equal to $$X$$
So, $$3frac{3}{4} imes 4frac{5}{6}-X=2frac{3}{4}$$
Therefore, $$frac{15}{4} imes frac{29}{6} - X = frac{11}{4}$$
Therefore, $$frac{145}{8} - X = frac{11}{4}$$
Therefore $$X = frac{123}{8} = 15frac{3}{8}$$ Hence, the correct answer is option (d)

We need to find the value of $$12 imes 3.5 - 8.5 imes 3.2$$ $$12 imes 3.5 = 42$$
and, $$8.5 imes 3.2 = 27.2$$ Hence, the difference equals $$42 - 27.2 = 14.8$$

We need to find the value of $$ 8424 div 135 imes 6$$ $$8424 = 27 imes 312$$
$$135 = 27 imes 5$$ Hence, the given expression is equal to $$312 div 5 imes 6 = 624 imes 6 div 10 = 3744 div 10 = 374.4$$ Hence, the correct answer is option (c)

We need to find the value of $$frac{2}{5} imes frac{3}{4} imes frac{5}{8} imes 480$$ This equals $$frac{3}{16} imes 480 = 3 imes 30$$
This equals $$90$$ Hence, the correct answer is option (a)

We need to find the value of $$12 frac{3}{5}+4frac{1}{5} imes 3frac{2}{3}$$ This is equal to $$frac{63}{5} + frac{21}{5} imes frac{11}{3}$$
So, this equals $$frac{63}{5} + frac{77}{5} = frac{140}{5} = 28$$ Hence, the correct answer is option (c)

We need to find the value of $$4495 div 145 imes 656 div 16$$ $$4495 div 145 = 31$$
and, $$656 div 16 = 41$$ Hence, the product becomes $$31 imes 41 = 1271$$

We need to find the value of $$7986 div 165 imes 7$$ Note that $$7986 = 3 imes 11 imes 242$$ and $$165 = 3 imes 11 imes 5$$ Hence, the expression is equal to $$242 div 5 imes 7$$
This equals $$484 imes 7 div 10 = 3388 div 10 = 338.8$$ Hence, the correct answer is option (a)

We need to find the value of $$frac{28 imes 5-14 imes 4}{8^{2}+sqrt{225}+(14)^{2}}$$ Let us find the value of the numerator first $$28 imes 5 - 14 imes 4 = 140 - 56 = 84$$
And the value of the denominator equals $$8^2 sqrt{225} +14^2 = 64 + 15 + 196 = 275$$ Hence, the value of the fraction is $$frac{84}{275}$$ Hence, the correct answer is option (b)

We need to find the value of $$frac{3}{5} imes frac{5}{7} imes frac{2}{9} imes 630$$ Note that $$630 = 2 imes 5 imes 7 imes 9$$
So, the value equals $$frac{3}{5} imes frac{5}{7} imes frac{2}{9} imes 2 imes 5 imes 7 imes 9$$
Which equals $$3 imes 5 imes 2 imes 2 = 60$$ Hence, the correct answer is option (d)

We need to find the value of $$6frac{1}{2}+5frac{1}{4} imes 1frac{3}{7}$$ This equals $$frac{13}{2} + frac{21}{4} imes frac{10}{7}$$
Which is $$frac{13}{2} + frac{15}{2} = frac{28}{2} = 14$$ Hence, the correct answer is option (c)

Let the number to replace the question mark be equal to $$X$$
So, $$ 4frac{2}{5} imes 3frac{1}{3}-X= 5frac{1}{3} $$
Therefore, $$frac{22}{5} imes frac{10}{3} - X = frac{16}{3}$$
Or, $$frac{44}{3} - X = frac{16}{3}$$
So, $$X = frac{28}{3} = 9frac{1}{3}$$

We need to calculate the value of $$ 14 imes 4.5-7.4 imes 3.5 $$ $$14 imes 4.5 = 63$$
$$7.4 imes 3.5 = 25.9$$ Hence, the difference equals $$63 - 25.9 = 37.1$$

We need to find the value of $$420 div 28 imes 288 div 32$$ $$420 div 28 = 15$$ and $$288 div 32 = 9$$ So, the given expression equals $$15 imes 9 = 135$$ and the correct answer is option (e)

Let the number to replace the question mark be equal to X. So, $$17frac{2}{5} imes frac{5}{8} + X=46frac{7}{8}$$
So, $$frac{87}{5} imes frac{5}{8} + X = frac{375}{8}$$
So, $$ frac{87}{8} + X = frac{375}{8}$$ Therefore, $$X = frac{288}{8} = 36$$ So, the correct answer is option (b)

We need to find the value of $$frac{14 imes 25-5^{3}}{24 imes 5+8 imes 9}$$ Let us first find the value of numerator. It equals $$14 imes 25 - 5^3 = 350 - 125 = 225$$
The value of the denominator equals $$24 imes 5 + 8 imes 9 = 120 + 72 = 192$$ Hence, the answer is $$frac{225}{192} = frac{75}{64} = 1frac{11}{64}$$ So, the correct answer is option (c)

We need to find the value of $$32.25 imes 2.4 imes 1.6$$ This equals $$64.5 imes 1.2 imes 1.6 = 129 imes 0.6 imes 1.6$$
This equals $$129 imes 0.96 = 123.84$$ Hence, the correct answer is option (b)

We need to find the value of $$frac{5}{11} imes frac{4}{5} imes frac{11}{16} imes 848$$ This equals $$frac{1}{4} imes 848 = 212$$ Hence, the correct answer is option (d)

16.45 x 5.2 x2.5 = 16.45x1.3x10= 213.85 

We have to find the value of $$frac{5}{8} imes frac{2}{3} imes frac{3}{5} imes 2104$$ Note that $$2104 = 2 imes 2 imes 2 imes 263$$
The fraction preceding $$2104$$ equals $$frac{5}{8} imes frac{2}{3} imes frac{3}{5} = frac{1}{4}$$ Hence, the product equals $$2 imes 263 = 526$$
So, the correct option is option (c)

Let the number to replace the question mark be equal to $$X$$ So, $$8frac{1}{3} imes 4frac{2}{5}+X=44frac{2}{5}$$
Hence, $$frac{25}{3} imes frac{22}{5} + X = frac{222}{5}$$
Or, $$frac{550}{15} + X = frac{222}{5}$$ So, $$X = frac{222}{5} - frac{550}{15} = frac{666 - 550} {15} = frac{116}{15} = 7 frac{11}{15}$$

In order to find the value of the expression, let us find the value of the numerator and denominator separately. The numerator is $$17 imes 4+18 imes 3 = 68 + 54 = 122$$
The denominator is $$sqrt{441} imes 5+139 = 21 imes 5 + 139 = 105 +139 = 244$$ Hence, the value of the expression is $$frac{122}{244} = frac{1}{2}$$

