CSIR NET Mathematics Mock Test - 10 - CSIR NET Mathematics MCQ

The median of six numbers:

Formative evaluation helps students in the following ways:

• It provides constant feedback to both teacher and student concerning learning successes and failure while instruction is in process.
• It often happens during the course of instruction. Teacher clarifies the doubts of students in the class itself.
• Feedback to candidates reinforces successful learning and locates the particular learning errors that need correction.
• The teacher raises learner’s motivation through a question-answer session.

The objective of Research is to makes accurate use of concepts. The Research can also be done to find out the hidden truth. The Research’s objective should be highly focused and feasible.

The Hungarian brothers, Laszlo and George Biro, made the first ball point pen in 1894. It followed the first workable fountain pen which was invented by L.E. Waterman in 1884.

Since the U - 238 is an unstable atomic nucleus. The nucleus has an even number of protons and neutrons then that nucleus will be stable.

After splitting into two identical parts it produced two stable nuclei because both have an even number of protons and neutrons.

Indian rivers can be divided into West flowing (Arabian Sea) rivers and East flowing (Bay of Bengal). Chenab river does nor flow into the Arabian Sea.

Stronger intermolecular force in solid Explanation: In solids, the particles are arranged in a regular pattern, touching each other. They attract each other with a strong force (because they are so small and so close). This means that they cannot change places. So solids cannot change its shape.

P + Q → P is the father of is brother of R R - S → R is mother of S

Q is maternal uncle of S

Two liquids of densities 3 kg upon metre cube and 4 kg per metre cube.
Let mass of liquid 1 be "m" and mass of liquid 2 be "m"
Formula: Density
Volume of liquid 1,
Volume of liquid 2,
After mixing two liquid
Volume of mixture is
Mass of mixture would be
Let density of mixture be
Thus,

Lagrange's subsidiary equation are

First and second,

First and third,

Let is zero polynomial

And fix

for

unique

So (1), (3) and (4) options are incorrect

So choice ( 2 ) is answer

Real unitary matrix :

A^T = A^–1 ⇒ AA^T = AA^–1 = I.

And

Here

∴ A is Skew-Hermitian.

Option A is correct answer.

v = e^–t u

Hence option A is correct.

Is attained at a boundary point of Δ

Hence option D is correct.

If A² = I, then A is diagonalisable over real numbers

Hence option B is correct.

A has 4 distinct eigenvalues

Hence option C is correct.

Let,

A Volterra's integral equation of second kind.

Trick [No. of element - no. of L. I condition = dimension
Now
. No. of element of
No of L.I condition of
so dim

Since the set of rational number is countable, it is Lebesgue measurable and its Lebesgue outer measure is equal to zero.

The integrand is negative in the interval [0, 1] and we, therefore, consider

The integrand is proper if , in as much as the integrand, in that caseand accordingly 0, is not a point of infinite discontinuity in this case.
Let so that we have now to examine the convergence at 0. Let m be a positive number such that

We have,

so that E being a given positive number,

for values of x, sufficiently near 0.

Now, the integral of converges at 0 if and

only if .
It is possible to choose a number such that

if and only if .
Thus the integral converges if

When n = 0, the integrand becomes .
We have,

which this integral converges to infinity as .
When n < 0 we have,

so that in this case also the integral does not converge.

Thus, the given integral converges if and only if n > 0

Since D is a closed set, it contains all its points of closure, and , a complement of closed set is open, therefore, is a open set.

The hazard function is an increasing function for some α

According to given question

Option (D) i.e There exist an unbounded open subset B of C and an entire function f such that ∂(f (B)) ⊆ f (∂B) is true .