Mathematics Test 208

Result

Mathematics Test 208

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Weekly Quiz Competition

Question 1
4 / -1

For a random variable X, if E(X) = 5 and Var(X) = 6, then E(X²) is equal to

A
31

B
19

C
61

D
11

Solution

We know that, variance of a random variate X is equal to difference of expectation of the variate X² and square of the expectation of the variate X.
Question 2
4 / -1

A
-1

B
1/2

C
-2

D
0

Solution
Question 3
4 / -1

The area bounded by y = xe^|x| and the lines |x| = 1, y = 0 is

A
4 sq. units

B
6 sq. units

C
1 sq. units

D
2 sq. units

Solution
Question 4
4 / -1

The integral is equal to (where [.]. denotes the greatest integer function)

A

B
1

C
2 In (1/2)

D
0

Solution
Question 5
4 / -1

The domain of definition of the function

A
(1, ∞)

B
[1, ∞)

C
R - {1}

D
(−∞, −1)∪(1, ∞)

Solution

x²− 1 ≥ 0

⇒ x² ≥ 1

⇒ x ∈(−∞, −1] ∪ [1, ∞)…….(1)

and x − 1 > 0

⇒ x > 1

⇒ x ∈ (1, ∞) ……(2)

From (1) and (2)

x∈(1, ∞)
Question 6
4 / -1

A plane passes through (1, 2, 2) and is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4. Square of the distance of the plane from the point (52, 53, 57) is

A
5202

B
5201

C
5203

D
5200

Solution
Question 7
4 / -1

A
α > β

B
α = β

C
α < β

D
α + β = 2π

Solution
Question 8
4 / -1

A
x/y

B

C

D
y/x

Solution
Question 9
4 / -1

is equal to (where C is an arbitrary constant)

A

B

C

D
None of these

Solution
Question 10
4 / -1

If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B are

A
2⁹

B
9²

C
3²

D
2^9-1

Solution

A = {2,4,6 ; B = {2,3,5}

∴ A × B contains 3 × 3 = 9 elements.

Hence, the number of relations from A to B = 2⁹.