First, we have to divide by 21 and then multiply by 1.7 Dividing 7231 by 21, 7231÷21~344 Now, multiplying by 1.7, 344×1.7=584.8~585

The sum can be obtained quickly by rounding off, 508+253+200=961 to which closest answer is 960.

$$frac{5}{8}+frac{1}{4}+frac{7}{12}=?$$ Simplifying, $$frac{7}{8}+frac{7}{12}=?$$ The equation reduces to, 7*{(1/8)+(1/12)}=(35/24) Now converting $$frac{35}{24}$$ to mixed fration, we get $$1frac{11}{24}$$

$$(8536¬sqrt{2209}) imes0cdot3=?$$ $$(8536¬47) imes0cdot3=?$$ $$(8489) imes0cdot3=?$$ This reduces to, 8489*(.3) = 2546.7

Assuming the unknown quantity to be x, x * (32000) * (3/4) * (1/2) = 4800 Which reduces to, x * (32000) *3/8 = 4800 x = 4800*(8/3)*(1/32000) x = 2/5

$$526 imes 12 = 6312$$ $$6312 + 188 = 6500$$ Let the number in the question mark be X. So, $$X imes 50 = 6500$$ $$X = 130$$

$$frac{31}{43} imesfrac{86}{95} imesfrac{41}{93}=?$$ Can be rewritten as, $$frac{31}{93} imesfrac{86}{43} imesfrac{41}{43}$$ which solves out to be, $$frac{1}{3} imesfrac{2}{1} imesfrac{41}{43}$$ And hence, the answer is, $$frac{82}{285}$$

The given series is Arithmetic Progression with common difference $$frac{1}{4}$$. Hence, the next term will be $$1frac{3}{4}$$ + $$frac{1}{4}$$ = 2

Expression : $$635 imes 455 div 403 = ?$$ = $$635 imes 455 imes frac{1}{400}$$ = $$722 approx 715$$

$$frac{1}{4}$$ is added to each number $$frac{1}{4}$$ + $$frac{1}{4}$$ = $$frac{1}{2}$$ $$frac{1}{2}$$ + $$frac{1}{4}$$ = $$frac{3}{4}$$
$$frac{3}{4}$$ + $$frac{1}{4}$$ = 1 1 + $$frac{1}{4}$$ = $$1frac{1}{4}$$
$$1frac{1}{4}$$ + $$frac{1}{4}$$ = $$1frac{1}{2}$$
$$1frac{1}{2}$$ + $$frac{1}{4}$$ = $$1frac{3}{4}$$
$$1frac{3}{4}$$ + $$frac{1}{4}$$ = 2

Expression : $$(5863-sqrt{2704}) imes0.5=?$$ = $$(5863 - 52) imes frac{1}{2}$$ = $$frac{5811}{2} = 2905.5$$

Expression : $$283 imes 56 + 252 = 20 imes ? $$ => $$15848 + 250 = 20 imes ?$$ => $$? = frac{16100}{20} = 805$$

Expression : $$frac{9}{10}+frac{3}{11}+frac{7}{15}= ?$$ = $$frac{297 + 90 + 154}{330}$$
= $$frac{541}{330} = 1frac{211}{330}$$

Expression : $$(7921 div 178) - 5.5 = sqrt{?}$$ => $$sqrt{?} = (frac{7921}{178}) - 5.5$$ => $$sqrt{?} = 44.5 - 5.5 = 39$$ => $$? = (39)^2 = 1521$$

Expression : $$frac{7}{5}offrac{30}{63}offrac{558}{3}=?$$ = $$frac{7}{5} imes frac{30}{63} imes frac{558}{3}$$ = $$frac{558 imes 2}{9}$$ = $$62 imes 2 = 124$$

Expression : $$71 + 897 div 13 imes 3 = ?$$ = $$71 + frac{897 imes 3}{13}$$ = $$71 + 207 = 278$$

Expression : $$3.1 imes 2.6 imes 1.5 =?$$ = $$12.09$$

Expression : $$frac{15}{31}divfrac{90}{186} imesfrac{729}{9}=(?)^{2}$$ => $$?^2 = frac{15}{31} imes frac{186}{90} imes 81$$ => $$?^2 = 1 imes 81 = 81$$ => $$? = sqrt{81} = pm9$$

P is greater than Q which is greater than or equal to R. Hence, we can say that P is greater than R.
Hence, conclusion I follows.

R is greater than A but I and A are equal. Therefore, R is greater than I.
Hence, conclusion II follows.

Both I and II follow.
Option E is correct.

Conclusions:
I. B < O, we cannot establish any direct relationship between B and O as no such data is provided.
II. T < S, no relationship can be established between T and S as data provided is inadequate.

Hence, conclusions I and II do not follow.
Therefore, option D is correct.

I. O >R. This is a correct coclusion because Q is greater than R. P is greater than Q while I is greater than or equal to R. Hence, O is greater than R.
II. $$Pleq G$$. We cannot draw any conclusion between relationship of P with G.
Only conclusion I follows.

T is greater than or equal to M. But T is equal to K. K is greater than or equal to M. O is equal to M.
Therefore, K is greater than or equal to O.
Hence, conclusion I follows.
We cannot establish a relation between F and M even both are known to be less than F.
Hence, this conclusion II does not follow.

Option A is correct.

As we can see that equation can be written as $$(frac{17}{24} imes frac{24}{68}) imesfrac{95}{380}$$ Hence, answer will be $$frac{1}{4}$$

As we can see in the given equation that after cancellation of various factors we will get $$ frac{8}(9}$$ of 567 = 504 504 x 7/4 = 882 882 x 2/28 = 63

Expression : $$(9.8 imes 2.3 + 4.46) div 3 = (3)^{?}$$ => $$(22.54 + 4.46) div 3 = 3^x$$ => $$frac{27}{3} = 3^x$$ => $$3^2 = 3^x$$ => $$x = 2$$

Expression : $$17 imes 19 imes 4 div ? = 161.5$$ => $$frac{323 imes 4}{x} = frac{323}{2}$$ => $$x = 4 imes 2 = 8$$

Expression : $$1frac{4}{5}+3frac{3}{5}=?-4frac{3}{10}$$ => $$x = 1frac{4}{5}+3frac{3}{5} + 4frac{3}{10}$$ => $$x = (1 + 3 + 4) + (frac{8}{10} + frac{6}{10} + frac{3}{10})$$ => $$x = 8 + frac{17}{10} = frac{97}{10}$$ => $$x = 9frac{7}{10}$$

Expression : $$frac{210}{14} imesfrac{17}{15} imes?=4046$$ => $$15 imes frac{17}{15} imes x = 4046$$ => $$x = frac{4046}{17} = 238$$

