# Integer and Sq Cm

QUANTITATIVE APTITUDE

Questions asked in XLRI Examination held on January 9, 2005

Directions: In each question below, choose the correct alternative from the four options provided. 1. Last year Mr Basu bought two scooters. This year he sold both of them for Rs 30,000 each. On one, he earned 20% profit, and on the other he made a 20% loss. What was his net profit or loss? (A) He gained less than Rs 2000 (B) He gained more than Rs 2000 (C) He lost less than Rs 2000 (D) He lost more than Rs 2000 2. In an examination, the average marks obtained by students who passed was x%, while the average of those who failed was y%. The average marks of all students taking the exam was z%. Find in terms of x, y and z, the percentage of students taking the exam who failed. ( z – x) (A) ( y – x) ( x – z) (B) ( y – z)

and at the point P, forming a loop. The straight line OP divides the loop into two parts. What is the ratio of the areas of the two parts of the loop? (A) 3 : 1 (B) 3 : 2 (C) 2 : 1 (D) 1 : 1 7. How many numbers between 1 to 1000 (both excluded) are both squares and cubes? (A) none (B) 1 (C) 2 (D) 3 8. An operation ‘$’ is defined as follows: For any two positive integers x and y, x$y =

F GH

x + y

y x

I JK then which of the following is an

(C)

( y – x) (z – y)

(D)

( y – z) ( x – z)

3. Three circles A, B and C have a common centre O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle is: 1 2 (A) (B) 3 5 (C)

integer? (A) 4$9 (B) 4$16 (C) 4$4 (D) None of the above 9. If f(x) = cos(x) then 50th derivative of f(x) is: (A) sin x (B) – sin x (C) cos x (D) – cos x 10. If a, b and c are three real numbers, then which of the following is NOT true? (A) a + b ≤ a + b (B) a – b ≤ a + b (C) a – b ≤ a – b (D) a – c ≤ a – b + b − c 11. If R = {(1, 1), (2, 2), (1, 2), (2, 1), (3, 3)} and S = {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3)} are two relations in the set X = {1, 2, 3}, the incorrect statement is: (A) R and S are both equivalence relations (B) R ∩ S is an equivalence relations (C) R −1 ∩ S −1 is an equivalence relations (D) R ∪ S is an equivalence relations 12. If x > 8 and y > – 4, then which one of the following is always true? (A) xy < 0 (B) x2 < – y (C) – x < 2y (D) x > y 13. For n = 1, 2, .... let Tn = 13 + 23 + ... + n3, which one of the following statements is correct?

3 5

(D)

1 5

4. The sides of a rhombus ABCD measure 2 cm each and the difference between two angles is 90° then the area of the rhombus is: (A) 2 sq cm (B) 2 2 sq cm (C) 3 2 sq cm (D) 4 2 sq cm 5. If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is: (A) 1 : 3 (B) 2 : 3 (C) 1 : 4 (D) 1 : 5 6. The curve y = 4x2 and y2 = 2x meet at the origin O

620 ◆ FEBRUARY 2006 ◆ THE COMPETITION MASTER

O B J E C T I V E -T Y P E Q U E S T I O N S

(A) There is no value of n for which Tn is a positive power of 2. (B) There is exactly one value of n for which Tn is a positive power of 2. (C) There are exactly two values of n for which Tn is a positive power of 2. (D) There are more than two values of n for which Tn is a positive power of 2. 14. An equilateral triangle is formed by joining the middle points of the sides of a given equilateral triangle. A third equilateral triangle is formed inside the second equilateral triangle in the same way. If the process continues indefinitely, then the sum of areas of all such triangles when the side of the first triangle is 16 cm is: (A) 256 3 sq cm (B) (C) 19. If the roots of the equation x+a x+b + =1 x+a+c x+ b+c

are equal in magnitude but opposite in sign, then: (A) c ≥ a (B) a ≥ c (C) a + b = 0 (D) a = b...

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