CSIR NET Mathematics Mock Test - 1 - CSIR NET Mathematics MCQ

Let the four consecutive odd numbers be

Then,

Smallest number

So, distance between C and D = 180 – ( 50 + 50 + 35) = 45 km

The speed of light in a vacuum c = 3 x 10⁸ m/s For crown glass Refractive index (n) = 1.5

Nitrous oxide is commonly known as laughing gas or nitrous. It is a chemical compound and an oxide of nitrogen with the formula N₂O . At room temperature, it is a colourless non-flammable gas, with a slight metallic scent and taste.

Required percentage

= 60%

Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.

In the 10th inning, he scored 100 runs then average became (x+8). And he scored (x+8)*10 runs in 10 innings.

Now,

⇒ 9x + 100 = 10 x (x + 8)

or 9x + 100 = 10x + 80

or x = 100 - 80

or x = 20

New average = (x + 8)

= 28 runs

The pattern of the given series is as follows-

10 × 1.5 + 1.5 = 16.5

16.5 × 2 + 3 = 36

36 × 2.5 + 6 = 96

96 × 3 + 12 = 300

300 × 3.5 + 24 = 1074

Left and right letters of each term are consecutive consonants while middle letter is consecutive vowel.

128 = (2 × 2) × (2 × 2) × (2 × 2) × 2

So, we have to multiply by 2 so that it becomes a perfect square

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

Minimize (total cost) = 3x₁ + 5x₂ Subject to the constraints

x₁ + x₂ = 200, x₁ ≤ 80, x₂ ≥ 60 x₁ ≥ 0 and x₂ ≥ 0

Drawing the lines x₁ + x₂ = 200, x₁ = 80 and x₂ = 60 on a graph sheet, we get the following figure:

It may be observed from the adjoining figure that the given problem has no feasible solution space (shaded area) but has only one feasible point with its co-ordinates x₁ = 80 and x₂ = 120 

Hence the optimal solution is to mix 80 kg of ingredients X₁ and 120 Kg of ingredients X₂ to have a minimum cost of Rs. 840 .

Dy

Then is:

But

(two values)

Given diff. Eqn.

and

We know that,

Difference of two Sets:

Let A and B be two sets. The difference of A and B is denoted as (A - B).

It is the set of all those elements of A which are not present in B i.e and .

The Venn diagram representation of the difference between the two sets is shown below:

Given:

is a prime natural number,

is a prime natural number,

The value is .

The required no. of elements is

There are three cases: -

Case-1 All flavours are different. Then

Case AII Flavours are same

Case Two Flawomrs are same and one is different

Combinations

Matrix with each element as unity is one

Here f(x) = sin_nx is an odd function

f'(x) = cos_nx, which is an even function

We know that,

Continuity of a function:

We say f(x) is continuous at x = c if:

Differentiability of a function:

A function f(x) is differentiable at a point x = a, in its domain if its derivative is continuous at a.

 This means that f′(a) must exist, or equivalently:

To check the continuity,

∴ The function is continuous at x = 0

Therefore, the function can be differentiable or not differentiable.

To check the differentiability,

And

By Milne's Method

By induction on n.

for n = 2, 2 is a prime number

for n = 3, 3 is a prime number

for n = 4, 4 is the product of 2.

Assume this holds every integer k, 1 < k < n.

If n is not a prime, there is 1 < d < n : d/n

⇒ n = cd for some 1 <c<n, each c and d are

prime or product of prime, thus n is a product of

prime.

The right hand limit

The left hand limit

∴ The function f (x) is not differentiable at
x = 0

product of the roots of the polynomial is -1 and it is a monic polynomial. If it has a root whose modulus is greater than one then it must have a root whose modulus is less than one which gives a contradicton. So it has roots 1 or -1. Since one root is -1 and product of the roots is -1 then it has a root -1. So 1 is true and 4 is false.

All of above

Hence option D is correct.

This sequence is bounded and Cauchy but not convergent in Q

Hence option D is correct.