Expression : $$4frac{5}{6}+7frac{1}{2}-5frac{8}{11}=?$$ = $$(4 + 7 - 5) + (frac{5}{6} + frac{1}{2} - frac{8}{11})$$ = $$6 + frac{8}{6} - frac{8}{11}$$ = $$6 + frac{20}{33} = 6frac{20}{33}$$

Expression : $$3451 div 9.895 imes 3.0126 = ?$$ $$approx frac{3450}{10} imes 3$$ = $$345 imes 3 = 1035$$ $$approx 1050$$

Expression : $$17^{34.5} imes17^{68.9}div17^{27.4}=17^{?}$$ => $$(17)^{34.5 + 68.9 - 27.4} = (17)^x$$ => $$(17)^{76} = (17)^x$$ => $$x = 76$$

Expression : $$4 imes ? = 6924 div 15$$ => $$4 imes x = frac{6924}{15}$$ => $$x = frac{6924}{15 imes 4} = 115.4$$

Expression : $$17frac{2}{3} imes1frac{17}{106}=?$$ = $$frac{53}{3} imes frac{123}{106}$$ = $$frac{41}{2} = 20frac{1}{2}$$

Expression : $$12.5 imes 6.7 imes 4.2 = ?$$ = $$52.5 imes 6.7$$ = $$351.75$$

Expression : 13/63 $$div$$ 104/14 $$ imes$$ 52/19 = $$frac{13}{63} div frac{104}{14} imes frac{52}{19}$$ = $$frac{13}{63} imes frac{14}{104} imes frac{52}{19}$$ = $$frac{13}{9} imes frac{1}{19} = frac{13}{171}$$

Expression : $$frac{9.8 imes 2.5 imes 7.6}{0.5}=?$$ = $$24.5 imes 7.6 imes 2$$ = $$49 imes 7.6 = 372.4$$

Expression : $$199 + 5^{3} div 4 imes 4^{2} = ?$$ = $$199 + 125 imes frac{4^2}{4}$$ = $$199 + 125 imes 4$$ = $$199 + 500 = 699$$

Expression : (42 $$ imes$$ 3.2) $$div$$ (16 $$ imes$$ 1.5) = ? = $$frac{42 imes 3.2}{16 imes 1.5}$$ = $$28 imes 0.2 = 5.6$$

Expression : $$sqrt[3]{512}+sqrt[4]{16}+sqrt{576}=?$$
= $$8 + 2 + 24$$ = $$34$$

Expression : $$7^{8.9} div (343)^{1.7} imes (49)^{4.8} = 7^{?}$$ => $$(7)^{8.9} imes frac{1}{(7)^{3 imes 1.7}} imes (7)^{2 imes 4.8} = (7)^x$$ => $$(7)^{8.9 - 5.1 + 9.6} = (7)^x$$ => $$x = 8.9 + 9.6 - 5.1 = 13.4$$

Expression : $$152 imes 8 + (228 div 19)^{2} = ?$$ = $$1216 + (frac{228}{19})^2$$ = $$1216 + (12)^2$$ = $$1216 + 144 = 1360$$

Expression : (12 $$ imes$$ 19) + (13 $$ imes$$ 8) = (15 $$ imes$$ 14) +? => $$228 + 104 = 210 + x$$ => $$x = 332 - 210 = 122$$

Expression : 16.046 $$div$$ 2.8 $$ imes$$ 0.599 = ? = $$frac{16}{3} imes 1$$ = $$5.33 approx 5.6$$

Expression : 16.928 + 24.7582 $$div$$ 5.015 = ?
$$approx 17 + frac{25}{5}$$ = $$17 + 5 = 22$$

Expression : 67 % of $$sqrt{676} div 0.01=?+577$$ => $$frac{67}{100} imes frac{26}{0.01} = x + 577$$ => $$x + 577 = frac{67}{100} imes 26 imes 100$$ => $$x + 577 = 1742$$ => $$x = 1742 - 577 = 1165$$

Expression : $$(sqrt{125.44} imes 85 div 8 )-11=(?)^{2} div 3$$ => $$(frac{11.2 imes 85}{8}) - 11 = frac{x^2}{3}$$ => $$119 - 11 = frac{x^2}{3}$$ => $$x^2 = 108 imes 3 = 324$$ => $$x = sqrt{324} = 18$$

Expression : $$(2.25))^{2} div (3.375)^{4} imes (1.5)^{5} = (1.5)^{?-7}$$ => $$(1.5)^{2 imes 2} imes frac{1}{(1.5)^{3 imes 4}} imes (1.5)^5 = (1.5)^{x - 7}$$ => $$(1.5)^{4 - 12 + 5} = (1.5)^{x - 7}$$ => $$-3 = x - 7$$ => $$x = 7 - 3 = 4$$

Expression : $$2frac{4}{6}+3frac{6}{7}+4frac{5}{7}+3frac{2}{3}=?$$ = $$(2 + 3 + 4 + 3) + (frac{4}{6} + frac{6}{7} + frac{5}{7} + frac{2}{3})$$ = $$12 + frac{4}{3} + frac{11}{7}$$ = $$12 + frac{61}{21} = 12 + 2frac{19}{21}$$ = $$14frac{19}{21}$$

Expression : $$59^{2} - 49^{2} = 2^{?} imes 3^{3} imes 5$$ => $$(59 + 49) (59 - 49) = 2^? * 27 * 5$$ => $$2^? = frac{108 * 10}{27 * 5}$$
=> $$2^? = 8 = 2^3$$ => $$? = 3$$

Expression : $$frac{11}{51}offrac{13}{15}offrac{17}{19}of?=95frac{1}{3}$$ => $$frac{11 imes 13}{45 imes 19} = frac{286}{3}$$
=> $$? = frac{286 imes 45 imes 19}{3 imes 11 imes 13}$$ => $$? = 570$$

Expression : $$4frac{4}{5}-3frac{3}{5}-5frac{5}{6}+6frac{6}{7}=?$$ = $$(4 - 3 - 5 + 6) + frac{4}{5} - frac{3}{5} - frac{5}{6} + frac{6}{7}$$ = $$2 + frac{1}{5} + frac{1}{42}$$ = $$2 + frac{47}{210}$$ = $$2frac{47}{210}$$

Expression : $$frac{(4.5)^{2} imes(3.6)^{2}}{(0.9)^{2} imes(0.5)^{2} imes(?)^{4}}=1$$ = $$(?)^4 = frac{(4.5)^2 imes (3.6)^2}{(0.45)^2}$$ = $$(?)^4 = (10)^2 imes (3.6)^2$$ = $$(?)^4 = 36^2 = 6^4$$ => $$? = 6$$

Expression : $$sqrt{5} imes5sqrt{3}divsqrt{15}=?-1$$ => $$frac{sqrt{5} imes 5sqrt{3}}{sqrt{15}} = x - 1$$ => $$frac{5 sqrt{15}}{sqrt{15}} = x - 1$$ => $$5 = x - 1$$ => $$x = 5 + 1 = 6$$

