CSIR NET Mathematics Mock Test - 3 - CSIR NET Mathematics MCQ

Number of runs made by running between the wickets

Required percentage

When any teacher wants to clarify the basics and concepts about a particular topic then they use instructional aids.

Research is an investigation which comprises creative work undertaken on a systematic and logical basis to increase the stock of knowledge, culture and society. It deals with the verification of hypothesis, data analysis, interpretation and formation of principles and by using this stock of knowledge (research) new applications are being devised. Research is also an intellectual enquiry towards truth.

=Rs. 1380

We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5,75 divided 34 gives remainder 7 and so on.

[Number Multiplied]

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder We can use any one of negative or positive remainder at any time.

Required remainder

Acetylene is used to generate light, to weld metals. Oxygen and Acetylene are the gases used to produce the welding flame. The flame will only melt the metal. A flux is used during welting to prevent oxidations and to remove impurities. Metals 2mm to 50mm thick are welded by gas welding.

There are two main types of coalmine explosions: methane and coal dust. Methane explosions occur when a buildup of methane gas contacts a heat source and there is not enough air to dilute the gas level below its explosion point.

Ratio of wages = (8 × 7) : (5 × 9) = 56 : 45

The Lagrange's subsidiary equations are

First and fourth,

First and second,

First and third,

The appropriate mathematical formulation of the given problem as L.P. model is

Maximize

Subject to

The value of objective function at each of these extreme points is as follows:

The optimal value of the objective function:

The maximum value of the objective function Z = 1,01,000 occurs at the extreme point Hence, optimal solution to the given L.P. problem is Max.

The Lagrange auxiliary equation is

By (2) and (3) fraction of (1), we get

(2)

By first and IInd fraction of (1), we get

It is bounded as at

So choice (C) is answer.

D is Answer

So it is not closed w. r. t. vector addition

So it is not closed under scalar multiplication

Let defined by

is one to one and range of

So is not onto

So choice (1) is not true

Now if we define

Range of contains only irrationals

So choice (2) are not true

Let

So Choice (C) is Answer

Given is continuous and
Let
is continuous and

is satisfies it
Now, we check options

Choice (3) & (4) options are not true


Also, from options (1) & (2) one of them is true

So choice ( 2 ) is answer

Then the matrix A is

Involutory matrix : A² = I

Transformation does not alter the rank of matrix.

 is bounded and also is monotone sequence

V₁ and V₃ are open sets in R²

Hence option B is correct.

4

Hence option C is correct.

The given D. E. is

since

(i) is continuous function over the given interval

(ii) is bounded over the given interval

So there exists a solution of the problem

Now

where max

Thus the largest interval is

Let

Since has real roots both less than 3 .

Therefore, and

For

and also ;

or

Combining both the conditions we get as the required condition.

So V is not subspace of R²

Let x be a point of closure of [a, b], then for every δ > 0, there is y ∈ [a, b], such that |x – y| < δ.

A closed interval [a, b] is closed set if it contains all its points of closure, i.e., x ∈ [a, b].

On the contrary, let x ∉ [a, b]

Choose δ = min {b – y, y – a}, for every y ∈ [a, b],

Such that |x – y| < δ, x ∈ [a, b], which is the contradiction.

Thus x ∈ [a, b].

⇒ [a, b] contains all its closure points.

⇒ [a, b] is a closed set.

Suppose S is bounded. If T is an infinite subset of S, then T is bounded (since S is bounded set) and hence by Bolzano-Weierstrass theorem there is atleast one point which is also an accumulation point of T and x is also accumulation point of S.

Since S is closed, therefore, . Which proves the given statement.

(i) at
(ii)
(iii)

(a) has jump at
(b) has discontinuity of first kind.
(c) Measure of discontinuity is 2

If β > 1 then f is a constant function

Option C is correct answer.