Mathematics Test

Result

Mathematics Test - 12

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

A

2

B

4

C

0

D

8
Question 2
1 / -0

A

2

B

1

C

3

D

4
Question 3
1 / -0

Let f : (-π/2, π/2 ), → R be given by f(x) = (log(sec x + tan x))^3. Then

A

All of these

B

f (x) is an odd function

C

f (x) is an onto function

D

f (x) is a one-one function
Question 4
1 / -0

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 + y^2 = 16 and x^2 + y^2 = 1. Then

A

radius of S is 8

B

centre of S is (8, 1)

C

radius of S is 7

D

None of these
Question 5
1 / -0

In a triangle the sum of two sides is x and the product of the same two sides is y. If x^2 - c^2 = y, where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

A

3y/4x(x+ c)

B

3y/4c(x+ c)

C

3y/2x(x+ c)

D

3y/2c(x+ c)
Question 6
1 / -0

A

7

B

9

C

8

D

6
Question 7
1 / -0

From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that angle QPR is a right angle, then the possible value(s) of λ is(are)

A

-1

B

1

C

√2

D

-√2
Question 8
1 / -0

A

5

B

3

C

4

D

2
Question 9
1 / -0

If the coefficients of x^3 and x^4 in the expansion of (1 + ax + bx^2) (1 - 2x)^18 in powers of x are both zero, then (a, b) is equal to

A

(16, 272/3)

B

(14, 251/3)

C

(14, 272/3)

D

(16, 251/3)
Question 10
1 / -0

Let a, r, s, t be non-zero real numbers. Let P(at^2 , 2at), Q, R(ar^2 , 2ar) and S(as^2, 2as) be distinct points on the parabola y^2 = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0).If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

A

a(t^2 + 2)^2 / 2t^3

B

a(t^2 + 1)^2 / 2t^3

C

a(t^2 + 1)^2 / 2t^2

D

(t^2 + 1)^2 / 2t^3