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Practice Test - Mathematics 20

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Question 1

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation

Question 2

Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of mid-point of PQ is

Question 3

The equation of the tangent to the curve, that is parallel to the x-axis is

Question 4

If ω (≠ 1) is a cube root of unity, and (1 + ω)⁷ = A + Bω. Then (A, B) equals:

Question 5

Area of the greatest rectangle that can be inscribed in the ellipse

Question 6

If I₁ =

, I₃ =

dx then

Question 7

If a² + b² + c² = -2 and f(x) =

then f(x) is a polynomial of degree

Question 8

The shortest distance between the line y – x = 1 and the curve x = y² is

Question 9

A bird is sitting on the top of a vertical pole which is 20 m in height and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from point O is reduced to 30°. Calculate the speed (in m/s) of the bird.

Question 10

, then the value of (A, B) is

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Feb 21JEE & BITSAT