Quant Paper - 1 For Jmet For Practice

JMET PAPER - 1 1

2

If µ = {1, 2, 3, 4, 5, 6, 7}, A = {3, 5, 6} and A ∩ B = {3, 5}, then how many subsets of µ can B represent? (1) 16 (2) 32 (3) 8 (4) Cannot be determined

x On the xy plane, a1 a2

y 1 b1 1 = 0 represents a b2 1

(1) circle passing through (a1, b1) and (c2, b2). (2) parabola passing through (a1, b1) and (c2, b2). (3) ellipse passing through (a1, b1) and (a2, b2). (4) straight line passing through (a1, b1) and (a2, b2). 3.

The lengths of two of the sides of a triangle are given by the roots of x − 2 5 x + 1 = 0. If the o angle between the above mentioned sides is 60 , then the length of the third side is 2

(1) 3 2 units (3) 4.

(2) 2 3 units

11 units

(4) None of these

The top of a cliff is observed from two points A and B and the angles of elevation are found to be α and β respectively. Given that the point B is ‘x’m vertically above A, what is the height of the cliff? x cot α x cot β (2) (1) cot β − cot α cot β − cot α x tan β x tan β (4) (3) tan α − tan β tan β − tan α ∧

5.

∧

∧

∧

∧

∧

If the vectors a = l i + m j + n k, b = i + j + k and ∧

∧

∧

( )

c = m i + n j + l k , then a ⋅ b × c = 3 3 3 (1) l + m + n − 3lmn 3 3 (2) l + m + 1 − 3lm (3) l2 + m2 + n2 + lm + mn + ln 2 2 2 (4) l + m + n − lm − mn − nl 6.

Given that f(x + y) = f(x) f(y), for all x, y ∈ R. Suppose that f(5) = 4 and f'(0) = 9, then f '(5), is equal to (1) 25 (2) 36 (3) 16 (4) None of these

7.

Two integers x and y are chosen at random between 1 and 100 (inclusive), what is the x y probability that 7 + 7 is a multiple of 10? (1) 1/8 (2) 1/7 (3) 1/4 (4) 1/9 π

8

e cos x dx

= e cos x + e −cos x (1) e (2) π ∫

0

(3) π/2

(4) 0

9.

Each of the value a, b and c of a quadratic 2 equation ax + bx + c = 0 is determined by throwing an ordinary die. What is the probability that the roots of the quadratic equation thus obtained are equal? (1) 1/54 (2) 5/216 (3) 1/36 (4) 7/216

10. How many ways the letters of word EDUCATION be internally arranged, so that the vowels appear in the same order from left to right as they appear in the dictionary? (1) 4096 (2) 3024 (3) 2048 (4) 2576 11. The number of values that ‘x’ can take in order to satisfy the equation cot–1 (2x + 1) + cot–1 (4x + 1) –1 2 = cot (x /2) is (1) 0 (2) 1 (3) 2 (4) 3 12. The equation 25x2 – 100x – 144y + 16y2 = 44, represents a/an (1) hyperbola (2) ellipse (3) pair of straight lines (4) None of these 13. If y = x – x3/3! + x5/5! – x7/7! + ……, then dy/dx = (1) sin x (2) cos x (3) tan x (4) None of these 14. If R and S are two non-void relations defined on a non-empty set A. Which of the following statements is not necessarily true? (1) R and S are reflexive ⇒ R ∩ S is reflexive (2) R and S are transitive ⇒ R ∩ S is transitive (3) R and S are transitive ⇒ R ∪ S is transitive (4) R and S are symmetric ⇒ R ∪ S is symmetric 15. The graphs y = logax (a > 1) and y = logax (0
n

19. If f(x) = (1 – x) , then find the value of f(a) + f 1 (a ) f 2 ( a ) f 3 (a ) f n (a ) , for a = 0 and + + + ....... 1! 2! 3! n! n th n = 6. f (x) indicates n derivative of f(x). (1) 63 (2) 127 (3) 64 (4) 128 20. If x satisfies the inequality:

log9 x 2 + (log3 x ) < 6, then x belongs to 2

(1) (− 3, 2) ⎛1 ⎞ (3) ⎜ , 27 ⎟ ⎝9 ⎠

(2) (0, 2) ⎛ 1 ⎞ (4) ⎜ , 9 ⎟ ⎝ 27 ⎠

21. A question paper has 100 multiple choice questions with each question having 5 choices. The probability that Sonia knows the correct 2 answer to any question is . She attempts all 5 questions either by guessing or knowing the answer. A question attempted by her was found to have a correct response. Assuming that each question has exactly one correct choice, what is the probability that she has guessed it? 10 7 3 9 (1) (2) (3) (4) 13 13 13 13 22. Minimum value of the positive integer n for which both the roots of the equation: 2 nx − (2n + 1) (n + 1) = 0 are less than 6/5 is (1) 5 (2) 6 (3) 7 (4) 3 23. If f: Z → N is defined as ⎧x + 1, if x is even ⎪⎪ f(x) = ⎨ 3 ⎪ x + 1 , if x is odd ⎪⎩ 2 −1 then f (90) is (1) 181 (2) 179 (3) 267

their conditions listed. This is continued until two consecutive defectives are observed or four items have been checked, whichever occurs first. The sample space corresponding to this experiment is (1) {00, 100, 1100} (2) {0100, 100, 00, 0110} (3) {00, 100, 0100, 1100, 0101, 0110, 0111, 1010} (4) None of these

