CSIR NET Mathematical Science Mock Test - 8 - UGC NET MCQ

Let the cost price be Rsx 

S.P. of

New C.P. = 80% of

New gain 40%,

New S.P. of

Therefore, x = 250 

Cost price of the article = Rs250

The steps which are required to design a questionnaire includes the aim of the study i.e. writing primary and secondary aims of the study, to prepare a draft of questionnaire in which number of questions will be asked related to the topic, review the literature so as to frame the relevant questions and revision of the draft for making it error free.

Exploratory Research is to gain familiarity with a phenomenon or achieve new insights into it. Explanatory Research is the research whose primary purpose is to explain or elaborate on how the events are occur to build, elaborate or extend. Applied Research is a research phenomenon which tries to add the basics of a discipline by eliminating the theory. Variable research is not a type of research. So, option D is correct.

The best example of changing into electric energy from chemical energy is primary cells or batteries, the dry cell is also made up in this phenomenon.

Pattern is-

8 × 3 + 3 = 27

27 × 5 + 6 = 141

141 × 7 + 9 = 996

996 × 9 + 12 = 8976

Pattern is-

6 + 6² = 42

42 + 11² = 163

163 + 16² = 419

419 + 21² = 860

Father of my son’s father -> Radhika’s Father in law

Radhika 's Father-in-law brother -> Radhika 's Uncle

Let the cost price = 100

Marked Price = Rs 125

To gain 10 %, Selling Price = Rs 110

Required Discount Percentage = (125 − 110)/125 × 100 = 12%

Expansion of the product
(a₁ + a₂ + a₃) (b₁ + b₂ + b₃ + b₄) (c₁ + c₂ + c₃ + c₄ + c₅)
No. of terms = 3, 4, 5
∴ Product of terms = 3 × 4 × 5 = 60

Given:

Put

and

becomes,

Integrating both sides, we get:

If and then

If m > n

Then no. of on-to-functions are

Now, here m = 4, n = 3

Then no, of onto functions are

Power set P ({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Therefore, P({0, 1, 2}) = {null, {0}, {1}, {2}, {0, 1}, {0,2}, {1, 2}, {0, 1, 2}}.

Let

Let

Where θ is Argument of z

So polar form

i

So B is Answer

The given curves are and .

Solving the equations, we get,

,

A^–1 exist ⇔ A is non-singular ⇔ |A| ≠ 0.

is bounded

is bounded.

The level of significance

Option C is correct answer.

Let

Given, U is a harmonic function

Treating z and as independent variable and

is harmonic function. Then

Let

Thus the set of all limit point of

So, choice ( 1 ) is answer

Let
Now





is a subspace

A – B = {x : x ∈ A and x ∉ B}

= {x : x ∈ A and x ∈ Bc}

= A ∩ B^c

Since B is closed set, its complement Bc is open set.

∴ A – B is open set, because intersection of

two open sets is open set.

B – A = {x : x ∈ B and x ∉ A}

= {x : x ∈ B and x ∈ A^c}

= B ∩ A^c

Since A is closed, Ac is open and intersection

of two closed sets is closed, i.e., B – A is closed.

Let A be any set. Then (a, ∞) is Lebesgue measurable if

If m ∗ A = ∞ it is proved. If m ∗ A < ∞ , then given ε > 0, there is a countable collection { I_n} of open intervals, which covers A and for which


Thus


Hence (a, ∞) is measurable.

Let E = {x : f(x) ≠ g(x)} the functions f = g almost everywhere, we have mE = 0, and so {x : g(x) > α} = [{x : f(x) > α} ∪ {x ∈ E : g(x) > α}] ~ {x ∈ E : g(x) ≤ α}

Here {x : f(x) > α} is a measurable set since f is a measurable function.

The sets {x : f(x) > α} and {x ∈ E : g(x) ≤ α} are subsets of E and mE = 0 so they are measurable. Thus {x : g(x) > α} is measurable for each α and so g is measurable.

Ans (D)

is a consistent estimator of

This statement is true regarding given statement.

We can see that V has dimension 5 . Looking at the minimal polynomial of T, we find the Jordan canonical form for T must be

which implies (1) is true and (2) is false.

since we have naturally isomorphic to
Thus the induced operator on the quotient space is nilpotent, so (3) is true.
However, if we look at , the induced operator on has as its minimal polynomial which implies (4) is false. We can see this by considering the Jordan form of  (It's the lower right submatrix of the above matrix.) Alternatively, let Then If we let , then 
As we again have that (4) is false.

Both B and D

Option C is correct answer.