SSCCGL2012Tier18JulyNZEveningII Related Question Answers

101. Given that ∠ABC = 90°, BC is parallel to DE. If AB = 12, BD = 6 and BC = 10, then the length of DE is

102. AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, is

103. A chord AB of length 3$$\sqrt{2}$$ unit subtends a right angle at the centre 0 of a circle. Area of the sector AOB (in sq. units) is

104. If sin p + cosec p = 2, then the value of $$sin^{7}p + cosec^{7}p$$ is

105. If $$sin θ + sin^2θ + sin^3θ = 1$$, then $$cos^6θ - 4cos^4θ + 8cos^2θ$$ is equal to

106. sin (45 + θ) - cos (45 - θ) is

107. A man is climbing a ladder which is inclined to the wall at an angle of 30°. If he ascends at a rate of 2 m/s, then he approaches the wall at the rate of

108. Value of $$2 (sin^6 θ + cos^6 θ) - 3 (sin^4 θ + cos^4 θ) + 1 $$is

109. If $$tanθ = \frac{a}{b}$$, then $$\frac{a sin \theta + b cos \theta}{a sin \theta - b cos\theta}$$ is

110. The value of $$\frac{sin39^{\circ}}{cos51^{\circ}}$$ + $$2 tan11^{\circ} tan31^{\circ} tan45^{\circ} tan59^{\circ} tan79^{\circ}$$ - $$3(sin^{2}21^{\circ} + sin^{2}69^{\circ})$$ is

111. If x = 27 and $$\sqrt[3]{x} + \sqrt[3]{y} = \sqrt[3]{729}$$, the y =

112. The value of $$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$ is

113. If $$\frac{3-5x}{x} + \frac{3-5y}{y} + \frac{3-5z}{z} = 0 $$, the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$ is

114. If ab > 0 and the point (a, b) lies in the third quadrant, the quadrant in which the point (5, - a) lies is

115. If $$x = \frac{\sqrt{5}-2}{\sqrt{5}+2}$$, then $$x^4 + x^{-4}$$ is

116. If $$ x + \frac{1}{x} = 3$$, the value of $$x^5 + \frac{1}{x^5}$$ is

117. ABC is a triangle with AC = BC and ∠ABC = 50°. The side BC is produced to D so that BC = CD. ∠BAD is

118. If a straight line L makes an angle θ (θ > 90°) with the positive direction of x axis, then the acute angle made by a straight line L 1 , perpendicular to L, with the yaxis is

119. The radius of a circle is 6 cm. An external point is at a distance of 10 cm from the centre. Then the length of the tangent drawn to the circle from the external point upto the point of contact is

120. If G be the centroid of AABC and the area of AGBD is 6 sq. cm, where D is the midpoint of side BC, then the area of AABC is

121. A triangle is inscribed in a circle and the diameter of the circle is its one side. Then the triangle will be

122. AB and BC are two chords of a circle with centre O. If P and Q are the midpoints of AB and BC respectively, then the quadrilateral OQBP must be

123. In any triangle ABC, the base angles at B and C are bisected by BO and CO respectively. Then ∠BOC is

124. An article was sold ford 96. If percentage of profit was numerically equal to the cost price, the cost price of the article is

125. The average of 7 numbers is 8. If one number is added, their average is 9. Then the added number is

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SSCCGL2012Tier18JulyNZEveningII Related Question Answers

101. Given that ∠ABC = 90°, BC is parallel to DE. If AB = 12, BD = 6 and BC = 10, then the length of DE is

102. AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, is

103. A chord AB of length 3$$\sqrt{2}$$ unit subtends a right angle at the centre 0 of a circle. Area of the sector AOB (in sq. units) is

104. If sin p + cosec p = 2, then the value of $$sin^{7}p + cosec^{7}p$$ is

105. If $$sin θ + sin^2θ + sin^3θ = 1$$, then $$cos^6θ - 4cos^4θ + 8cos^2θ$$ is equal to

106. sin (45 + θ) - cos (45 - θ) is

107. A man is climbing a ladder which is inclined to the wall at an angle of 30°. If he ascends at a rate of 2 m/s, then he approaches the wall at the rate of

108. Value of $$2 (sin^6 θ + cos^6 θ) - 3 (sin^4 θ + cos^4 θ) + 1 $$is

109. If $$tanθ = \frac{a}{b}$$, then $$\frac{a sin \theta + b cos \theta}{a sin \theta - b cos\theta}$$ is

110. The value of $$\frac{sin39^{\circ}}{cos51^{\circ}}$$ + $$2 tan11^{\circ} tan31^{\circ} tan45^{\circ} tan59^{\circ} tan79^{\circ}$$ - $$3(sin^{2}21^{\circ} + sin^{2}69^{\circ})$$ is

111. If x = 27 and $$\sqrt[3]{x} + \sqrt[3]{y} = \sqrt[3]{729}$$, the y =

112. The value of $$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$ is

113. If $$\frac{3-5x}{x} + \frac{3-5y}{y} + \frac{3-5z}{z} = 0 $$, the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$ is

114. If ab > 0 and the point (a, b) lies in the third quadrant, the quadrant in which the point (­5, - a) lies is

115. If $$x = \frac{\sqrt{5}-2}{\sqrt{5}+2}$$, then $$x^4 + x^{-4}$$ is

116. If $$ x + \frac{1}{x} = 3$$, the value of $$x^5 + \frac{1}{x^5}$$ is

117. ABC is a triangle with AC = BC and ∠ABC = 50°. The side BC is produced to D so that BC = CD. ∠BAD is

118. If a straight line L makes an angle θ (θ > 90°) with the positive direction of x­ axis, then the acute angle made by a straight line L 1 , perpendicular to L, with the y­axis is

119. The radius of a circle is 6 cm. An external point is at a distance of 10 cm from the centre. Then the length of the tangent drawn to the circle from the external point upto the point of contact is

120. If G be the centroid of AABC and the area of AGBD is 6 sq. cm, where D is the mid­point of side BC, then the area of AABC is

121. A triangle is inscribed in a circle and the diameter of the circle is its one side. Then the triangle will be

122. AB and BC are two chords of a circle with centre O. If P and Q are the mid­points of AB and BC respectively, then the quadrilateral OQBP must be

123. In any triangle ABC, the base angles at B and C are bisected by BO and CO respectively. Then ∠BOC is

124. An article was sold ford 96. If percentage of profit was numerically equal to the cost price, the cost price of the article is

125. The average of 7 numbers is 8. If one number is added, their average is 9. Then the added number is

114. If ab > 0 and the point (a, b) lies in the third quadrant, the quadrant in which the point (5, - a) lies is

118. If a straight line L makes an angle θ (θ > 90°) with the positive direction of x axis, then the acute angle made by a straight line L 1 , perpendicular to L, with the yaxis is

120. If G be the centroid of AABC and the area of AGBD is 6 sq. cm, where D is the midpoint of side BC, then the area of AABC is

122. AB and BC are two chords of a circle with centre O. If P and Q are the midpoints of AB and BC respectively, then the quadrilateral OQBP must be