Mathematics Test 136

Result

Mathematics Test 136

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Weekly Quiz Competition

Question 1
4 / -1

The solution to

A

B

C

D

Solution
Question 2
4 / -1

The area bounded by the curves x + 2|y| = 1 and x = 0 is:

A
1/3

B
1/2

C
2

D
3

Solution
Question 3
4 / -1

The length of the common chord of the circles x² + y² + 2x + 3y + 1 = 0 and x² + y² + 4x + 2 = 0 is

A
9/2

B

C

D
3/2

Solution

The equation of the common chord is S₂ - S₁=0
⇒ 2x + 1 = 0
Question 4
4 / -1

In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin³ x - k = 0, 0 < k < 1, then value of C is

A
π/3

B
π/2

C
2π/3

D
5π/6

Solution
Question 5
4 / -1

The value of

A
-5

B
-7

C
5

D
7

Solution
Question 6
4 / -1

Suppose a, b, c are in AP and a², b², c² are in GP. If a < b < c & a + b + c = 3/2, then the value of a is

A

B

C
1/2

D
None of these

Solution

Since, a<b<c, the above results are not satisfied.
If we consider ac= - 1/4, then
x² -x - (1/4) = 0
Question 7
4 / -1

The function

A
Increasing on (0, ∞)

B
Decreasing on (0, ∞)

C
Increasing on decreasing on

D
none of these

Solution
Question 8
4 / -1

If log₂(4^x+1+ 4)log₂(4^x + 1) = log₂ 8, then x equals

A
-1

B
0

C
16

D
64

Solution
Question 9
4 / -1

If ‘M’ and σ² are mean and variance of random variable X, whose distribution is given by –

Then

A
M = 1, σ²= 2

B

C

D

Solution

The mean of a probability distribution is given as
M = Σ P_ix_i = (¼ × 0) + (0 × 1) + (¼ × 2 ) + (0 × 3) + (½ × 4) + (0 × 5)= 5/2

σ² = Σ P_i (M – x_i)²
Question 10
4 / -1

If a,b,c are three unit vectors such that and b is not parallel to c, then the angle between a and c is:

A
π/6

B
π/4

C
π/3

D
π/2

Solution