Expression : $$sqrt{(176 imes2+3^{2})}=4+sqrt{?}$$ => $$sqrt{352 + 9} = 4 + sqrt{x}$$ => $$sqrt{361} = 4 + sqrt{x}$$ => $$19 = 4 +sqrt{x}$$ => $$sqrt{x} = 19 - 4 = 15$$ => $$x = (15)^2 = 225$$

Expression : $$frac{40 imes4div4^{2} imes2}{90div5 imes12}$$ = $$frac{40 imes 4 imes frac{1}{4^2} imes 2}{90 imes frac{1}{5} imes 12}$$ = $$frac{10 imes 2}{18 imes 12}$$ = $$frac{5}{54}$$

Expression : $$frac{2}{9}$$ of $$[1frac{3}{4}+1frac{5}{8}]=?$$ = $$frac{2}{9} imes (frac{7}{4} + frac{13}{8})$$ = $$frac{2}{9} imes frac{27}{8}$$ = $$frac{3}{4}$$

Expression : $$16frac{2}{7}+15frac{1}{4}+18frac{1}{2}=?$$ = $$(16 + 15 + 18) + (frac{2}{7} + frac{1}{4} + frac{1}{2})$$ = $$49 + (frac{8 + 7 + 14}{28})$$ = $$49 + frac{29}{28} = 49 + 1frac{1}{28}$$ = $$50frac{1}{28}$$

Expression : $$13^{2}-sqrt{(1764)} imesfrac{sqrt{(625)}}{21}=?$$ = $$169 - (42 imes frac{25}{21})$$ = $$169 - (2 imes 25)$$ = $$169 - 50 = 119$$

Expression : $$sqrt{(337+sqrt{(561+sqrt{225}})}+?=frac{576}{8}$$ => $$sqrt{(337 + sqrt{(561 + 15})} + x = frac{576}{8}$$ => $$sqrt{337 + sqrt{576}} + x = 72$$ => $$sqrt{337 + 24} + x = 72$$ => $$sqrt{361} + x = 72$$ => $$x = 72 - 19 = 53$$

Expression : $$frac{156.25}{12.5} imesfrac{1000}{2500}=frac{?}{28}$$ => $$12.5 imes frac{2}{5} = frac{x}{28}$$ => $$frac{25}{5} = frac{x}{28}$$ => $$x = 5 imes 28 = 140$$

Expression : $$frac{2560}{32}+frac{23}{45} of 855 = frac{7}{11} of ? + 391$$ => $$80 + (frac{23}{45} imes 855) = (frac{7}{11} imes x) + 391$$ => $$80 + (23 imes 19) = frac{7x}{11} + 391$$ => $$80 + 437 - 391 = frac{7x}{11}$$ => $$frac{7x}{11} = 126$$ => $$x = frac{126 imes 11}{7}$$ => $$x = 18 imes 11 = 198$$

Expression : $$frac{sqrt{(180)} imessqrt{(18)} imessqrt{(5)} imessqrt{(3)}}{sqrt{(96)} imes5}=?$$ = $$frac{sqrt{180 imes 18 imes 5 imes 3}}{sqrt{16 imes 6} imes 5}$$ = $$frac{sqrt{(18 imes 18) imes (5 imes 5) imes 6}}{sqrt{6} imes 4 imes 5}$$ = $$frac{18 imes 5 imes sqrt{6}}{20 imes sqrt{6}}$$ = $$frac{90}{20} = frac{9}{2}$$ = $$4frac{1}{2}$$

Expression : $$4^{3} imes2^{6} imes8^{frac{2}{3}}=2^{?}$$ => $$(2)^{2 imes 3} imes (2)^6 imes (2)^{3 imes frac{2}{3}} = (2)^x$$ => $$(2)^6 imes (2)^6 imes (2)^2 = (2)^x$$ => $$(2)^{6 + 6 + 2} = (2)^x$$ => $$x = 6 + 6 + 2 = 14$$

Expression : $$frac{2}{3}-frac{5}{7}$$ of $$frac{21}{23}$$ of $$frac{46}{51} = ?$$ of $$frac{8}{85}$$ => $$frac{2}{3} - (frac{5}{7} imes frac{21}{23} imes frac{46}{51}) = x imes frac{8}{85}$$ => $$frac{2}{3} - frac{10}{17} = frac{8x}{85}$$ => $$frac{4}{51} = frac{8x}{85}$$ => $$x = frac{4 imes 85}{51 imes 8}$$ => $$x = frac{5}{6}$$

Expression : $$64^{2}-36^{2}= ? imes 25$$ => $$(64 + 36) (64 - 36) = x imes 25$$ => $$100 imes 28 = x imes 25$$ => $$x = frac{100 imes 28}{25}$$ => $$x = 4 imes 28 = 112$$

Expression : $$5136div(523+333) of frac{3}{4}+459=?$$ = $$5136 div (856 imes frac{3}{4}) + 459$$ = $$(5136 div 642) + 459$$ = $$8 + 459 = 467$$

Expression : $$9^{2} imessqrt[4]{(1296)}-254=(? imes9+124)$$ => $$(81 imes 6) - 254 = (x imes 9) + 124$$ => $$486 - 254 = 9x + 124$$ => $$9x = 232 - 124 = 108$$ => $$x = frac{108}{9} = 12$$

Expression : $$frac{[1496-392]}{23} imes15=213+?$$ => $$frac{1104}{23} imes 15 = 213 + x$$ => $$48 imes 15 = 213 + x$$ => $$720 = 213 + x$$ => $$x = 720 - 213 = 507$$

Expression : $$(86-frac{742}{53})div2=?^{2}$$ => $$(86 - 14) div 2 = (x)^2$$ => $$frac{72}{2} = (x)^2$$ => $$36 = (x)^2$$ => $$x = sqrt{36} = 6$$

Expression : $$frac{(349+503)}{35.5}+428=frac{?}{9}$$ => $$frac{852}{35.5} + 428 = frac{x}{9}$$ => $$24 + 428 = frac{x}{9}$$ => $$452 = frac{x}{9}$$ => $$x = 452 imes 9 = 4068$$

Expression : $$frac{(415+223)^{2}+(415-223)^{2}}{(415 imes415+223 imes223)}=?$$ Let $$415 = a$$ and $$223 = b$$ => $$x = frac{(a + b)^2 + (a - b)^2}{a^2 + b^2}$$ = $$frac{(a^2 + b^2 + 2ab) + (a^2 + b^2 - 2ab)}{a^2 + b^2}$$ = $$frac{2a^2 + 2b^2}{a^2 + b^2}$$ = $$frac{2 (a^2 + b^2)}{a^2 + b^2} = 2$$

