Let a1, a2, .... an be a given

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let f : 0,   0,  be a differentiable function such that f(1) = e and limtx t2f2x - x2f2tt - x. If f(x) = 1, then x is equal to

  • 1e

  • 2e

  • 12e

  • e


2.

Contrapositive o the statement : 'If a function f is differentiable at a, then it is also continuous at a', is :

  • If a function f is not continuous at a, then it is not differentiable at a.

  • If a function f is continuous at a, then it is differentiable at a.

  • If a function f is not continuous at a. then it is differentiable at a.

  • If a function f is continuous at a, then it is not differentiable at a.


3.

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of

(1 + x)n + 5 are in the ratio 5 : 10 : 14, then the largest coefficient in the expansion is :

  • 330

  • 252

  • 792

  • 462


4.

The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x+ y2 – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the point :

  • 1, - 3

  • - 1, 3

  • ( - 3, 6)

  • ( - 3, 1)


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5.

The angle of elevation of a cloud C from a point P, 200 m above a still take is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to

  • 100

  • 4003

  • 2003

  • 400


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6.

Let a1, a2, .... an be a given A.P. whose common difference is an integer and Sn= a1 + a2 + ... + an. If a1 = 1, a1 = 300 and 15  n  50, then the ordered pair (Sn  4, an  4) is equal to :

  • (2490, 248)

  • (2490, 249)

  • (2480, 249)

  • (2480, 248)


A.

(2490, 248)

an = a1 + n - 1d 300 = 1 + n - 1d d = 299n - 1 = 13 × 23n - 1 = integerso n - 1 = ± 13, ± 23, ± 299, ± 1 n = 14, - 12, 24, - 22, 300,  - 298, 2, 0But n 15, 50  n = 24  d = 13Hence Sn - 4 = S20 = 20221 + 20 - 113 = 102 + 247 = 2490an - 4 = a20 = a1 + 19d= 1 + 19 × 13= 1 + 247= 248


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7.

Let i = 150X = i = 1nyi = T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi's and exactly 6 of sets Yi's then n is equal to :

  • 45

  • 15

  • 30

  • 50


8.

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 21. If P(1, β), β > 0 is a point on this ellipse, then the equation of the normal to it at P is

  • 7x - 4y = 1

  • 4x - 2y = 1

  • 8x - 2y = 5

  • 4x - 3y = 2


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9.

The distance of the point (1,  2, 3) from the plane x  y + z = 5 measured parallel to the line x2 = y3 = z - 6 is :

  • 17

  • 7

  • 1

  • 75


10.

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to – 4, then a value of k is ;

  • 15

  •  4

  •  - 2

  • 14


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