27. The sequence 3, 7, 11, …… is grouped as: {3}, {7, 11},{15, 19, 23, 27}, …. The first number in the 8th group is (1) 503 (2) 507 (3) 511 (4) 515 28. A is a fixed point on the circumference of a circle whose center is O and whose radius is r meters. A particle P starting from A describes the circle uniformly in 1 second. The rate at which the area of the triangle AOP is changing at the instant where ∠AOP = 60° is 2 2 (1) π/2 (2) πr (3) r /8π (4) πr /2 29. A submarine telegraph consists of a core of copper wires with a covering made of nonconducting material. If x denotes the ratio of the radius of the core to the thickness of the covering, it is known that the speed of signalling 2

varies as x log when x equals

3 1 (4) e

(1) e

+

1 . The greatest speed is attained x

(3)

(2)

1 e

30. The area enclosed by the loop of the curve

(4) 184

⎛ ⎞ 2x 2 3 x 3 4 x 4 24. If sin −1 ⎜ x − + − + .....n terms ⎟⎟ + ⎜ 3 4 5 ⎝ ⎠ ⎛ ⎞ π 2x 4 3 x 9 4 x 16 cos −1 ⎜⎜ x 2 − + − + ..n terms ⎟⎟ = , 3 4 5 ⎝ ⎠ 2 then the value of x can be (1) 2 (2) 3 (3) 1 (4) 1/2

y 2 = x (x − 2) 2 is revolved about the x–axis. The volume generated is 8π π 2π 4π (1) (2) (3) (4) 3 3 3 3

31. Which of the following best describes the graph of the given function? | x + 1 | − | x − 1 |, f(x) = ,x rel="nofollow"> 0 . x (1) (2)

25. If A 1, A 2, ……, An are the vertices of a regular plane polygon with n sides and O is its centre,

)

(

n−1 i=1

) ( (3) (n − 1) (OA × OA ) (4) n (OA × OA ) 2

2

1

1

(1) 0

(2) (1 − n) OA 2 × OA 1

2

2

then ∑ OA i × OA i+1 =

(3)

(4)

1

1

26. Items coming off a production line are marked defective (designated as zero) or non defective (designated as one). Items are observed and

2

2 1

1

2

32. The roots α, β of the equation ax 2 + b x + c = 0 are real and –3 < α < –1 and β > –1. Then the roots of the equation a(x − 2 )2 + b (x − 2 ) + c = 0 (1) are both greater than –1 (2) are both less than –3 (3) lie between –3 and –1 (4) are such that one is less than – 4 and the other lies between –3 and – 1

33. The set of values of x for which the area of the triangle formed by vertices of the form (x, 2), (2, x) and (3, 4) is less than 5 is (1) (0 ,7) (2) (0 , 2) ∪ (5 , 7) (3) (−∞ , 5) ∪ (2 , ∞) (4) (−∞ , 7) 34. Let f(x) = min {x, x } and g(x) = max{x, x }; x∈R then (1) f(x) + g(x) = x3. (2) f(x) = g(x), only for x = 0, 1. (3) fog(x) = x3. (4) gof(x) = x . 3

3

35. A large family has 15 children including 2 sets of identical twins, 3 sets of identical triplets and two individual children. The number of ways to seat these children in a row if the identical twins or triplets cannot be distinguished from one another and if the two sets of identical twins have to occupy the two extreme positions, one set each, is 11! 11! (2) (1) 3! (3 !)3 (3)

2 × 11!

(3 !)

3

(4)

11! × 2 3 (3 !)

36. The line x + y = 1 meets the x-axis at A and y-axis at B. Let P be the midpoint of AB. The perpendicular from P on OA meets OA at P1. M1 is the foot of perpendicular from P1 on OP. P2 is that of M1 on OA, M2 is that of P2 on OP and the process is continued indefinitely. Find the sum of

the areas of the triangles OAB, AP1P, P1P2M1, P2P3M2,….. . (1) 2/3 (2) 3/4 (3) 8/7 (4) 7/8

37. The coordinates of the points on the curve 20 y = where the tangent is parallel to the line x y = 2 – 5x are (1) (2, 10) and (4,5) (2) (2, 10) and (–2, –10) (3) (5,4) and (–5, –4) (4) There does not exist any such point. 38. A curve passes through the point (0, 1) and 2x − x 2 . the gradient at any point (x, y) is 2 The equation of the curve is x2 x3 (2) y = (1) y = x 2 + 1 − +1 2 6

(3) y =

x3 − 2x + 1 2

(3) y =

x3 + 2x + 1 6

39. The angle of elevation of a stationary cloud from a point 2500 cm above a lake is 15° and the angle of depression of its reflection in the lake is ° 75 . The height of the cloud above the lake level is

(1) 2500 3 cm

(2) 25 m

(3) 250 3 cm

(4) None of these

r r r x, y, z be vectors of lengths 2, 3, 4 r r r respectively and x is perpendicular to y + z , r r v v z+x , z perpendicular to is y is r r perpendicular to x + y , then the length of the r r r vector x + y + z is

40. If

(1)

29

(2)

(3)

40

(4) None of these

129

3