Expression : $$3.7 imes24div5=?div3.3$$ => $$3.7 imes 4.8 = frac{x}{3.3}$$ => $$17.76 = frac{x}{3.3}$$ => $$x = 17.76 imes 3.3 = 58.6$$

Expression : $$(36divsqrt{18} imessqrt{6})div3=?$$ = $$(frac{36}{3 sqrt{2}} imes sqrt{6}) div 3$$ = $$frac{12 sqrt{3}}{3}$$ = $$4 sqrt{3}$$

Expression : $$(frac{2}{3}+1frac{1}{5}) imes3=?$$ = $$(frac{2}{3} + frac{6}{5}) imes 3$$ = $$(frac{10 + 18}{15}) imes 3$$ = $$frac{28}{15} imes 3$$ = $$frac{28}{5} = 5frac{3}{5}$$

Expression : $$(sqrt{frac{324}{9}} imes1.5)^{2}=?$$ = $$(frac{18}{3} imes 1.5)^2$$ = $$(6 imes 1.5)^2$$ = $$(9)^2 = 81$$

Expression : $$sqrt{?} + 14= sqrt{2601}$$ => $$sqrt{x} + 14 = 51$$ => $$sqrt{x} = 51 - 14 = 37$$ => $$x = (37)^2 = 1369$$

Expression : 3939 $$div$$ 3 + 6363 $$div$$ 3 -­ 9696$$div$$6 = ? = $$(frac{3939}{3}) + (frac{6363}{3}) - (frac{9696}{6})$$ = $$1313 + 2121 - 1616$$ = $$3434 - 1616 = 1818$$

Expression : $$sqrt[3]{17.576} imes 15 = ?$$ = $$sqrt[3]{2.6 imes 2.6 imes 2.6} imes 15$$ = $$2.6 imes 15$$ = $$39$$

Expression : $$8frac{1}{4} imes 2frac{2}{5} imes ? =12$$ => $$frac{33}{4} imes frac{12}{5} imes x = 12$$ => $$frac{33 imes 3}{5} imes x = 12$$ => $$x = frac{12 imes 5}{33 imes 3}$$ => $$x = frac{20}{33}$$

Expression : $$sqrt{729} div 45 imes 540 = ?^{2}$$ => $$27 imes frac{1}{45} imes 540 = (x)^2$$ => $$27 imes 12 = (x)^2$$ => $$(x)^2 = 324$$ => $$x = sqrt{324} = 18$$

Expression : 50% of $$(3frac{3}{8} + 1frac{7}{10})=?$$ = $$frac{50}{100} imes (frac{27}{8} + frac{17}{10})$$ = $$frac{1}{2} imes (frac{135 + 68}{40})$$ = $$frac{1}{2} imes frac{203}{40}$$ = $$frac{203}{80} = 2.53$$

Expression : $$frac{2.6 imes 3 + 1.8 imes 9}{6}=?$$ = $$(frac{2.6 imes 3}{6}) + (frac{1.8 imes 9}{6})$$ = $$(1.3 imes 1) + (0.9 imes 3)$$ = $$1.3 + 2.7 = 4$$

Expression : $$sqrt{frac{160 imes 8}{5}} imes 8=?$$ = $$sqrt{32 imes 8} imes 8$$ = $$sqrt{16 imes 16} imes 8$$ = $$16 imes 8 = 128$$

Expression : 57 - 1725 $$div$$ 69 = 4 $$ imes$$ ? => $$57 - frac{1725}{69} = 4 imes x$$ => $$57 - 25 = 4 imes x$$ => $$4x = 32$$ => $$x = frac{32}{4} = 8$$

Expression : 800 $$div$$ 24 $$ imes$$ ? = 600 => $$frac{800}{24} imes x = 600$$ => $$frac{100x}{3} = 600$$ => $$x = frac{600 imes 3}{100}$$ => $$x = 6 imes 3 = 18$$

Expression : 120% of $$(11frac{1}{6}+frac{5}{6}) +?=26$$ => $$frac{120}{100} imes (frac{67}{6} + frac{5}{6}) + x = 26$$ => $$frac{6}{5} imes (frac{72}{6}) + x = 26$$ => $$frac{72}{5} + x = 26$$ => $$x = 26 - frac{72}{5}$$ => $$x = 26 - 14.4 = 11.6$$

Expression : $$4frac{1}{3}+4frac{1}{5} imes 2frac{7}{9}=?$$ = $$(frac{13}{3}) + (frac{21}{5} imes frac{25}{9})$$ = $$frac{13}{3} + frac{35}{3}$$ = $$frac{13 + 35}{3}$$ = $$frac{48}{3} = 16$$

Expression : $$sqrt{frac{2.76 imes 3}{2.3 imes 2.5}}=?$$ = $$sqrt{frac{276 imes 3}{23 imes 25}}$$ = $$sqrt{frac{12 imes 3}{25}}$$ = $$sqrt{frac{36}{25}}$$ = $$frac{6}{5} = 1.2$$

Expression : 2 $$ imes$$ 4.5 + 12 $$ imes$$ 1.5 = ? = $$9 + 18$$ = $$27$$

Expression : 1/5+2/15+?+1/6= $$1frac{1}{6}$$ => $$frac{1}{5} + frac{2}{15} + x = frac{1}{6} = frac{7}{6}$$ => $$frac{3}{15} + frac{2}{15} + x = frac{7}{6} - frac{1}{6}$$ => $$frac{5}{15} + x = frac{6}{6}$$ => $$frac{1}{3} + x = 1$$ => $$x = 1 - frac{1}{3} = frac{2}{3}$$

Expression : (29.55 + 95.45) $$ imes$$ ? = 150 => $$125 imes x = 150$$ => $$x = frac{150}{125} = frac{6}{5}$$ => $$x = 1.2$$

Expression : $$10^{?} - 162 imes 1frac{1}{3} = 28^{2}$$ => $$(10)^x - (162 imes frac{4}{3}) = 784$$ => $$(10)^x - 216 = 784$$ => $$(10)^x = 784 + 216 = 1000$$ => $$(10)^x = (10)^3$$ => $$x = 3$$

± {[5064 $$div$$ 81- [1599 $$div$$ 3]} ± [ 1688 $$div$$ 3 - 1599$$div$$3 ]
± (89 $$div$$ 3)
± 29.66 ≥ -100

$$44,979 imes 20.011 div 9.968$$ can be rewritten as approx = $$45 imes20 div10$$ $$900div10$$ 90

$$4frac{9}{13} imes 3frac{6}{19} div 4frac{4}{7}$$ $$frac{61}{13} imes frac{63}{19} div frac{32}{7}$$ =3.4 = 3 (approx)

$$1679 + 14.95 imes 5.02$$ can be simplified as
$$1680 + 15 imes 5 $$
= 1680+75
= 1755

$$447.75 div 28 imes 4.99 = ?$$
The given expression can be approximated as
$$448 div 28 imes 5 = ?$$
$$16 imes 5 = ?$$
80 = ?

