Find the sum of the expression

**A. ** 7

**B. ** 8

**C. ** 9

**D. ** 10

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

**Explaination / Solution: **

The expression can be written as

The expression can be written as

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Which one of the following is NOT necessarily a property of a Group?

**A. ** Commutativity

**B. ** Associativity

**C. ** Existence of inverse for every element

**D. ** Existence of identity

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of
**A. ** n^{4}

**B. ** 4^{n}

**C. ** 2^{2n-1}

**D. ** 4^{n-1}

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

**Explaination / Solution: **

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If f(x^{7}) = 2x^{7} + 3x - 5, which of the following is a factor of f(x)?

**A. ** (x3 + 8)
**B. ** (x-1)

**C. ** (2x-5)

**D. ** (x+1)

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

**Explaination / Solution: **

from the option (b0 substitute x=1 in

from the option (b0 substitute x=1 in

2x7 + 3x - 5 = 0

2(1)7 + 3(1) - 5 = 0

5 - 5 = 0

So (x - 1) is a factor of f (x)

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Consider the following system of equations

**A. ** A unique solution

**B. ** No solution

**C. ** Infinite number of solutions

**D. ** Five solutions

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

**Explaination / Solution: **

No Explaination.

2x1 + x2 + x3 = 0,

x2 - x3 = 0,

x1 + x2 = 0.

This system has

No Explaination.

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The inverse Laplace transform of 1/(s^{2} + s) is

**A. ** 1 + et
**B. ** 1 - et

**C. ** 1 - e-t

**D. ** 1 + e-t

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x_{1} and x_{2} respectively. Then the eigenvalues and eigenvectors of the matrix A^{2 }− 3A + 4I would, respectively, be

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

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Consider the set of all functions f : {0,1,...,2014} → {0,1...,2014} such that f (f (i)) = i for 0 ≤ i ≤ 2014. Consider the following statements.

**A. ** P, Q and R are true

**B. ** Only Q and R are true

**C. ** Only P and Q are true

**D. ** Only R is true

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

**Explaination / Solution: **

No Explaination.

P. For each such function it must be the case that for every i, f(i) = i,

Q. For each such function it must be the case that for some i,f(i) = i,

R. Each such function must be onto.

Which one of the following is CORRECT?

No Explaination.

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A hard disk has 63 sectors per track, 10 platters each with 2 recording surfaces and 1000 cylinders. The address of a sector is given as a triple〈c, h, s〉, where c is the cylinder number, h is the surface number and s is the sector number. Thus, the 0th sector is addressed as 〈 0, 0, 0〉 , the 1st sector as 〈 0, 0, 1〉 and so on.

The address of 1039No Explaination.

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You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

**A. ** 1/4

**B. ** 1/3

**C. ** 1/2

**D. ** 2/3

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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