CSIR NET Mathematical Science Mock Test - 9 - UGC NET MCQ

Let the number of girls be x.

∴ Number of boys = 2x 

Total number of students = x + 2x = 3x 

135 = 3x

Number of girls = 45

Number of boys = 45 x 2 = 90 

Number of girls who failed in the examination = 45 x 1/3 = 15 

Number of boys who failed in the examination = 90 x 1/6 = 15 

Total number of students who failed in the examination = 15 + 15 = 30 

Percentage of students who failed in the examination = 30/135 x 100 = 22.22%

∴ Percentage of students who passed the examination = (100 - 22.22)% = 77.8% 

So named because it resists (or inhibits) the flow of current.

The British Geological Survey reports that as of 2005, Kodarma district in Jharkhand state in India had the largest deposits of mica in the world.

Lara > Smith > Waqar > Warner

As Anjali is the sister of Vishal, Vishal is the son of Manoj. Manoj and Rohit are brothers because both are the sons of Rakesh. It means Rohit is the paternal uncle of Vishal and Anjali.

Here, in the diagram the starting point (shown as point P) and (end point shown as point Q). So, with respect to the starting point Lokesh is in the west direction.

Freezing point of alcohol is −115⁰C while freezing point of mercury is −39⁰C Hence, to measure below −39⁰C alcohol thermometer is used.

In a leap year the no. of days = 366
∴ No. of weeks = 52 weeks + 2 days
∴ No. of Saturdays and Sundays.
= 52 × 2 + 2
= 104 + 2
= 106

Given

Compare it with

We get

in the second and fourth quadrants

Given

By given condition

If are intersect then

Which is not possible

So are never intersect

Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}.

Then, Cardinality of set S = |S| which is 5.

Consider the polynomial

If is odd, and has a root, then there must exist a real number with the property .

To prove this, we assume that the set of contains only integers and If not, we can easily multiply the values to make the assumption true. This means that is continuous over the set of real numbers.

Also, the limit of as goes to either infinty or minus infinity.

This means and have the same sign at extreme values of but since is odd, must have opposite signs for and

So there must be real values of with the property and

The Intermediate Value Theorem states that there must be a real number on the interval with the property .

Where f and g are twice differentiable functions

Taking x- axis as the zero potential energy level, the potential energy of bend is

⇒ Series is convergent

(bounded below)
(bounded above)
is bounded sequence

{(1, 0, 1), (0, 1, 0)}

Option A is correct answer.

3/8

Hence option A is correct.

Given differential equation 

Integrating both sides of the given differential equation, we get

The required integral equation

If A is a set containing ‘n’ elements, then number of subset of B=2ⁿ

Then, number of subset of a set of 6 elements is 2⁶

So choice (4) is answer

Let cos is a harmonic function

Then

Now

A. Sup R = + ∝

B. Inf R = – ∝

C. + ∝, – ∝ ∈ R

For each x ∈ X there is a function f_x in L such that fx(x) < h(x) + ε/3.
since and are continuous, there is an open set containing such that

Hence for all in Now since the sets cover , and by compactness there are a finite number of them, say which cover X. Let
Then and given we may choose so that  hence

The first term of the sequence

Second term of the sequence

Third term of the sequence

Fourth term of the sequence

The th term of the sequence

Ans (B) States 1, 2, 3, 4 are recurrent and state 5 is transient

All of the options