$$-((sqrt{225}-sqrt{144}) imes-(1.5))=?$$
= - (15-12) $$ imes $$ (-1.5)
= (-3)$$ imes $$(-1.5) =4.5

$$0.0004 div 0.0001 imes 36.000009 $$ $$=4 imes36.0000009$$ =144.000036 ~145 Hence Correct Option is C

$$13.5 imes 16.3 imes 12.8=?$$
This equals $$13.5 imes 16.3 imes 12.8= 220.05 imes 12.8$$
This equals $$2816.64$$

Let the required number be equal to X.
Therfore, $$7825-9236+5234= X imes 25$$
Hence, $$3823 = X imes 25$$
Therefore $$3823 imes 4 = X imes 100$$
So, $$15292 = X imes 100$$ Hence, $$X = 152.92$$

$$2frac{4}{5}-1frac{3}{8}+3frac{1}{2}=frac{14}{5} - frac{11}{8} + frac{7}{2}$$ =$$ frac{197}{40}$$

$$frac{3}{7}divfrac{9}{14} imesfrac{6}{11}= frac{3}{7} imes frac{14}{9} imes frac{6}{11}$$
This equals, $$frac{3}{7} imes frac{14}{9} imes frac{6}{11} = frac{2}{3} imes frac{6}{11}$$
This equals $$frac{2}{3} imesfrac{6}{11} = frac{4}{11}$$
Hence, the correct option is option (c)

The statements are : R > J , J $$geq$$ M , M = K After combining the above inequalities, we get : R > J $$geq$$ M = K Conclusions : K = J and K < J Since, K $$leq$$ J Thus, either conclusion I or II is true.

Let the unknown value be x.
$$5437-3153+2284=x imes50$$
$$2284+2284= x imes50$$
$$4568 = x imes50$$
$$x = 4568/50$$
$$x = 91.36$$
Therefore, the correct option is B

$$frac{4}{5} imes2frac{3}{4}divfrac{5}{8}= frac{4}{5} imesfrac{11}{4}divfrac{5}{8}$$
                                                            =$$frac{11}{5} imesfrac{8}{5}$$
                                                            =$$frac{88}{25}$$ =$$3frac{13}{25}$$
Therefore, option D is correct answer.

Converting the mixed fraction into proper fraction, we get
$$5frac{1}{5}+2frac{3}{5}+1frac{2}{5}= frac{26}{5}+ frac{13}{5}+ frac{7}{5}$$
                                                      = $$frac{26+13+7}{5}$$
                                                      = $$frac{46}{5}$$
Reconverting the answer top mixed fraction,
$$frac{46}{5}$$ = $$9frac{1}{5}$$
Option D is the correct answer.

$$(5 imes5 imes5 imes5 imes5 imes5)^{4} imes(5 imes5)^{6}div(5)^{2}=(25)^{12} imes(25)^6div25$$                                                                                                              =$$(25)^{18}div25$$                                                                                                              = $$(25)^{17}$$
Hence, the correct value of unknown number is 17.
Therefore, the correct option is B.

Let the required number be equal to X.
So, $$(16\% imes 450) div (X\% imes 250) = 4.8$$
Therefore, $$72 imes (X\% imes 250) = 4.8$$
Or, $$X\% imes 250 = 15$$
So, $$X=6$$

F @ N which means F is smaller than or equal to N
N $$delta$$ R which means N is greater than R
H @ R which means H is smaller than or equal to R

We can deduce that, H is smaller than N as it is smaller than R which is smaller than N.
We cannot establish any relationship between F and R.
Therefore, both conclusion I and II do not follow.

The expression when simplified becomes  $$3frac{2}{3}+2frac{3}{4}+1frac{1}{2} = frac{11}{3} + frac{11}{4} + frac{3}{2}$$ This equals $$frac{44}{12} +frac{33}{12} + frac{18}{12} = frac{95}{12}$$ Hence, it equals $$7frac{11}{12}$$

The simplified expression equals $$(4 imes4 imes4 imes4 imes4 imes4)^{5} imes(4 imes4 imes4)^{8}div(4)^{3}= (4^6)^5 imes (4^3)^8 div 4^3 = 4^{30} imes 4^{24} div 4^3 = 4^{30+24-3} = 4^{51}$$ $$64 = 4^3$$ So, $$4^{51} = 4^{3 imes 17} = (4^3)^{17} = 64^{17}$$ Hence the correct answer is 17

$$frac{5}{8} imes frac{13}{5} div frac{4}{9} = frac{13}{8} imes frac{9}{4}$$ This equals $$frac{117}{32} = 3frac{21}{32}$$

D $ T which means D is equal to T.
T % M which means T is greater than or equal to M.
M* J which means M is smaller than J.
From, the above data we can conclude that,
M is smaller than or equal to D as T and D are equal.
Only statement II is true.

A $$leq$$ F $$geq$$ T = E $$leq$$ R

Conclusion 1. A can be equal to F, hence not certainly true
Conclusion 2. No relationship can be established between R and F.

Hence E

2001.14 ~ 2000 54.89 ~ 55 9.899 ~ 10 As we need to follow BODMAS Rule. So the question is (2000 ÷ 55) × 10 =363.3 As 363.3 is closest to option E. So the answer is 360

Here the approx values are 20.002 ~ 20 39.996 ~ 40 0.499 ~ 0.5
So , 20.002 × 39.996 × 0.499 = 20× 40× 0.5 = 400
Hence , option D is Correct.

Here , 1.992 ~ 2 24.998 ~ 25 49.987 ~ 50 So, 1.992 × 24.998 × 49.987 = 2 × 25 × 50 = 2500 So, option D is correct.

$$4244 div 4 + 4554 div 9$$ , the given question just test the concept of BODMAS Rule. $$frac{4244}{4}$$ + $$frac{4554}{9}$$ = 1061 + 506 = 1567 So option A is correct

Here the question is trying to check our ability to do faster calculations. so the only way to do this question is multiply and logically deduce that the digit at unit place after solving the given equation can be 8 only. So there are high chances of option B 72 × 4.3 × 0.8 = 247.68

$$frac{5}{7} + frac{2}{3} - frac{2}{7}$$ for this question first we need to take the LCM of (7, 7, 3) which is 21 Now, $$frac{5}{7} + frac{2}{3} - frac{2}{7}$$ = $$frac{15}{21} + frac{14}{21} - frac{6}{21}$$ = $$frac{23}{21}$$ = $$1frac{2}{21}$$ Hence the answer is option B

Try to see this question with little arrangement to simplify calculation : = $$frac{21}{25} imes frac{75}{56} imes frac{32}{33}$$ = $$frac{21}{33} imes frac{75}{25} imes frac{32}{56}$$ = $$frac{7}{11} imesfrac{3}{1} imesfrac{4}{7}$$
= $$frac{12}{11}$$ = $$1frac{1}{11}$$

Hence option C is correct

$$(10.97)^{2} + (4.13)^{3} imes 3.79$$.
~$$11^{2}+4^{3} imes4$$.
=$$121+256$$.
=$$377$$.
~376.
Hence, Option B is correct.

