76. In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of CBE to that of ADE?
77. In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC.
78.
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.At what time did X catch the thief?
79.
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.If another policeman had started the same chase along with X, but at a speed of 60 km/hr, then how far behind was he when X caught the thief?
80. What is the value of $$a^3 + b^3$$ ?
I. $$a^2 + b^2 = 22$$
II. $$ab = 3$$
81. Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.
82. A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?I. When the person has covered $$\frac{1}{3}$$ the distance, he is 3 km east and 1 km north of Mali.
II. When the person has covered $$\frac{2}{3}$$ the distance, he is 6 km east and 2 km north of Mali.
83. What is the value of x and y?
I. 3x + 2y = 45
II. 10.5x + 7y = 157.5
84. Three friends P, Q and R are wearing hats, either black or white. Each person can see the hats of the other two persons. What is the colour of P's hat? I. P says that he can see one black hat and one white hat. II. Q says that he can see one white hat and one black hat.
85. What is the speed of the car?I. The speed of a car is 10 (km/hr) more than that of a motorcycle.
II. The motorcycle takes 2 hr more than the car to cover 100 km.
86. What is the ratio of the volume of the given right circular cone to the one obtained from it?
I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2.
II. The height and the base of the new cone are one-third those of the original cone.
87. What is the area bounded by the two lines and the coordinate axes in the first quadrant?
I. The lines intersect at a point which also lies on the lines 3x - 4y = 1 and 7x - 8y = 5.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.
88. What is the cost price of the chair?
I. The chair and the table are sold at profits of 15% and 20% respectively.
II. If the cost price of the chair is increased by 10% and that of the table is increased by 20%, the profit reduces by Rs. 20.
89. After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time.I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.II. Gati can complete one entire lap in exactly 10 s.
90. Select the pair that best expresses a relationship similar to the one expressed in the question pair. Peel : Peal
91. Select the pair that best expresses a relationship similar to the one expressed in the question pair. Doggerel : Poet
92. Select the pair that best expresses a relationship similar to the one expressed in the question pair. Premise : Conclusion
93. Select the pair that best expresses a relationship similar to the one expressed in the question pair.Barge : Vessel
94. Select the pair that best expresses a relationship similar to the one expressed in the question pair. Love : Obsession
95. Select the pair that best expresses a relationship similar to the one expressed in the question pair. Reptile : Adder
96. Choose the set in which the third statement logically follows from the first two.
A. No bird is viviparous.
B. All mammals are viviparous.
C. Bats are viviparous.
D. No bat is a bird.
E. No bird is a mammal.
F. All bats are mammals.
97. Choose the set in which the third statement logically follows from the first two.
A. No mother is a nurse.
B. Some nurses like to work.
C. No woman is a prude.
D. Some prude are nurses.
E. Some nurses are women.
F. All women like to work.
98. Choose the set in which the third statement logically follows from the first two.
A. Oranges are sweet.
B. All oranges are apples.
C. Some sweet are apples.
D. Some oranges are apples.
E. All sweet are sour.
F. Some apples are sour.
99. Choose the set in which the third statement logically follows from the first two.
A. Zens are Marutis.
B. Zens are fragile.
C. Marutis are fragile.
D. Opels are fragile.
E. Marutis are Opels.
F. Opels are stable.
100. Choose the set in which the third statement logically follows from the first two.
A. Dogs sleep in the open.
B. Sheep sleep indoors.
C. Dogs are like sheep.
D. All indoors are sheep.
E. Some dogs are not sheep.
F. Some open are not sheep.
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