If E denotes expectation, the variance of a random variable X is given by

**A. ** E X − E X

**B. ** E X + E X

**C. ** E X

**D. ** E X

**Answer : ****Option A**

**Explaination / Solution: **

The variance of a random variable x is given by E X − E X

The variance of a random variable x is given by E X − E X

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The following plot shows a function which varies linearly with x . The value of
the integral is

**A. ** 1.0

**B. ** 2.5

**C. ** 4.0

**D. ** 5.0

**Answer : ****Option B**

**Explaination / Solution: **

The given plot is straight line whose equation is

The given plot is straight line whose equation is

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For |x| << 1, coth (x) can be approximated as

**A. ** x

**B. ** x^{2}

**C. ** 1/x

**D. ** 1/x^{2}
**Answer : ****Option C**

**Explaination / Solution: **

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Which one of following functions is strictly bounded?

**A. ** 1/X^{2}

**B. ** e^{x}

**C. ** x^{2}

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

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For the function e^{x} , the linear approximation around x = 2 is

**A. ** (3 - x)e^{-2}
**B. ** 1 − x

**C. ** [3 + 3√2 - (1 - √2)x]e-2

**D. ** e2

**Answer : ****Option A**

**Explaination / Solution: **

Neglecting higher powers

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Consider the function f (x) = x − x − . The maximum value of f (x) in the closed interval [− 4, 4] is

**A. ** 18

**B. ** 10

**C. ** -225

**D. ** indeterminate

**Answer : ****Option A**

**Explaination / Solution: **

We have

f (x) = x − x +

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An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is

**A. ** 0.5

**B. ** 0.18

**C. ** 0.12

**D. ** 0.06

**Answer : ****Option C**

**Explaination / Solution: **

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The solution of the differential equation under the boundary
conditions

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

(i) y = y_{1} at x = 0 and

(ii) y = y_{2} at x = ∞, where k, y_{1} and y_{2} are constants, is

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The equation x − x + x − = is to be solved using the Newton - Raphson method. If x = is taken as the initial approximation of the solution, then next approximation using this method will be

**A. ** 2/3

**B. ** 4/3

**C. ** 1

**D. ** 3/2

**Answer : ****Option B**

**Explaination / Solution: **

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