(33858$$div$$33)$$div$$18.
=(1026)$$div$$18.
=57.
Hence, Option A is correct.

2433 + 227 + 1278$$div$$142.
=2433+227+9.
=2669.
Hence, Option B is correct.

4/9 $$ imes$$ 1701 + 2/11 $$ imes$$ 1386.
=$$frac{4 imes1701}{9}+frac{2 imes1386}{11}$$.
=$$189 imes4+126 imes2$$.
=$$756+252$$.
=$$1008$$.
Hence, Option C is correct.

3/5 $$ imes$$ 4/9 $$ imes$$ 5894.92.
~3/5 $$ imes$$ 4/9 $$ imes$$ 5895.
=$$3 imes4 imes131$$.
=$$1572$$.
Hence, Option B is correct.

19.03 $$ imes$$ 16.98 $$ imes$$ 13.01.
~19 $$ imes$$ 17 $$ imes$$ 13.
=4199.
~4200.
Hence, Option C is correct.

$$3frac{3}{8} imes 6frac{5}{12}-2frac{3}{16} imes 3frac{1}{2}$$ $$frac{27}{8} imesfrac{77}{12}-frac{35}{16} imesfrac{7}{2}$$ $$frac{77 imes27}{96}-frac{35 imes7}{32}$$ = 21.656- 7.656 = 14 Hence option C is correct

Let the missing number be y $$(sqrt{7744 imes 11^2})div 2^3=(?)^2$$
$$frac{88 imes11}{8}=(y)^2$$ $$121=(y)^2$$ y = 11 Hence the correct option is B

=(1097.63 + 2197.36 - 2607.24) ÷ 3.5 Using BODMAS rule = 687.75 ÷ 3.5 =196.5 Hence option A is correct

= $$((441)^{1/2} imes 207 imes (343)^{1/3}div ((14)^2 imes (529)^{1/2}$$ = $$(21 imes207 imes7div(196 imes23))$$ Using BODMAS rule = $$frac{30429}{4508}$$ = 6.75 Hence option B is correct

Let the number be y $$4frac{1}{2}+(1div 2 frac{8}{9})-3frac{1}{13}=?$$ $$frac{9}{2}+(1div frac{26}{9})-frac{40}{13}$$ $$frac{9}{2}+frac{9}{26}-frac{40}{13}$$ $$frac{117+9-80}{26}$$ $$frac{46}{26}$$ $$frac{23}{13}$$

Let the missing number be y $$frac{sqrt{4356} imes sqrt{?}}{sqrt{6084}}=11$$ = $$frac{66 imessqrt{y}}{78}=11$$ = $$sqrt{y}$$ = 13 y = 169 Hence the option C is correct

This question is checking the concept of BODMAS rule. (973 ÷ 14) ÷ 5 × 11 = 69.5 ÷ 5 x 11 = 13.9 x 11 = 152.9 Hence option B is correct

Let the missing number be y $$3frac{6}{17}div 2frac{7}{34}-1frac{9}{25}=(y)^2$$ $$3frac{6}{17}$$ = $$frac{57}{17}$$ $$2frac{7}{34}$$ = $$frac{75}{34}$$ $$1frac{9}{25}$$ = $$frac{34}{25}$$ using BODMAS rule $$frac{57}{17} div frac{75}{34}$$ - $$frac{34}{25}$$
$$frac{38}{25}$$ - $$frac{34}{25}$$ = $$frac{4}{25} = (y)^2$$ y = $$frac{2}{5}$$

Let the missing number be y $$(216)^{4}$$ ÷ $$(36)^{4}$$ × y = $$(6)^{?}$$ Using BODMAS Rule $$6^{4}$$ x $$6^{5}$$ = $$(6)^{?}$$ x = 9 Hence option D is correct.

Let the number be y $$4frac{1}{2}+(1div 2 frac{8}{9})-3frac{1}{13}=?$$ $$frac{9}{2}+(1div frac{26}{9})-frac{40}{13}$$ $$frac{9}{2}+frac{9}{26}-frac{40}{13}$$ $$frac{117+9-80}{26}$$ $$frac{46}{26}$$ $$frac{23}{13}$$

$$frac{3}{8}$$ of $$(4624 div (564-428)$$ using BODMAS rule = $$frac{3}{8}$$ x $$(4624div 136)$$ = $$frac{3}{8}$$ x 34 =12.75

The given expression can be written as $$frac{57}{17}divfrac{75}{34}-frac{34}{25}$$=$$?^{2}$$ $$?^{2}= frac{57}{17}*frac{34}{75}-frac{34}{25}$$ $$?^{2}=frac{2*19}{25}-frac{34}{25}$$ $$?^{2}=frac{38}{25}-frac{34}{25}$$ $$?^{2}=frac{4}{25}$$ $$=> ?= frac{2}{5}$$ Option A is the right answer.

$$sqrt{?}$$ = $$frac{11*sqrt{6084}}{sqrt{4356}}$$
$$sqrt{?}$$ = $$frac{11*sqrt{169*36}}{sqrt{121*36}}$$
$$sqrt{?}$$ = 13
? = 169

The given expression can be written as $$left(frac{216}{36} ight)^{4}* 6^{5}$$ = $$6^{4}* 6^{5} = 6^{9}$$ Therefore, option D is the right answer.

(34.5 × 14 × 42) ÷ 2.8 = ?
34.5 × 5 × 42 = 345 × 21 = 7245

The given expression can be written as $$frac{27}{8}*frac{77}{12} -frac{35}{16}*frac{7}{2}$$ = $$frac{2079}{96} - frac{245}{32}$$ = $$frac{693}{32} - frac{245}{32}$$ = $$frac{448}{32}$$ =$$ 14$$ Option C is the right answer.

(?)² = $$frac{1682 * (43)^2}{841}$$
(?)² = $${2 imes (43)^2}$$
? = $$43sqrt{2}$$

? =456 ÷ 24 × 38 - 958 ÷ 364 × 182 ? =19 × 38 - 958 ÷ 2 ? =19 × 38 - 479
? = 722 - 479
? = 243

$$frac{3}{8}$$ of $$((4624 div (564-428))=?$$ $$frac{3}{8}$$ of $$((4624 div (136))=?$$ $$frac{3}{8}$$ of $$(34)=?$$ $$frac{51}{4}$$ 12$$frac{3}{4}$$

BODMAS rule is to be followed while evaluating the expression. $$1/3$$ of $$1/3$$ is $$1/9$$ $$3/(1/9) = 3*9 = 27$$ $$27*3 = 3^{4}$$ $$(3^{4})^{frac{1}{4}} = 3$$ $$ 3+ 3.4-4.4 = 3-1 =2$$ Option A is the right answer.

$$(sqrt{7744} imes (11)^2)/(2)^3=(?)^3$$
$$(11 imes8 imes (11)^2)/(2)^3=(?)^3$$
$$(1331)=(?)^3$$
11=(?)

