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General Questions Set 6:

Quiz Mode

AB = 2i^, PQ = -3i^. AB⃗ + PQ⃗ = XY⃗ = ____.

-1i^

1i^

-1j^

1j^

Solution:

Which of the following physical quantities is a vector?

Time

Distance

Mass

Force

Solution:

The analytic function f(z) = (z-1)/(z^2+1) has singularities at

1 and -i

i and -i

1 and -1

1 and 1

Solution:

If a matrix A is symmetric, then which of the following statements is true?

A^T = A

|A| = 0

A^T = -A

A^-1 = 0

Solution:

The system of linear equations 4x + 2y = 7 and 2x + y = 6 has:

no solution

an infinite number of solutions

exactly two distinct solutions

a unique solution

Solution:

The solution of the differential equation x.y' + y = x^3 with the condition y(1) = 3/4 is

y = x^3/3 + 1/x

y = x^4/4 + 1/x

y = x^3/4 + 1/(2x)

y = x^3/4 + 1/2

Solution:

The numerator of a fraction increases by 25%. What can be said about the resultant fraction?

It is 67% less than original

It depends on the number

The change cannot be determined

It is 25% more than original fraction

Solution:

Salesman A shows 2 Silk Sarees and 4 Cotton Sarees, while Salesman B shows 4 Silk Sarees and 5 Cotton Sarees to a customer. The customer buys a saree from both the salesmen. Find the probability that both the sarees are Cotton Sarees.

8/27

10/27

4/27

6/27

Solution:

Bag A contains 5 white balls and 4 black balls, and bag B contains 7 white balls and 9 black balls. A random ball is transferred from bag A to bag B, and then a ball is drawn from bag B. Find the probability that the drawn ball is white.

1/4

4/9

67/153

63/151

Solution:

As the radius of the circular region over which the maximum value of a 3D plane is to be found is increased, what happens to the maximum and minimum values?

Maximum value is invariant

Maximum value decreases

Maximum value increases and minimum value goes lesser

Minimum value goes higher

General Questions Set 6:

AB = 2i^, PQ = -3i^. AB⃗ + PQ⃗ = XY⃗ = ____.

Solution:

Which of the following physical quantities is a vector?

Solution:

The analytic function f(z) = (z-1)/(z^2+1) has singularities at

Solution:

If a matrix A is symmetric, then which of the following statements is true?

Solution:

The system of linear equations 4x + 2y = 7 and 2x + y = 6 has:

Solution:

The solution of the differential equation x.y' + y = x^3 with the condition y(1) = 3/4 is

Solution:

The numerator of a fraction increases by 25%. What can be said about the resultant fraction?

Solution:

Salesman A shows 2 Silk Sarees and 4 Cotton Sarees, while Salesman B shows 4 Silk Sarees and 5 Cotton Sarees to a customer. The customer buys a saree from both the salesmen. Find the probability that both the sarees are Cotton Sarees.

Solution:

Bag A contains 5 white balls and 4 black balls, and bag B contains 7 white balls and 9 black balls. A random ball is transferred from bag A to bag B, and then a ball is drawn from bag B. Find the probability that the drawn ball is white.

Solution:

As the radius of the circular region over which the maximum value of a 3D plane is to be found is increased, what happens to the maximum and minimum values?

Solution:

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