Mathematics Test

Result

Mathematics Test - 11

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

The image of the line (x-1)/3 = (y-3)/1 = (z-4)/ -5 in the plane 2x - y + z + 3 = 0 is the line

A

(x + 3)/3 = (y-5)/1 = (z-2)/ -5

B

(x + 3)/-3 = (y-5)/-1 = (z+2)/5

C

(x + 3)/3 = (y+ 5)/1 = (z-2)/-5

D

(x + 3)/-3 = (y-5)/-1 = (z-2)/5
Question 2
1 / -0

A

Option A

B

Option B

C

Option C

D

Option D
Question 3
1 / -0

The slope of the tangent to the curve (y - x^5)^2 = x(1 + x^2)^2 at the point (1, 3) is ______

A

9

B

8

C

7

D

10
Question 4
1 / -0

For x ∈ (0, π), the equation sinx + 2sin2x - sin3x = 3 has

A

one solution

B

three solutions

C

no solution

D

infinitely many solutions
Question 5
1 / -0

Let a ∈ R and let f : R → R be given by f (x) = x^5 - 5x + a, then

A

f (x) has three real roots if a > 4

B

f (x) has three real roots if a < - 4

C

f (x) has only one real roots if a > 4

D

None of these
Question 6
1 / -0

Let a, b, c be positive integers such that b/a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of (a^2 + a - 14)/(a + 1) is ________

A

4

B

5

C

6

D

3
Question 7
1 / -0

A

option B

B

Option C

C

Option A

D

Option D
Question 8
1 / -0

A

4

B

8

C

2

D

0
Question 9
1 / -0

A

Option A

B

Option B

C

Option C

D

All of these
Question 10
1 / -0

A bird is sitting on the top of a vertical pole 20 m high 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 O is reduced to 30°. Then the speed (in m/s) of the bird is

A

20(√3 - 1)

B

40(√3 - √2)

C

40(√2 - 1)

D

20√2