Q : If (x + 6y) = 8, and xy = 2, where x > O, what is the value of (x3+216y3)?
(A) 476
(B) 288
(C) 224
(D) 368
Correct answer: C
Q : Some students (only boys and girls) from different schools1 appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam'. A total of 90 students failed. Find the number of students that appeared for the exam.
(A) 500
(B) 350
(C) 400
(D) 420
Correct answer: A
Q : The ratio of the monthly incomes of A and B is 11 : 13 and the ratio of their expenditures is 9 : 11. If both of them manage to save ₹4,000 per month, then find the difference in their incomes (in ₹).
(A) 2,500
(B) 4,000
(C) 3,200
(D) 3,000
Correct answer: B
Q : The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x +1) cm and (x + 3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:
(A) 6
(B) 10
(C) 12
(D) 7
Correct answer: B
Q : AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 620, then find the measure of the minor arc AC.
(A) 310
(B) 620
(C) 560
(D) 280
Correct answer: D
Q : A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
(A) 5
(B) 4
(C) 6
(D) 2
Correct answer: B
Q : An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=400. Find the measure of ∠BCD.
(A) 500
(B) 500
(C) 200
(D) 300
Correct answer: C
Q : LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers is 240, then what is the other number?
(A) 1680
(B) 171
(C) 210
(D) 57
Correct answer: C
Q : Find the greatest number 23a68b, which is divisible by 3 but NOT divisible by 9.
(A) 239685
(B) 238689
(C) 239688
(D) 237687
Correct answer: A
Q : A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then bow much time will it take to go 39 km downstream and 30 km upstream?
(A) 3 h 40 m
(B) 2 h 40 m
(C) 3 h 10 m
(D) 2 h 50 m
Correct answer: C