The given expression can be written as $$frac{21*207*7}{196*23}$$ = $$frac{21*9}{28}$$ = $$6frac{3}{4}$$ Hence, option D is the right answer.

$$frac{6 imes 136div8+132}{628div 16-26.25}=?$$
$$frac{6 imes 17 + 132}{39.25 -26.25}=?$$
$$frac{102+132}{13}=?$$
$$frac{234}{13}=?$$
? = 18

$$frac{9}{2} + (1div frac{26}{9}) - frac{40}{13}$$ = $$frac{9}{2} + frac{9}{26} - frac{40}{13}$$ = $$frac{117-80+9}{26}$$ =$$frac{46}{26}$$ =$$1frac{10}{13}$$ Option E is the right answer.

As we know that the square root of 17424 will be 132 Hence, $$frac{132 imes 27}{66 imes 66 imes 11} = frac{9}{121}$$ So answer will be B

$$1097cdot63+2197cdot36-2607cdot24 = 687.75$$
Given equation will be equal to $$frac{687.75}{3.5} = 196.5$$

Given equation can be solved as follows: $$frac{57}{17} imes frac{34}{75} - frac{34}{25}$$ = $$frac{4}{25}$$ Hence, answer will be A

Given equation can be solved as following: $$ 4356 imes ? = 121 imes 6084$$ Hence, answer will be = $$frac{121 imes 6084}{4356}$$ = $$169$$

$$216 = 6^3$$ and $$36 = 6^2$$ So, given equation can be solved as follows: $$(6)^{12-8} imes 6^{5}$$ = $$6^{9}$$ Hence, answer will be 9

Equation can be solved as following: $$(34cdot5 imes14 imes42)div28$$ = $$(34cdot5 imes21)$$ = $$724.5$$

Given equation can be written as following: $$(frac{27}{8} imes frac{77}{12}) - (frac{35}{16} imes frac{7}{2})$$ $$frac{693-245}{32} = 14$$

Given equation can be written as follows: 3/8 of (4624/136) or 3/8 of 34 i.e. $$frac{51}{4}$$ Hence, answer will be D

Square root of 4356 will be = 66 Hence, $$frac{66*4}{11}$$ will be = 24 So, $$24 = sqrt{?} imes6$$ Hence, the answer is 16 So answer will be E

Given equation can be written as following: $$(88 imes 121 ) div 8 = 1331 = (11)^{3}$$ Hence, answer will be 11

Given equation can be written as follows: $$(21 imes 207 imes 7) div (196 imes 23)$$ = $$frac{189}{28}$$ = 6.75

After solving according to the BODMAS rule, numerator of the given equation will be = 102+132 = 234 Denominator will be = 39.25 - 26.25 = 13 Hence, answer will be = $$frac{234}{13} = 18$$

Given equation can be written as the following: $$frac{9}{2} + frac{9}{26} - frac{40}{13} = frac{46}{26}$$ = $$frac{23}{13}$$ Hence, answer will be E

$$frac{sqrt{frac{81}{25}} - sqrt{frac{144}{121}}}{sqrt{frac{1681}{484}}}$$ = $$frac{{frac{9}{5}} - frac{12}{11}}{frac{41}{22}}$$
= (39/55)/(41/22)
= (39*22)/(55*41)
= 78/205
Option C is the correct answer.

$$2frac{1}{5}$$ = 11/5
$$1frac{2}{5}$$ = 7/5
$$4frac{2}{5}$$ = 22/5
(11/5) * (7/22) = 7/10
Option E is the correct answer

In order to satisfy the condition i.e. ‘B > N’ as well as ‘D$$leq$$L’ for the given expression, the expression should be written as B > L = O = N ≥ D From this expression, it is clear that B > N and D

5223/36=145
145*0.93=134.93~135

The answer can be calculated quickly by rounding off, hence we can approximate 105.003~105, 307.993~308, 215.66~215.6
Their sum = 105+308+215.6=628.6~330, the nearest option.

Now, let unknown be x. 283*56=15848 15848+252=16100 20x=16100 x=805

$$sqrt{2704} = 52$$ Now,$$( 5863-52)*.5 = 2905.5$$.
Therefore, option B is the right answer. 

Let unknown be x, $$(7921div178)-5.5=sqrt{x}$$ Hence, x=[(7921/178)-5.5]^2=39^2=1521

In mathematical way, the question is intrepreted as, (1/4)*(1/2)*(3/4)*52000=(3/32)*52000 = 3*1625 = 4875

The expression, on reframing gives, $$frac{57}{171} imesfrac{32}{128} imesfrac{45}{67}$$ which on simplifying gives, (1/4)*(1/3)*(45/67) = (15/268)

(9/3)+(3/11)+(7/15) = (129/110) + 7/15 = (1/5)(129/22 +7/3) = 1/5(541/66) = 541/330 Converting 541/330 into mixed fraction we get $$1frac{211}{330}$$

Expression : $$( 8 * 16 div 256 * 512 ) imes 2^{?} = 1$$ => $$(frac{128}{256} imes 512) imes frac{1}{2^x} = 1$$ => $$(128 imes 2) imes frac{1}{2^x} = 1$$ => $$frac{256}{2^x} = 2^0$$ => $$2^{8 - x} = 2^0$$ => $$8 - x = 0$$ => $$x = 8$$

Expression : $$frac{256^{frac{1}{4}}}{1frac{3}{5}}-frac{3}{5}=?$$ = $$frac{4^{4 imes frac{1}{4}}}{frac{8}{5}} - frac{3}{5}$$ = $$frac{4 imes 5}{8} - frac{3}{5}$$ = $$frac{5}{2} - frac{3}{5}$$ = $$frac{25 - 6}{10}$$ = $$frac{19}{10} = 1frac{9}{10}$$

Expression : $$frac{frac{2}{5}}{1frac{1}{15}}-frac{1}{4}=?-frac{2}{3}$$ => $$frac{frac{2}{5}}{frac{16}{15}} = x + frac{1}{4} - frac{2}{3}$$ => $$frac{2}{5} imes frac{15}{16} = x - frac{5}{12}$$ => $$frac{3}{8} = x - frac{5}{12}$$ => $$x = frac{3}{8} + frac{5}{12}$$ => $$x = frac{9 + 10}{24} = frac{19}{24}$$

$$561204 imes58 = ? imes 55555$$ implies ? = $$561204 imes58 div 55555$$ = 586