CSIR NET Mathematics Mock Test - 4 - CSIR NET Mathematics MCQ
30 Questions MCQ Test - CSIR NET Mathematics Mock Test - 4
How many terms are there in 20, 25, 30......... 140
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Calculate the number of possible microstates when two particles are distributed in four states such that the resulting wave functions are anti-symmetric with respect to the exchange of the particle.
In which year of First World War Germany declared war on Russia and France?
If you save Rs. 1 today, Rs. 2 the next day, Rs. 3 the succeeding day and so on. What will be your total savings in 365 days?
A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
Cost of a dianond varies directly as the square of its weight. A diamond broke into four piece with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :
Seema purchased an item for Rs.9,600 and sold it for a loss of 5 percent. From that money she purchased another item and sold it for a gain of 5 percent. What is her overall gain/ loss?
A hemispherical bowl is being filled with water at a constant volumetric rate. The level of water in the bowl increases-
) is at every moment 
Area of cross section.
is increasing ( hemisphere), the rate of change of 
is decreasing ( while still being positive), so 
is growing slower than direct proportional to time.Let 
be a polynomial of degree 
, with 
. Then the initial value problem 
has always
is cube root of unity. Then 
is equal to
is cube root of unity
and 
Let 
is a group w, r. t. multiplication. Then identity of the group is
is the identity of the group G
Let 
form a fundamental set of solutions of
Where P(x) and q(x) are real valued continuous function on [a, b]. If 
, wih 
, are consecutive zeros of 
in (a, b), then
are linearly dependent Which is not true
is—
If B is the matrix obtained from A, by changing rows into columns and columns into row, then—
is convergent 
If the points x1, x2, …, xn are distinct, then for arbitrary real values y1, y2, …, yn the degree of the unique interpolating polynomial p(x) such that p(xi ) = yi (1 ≤ i ≤ n) is—
Amoebae are known to double in 3 min. Two identical vessels A and B, respectively contain one and two amoebae to start with. The vessel B gets filled in 3 hours. When will A get filled ?
Let f be a non constant entire function. Which of the following properties is possible for f for each z ∈ C?
Then, 
is entire (as 
is). Now
and given 
So 
is entire and bounded and hence constant. So 
is constant ,which contradicts. So, it is FALSE.
is bounded and entire and hence constant. So, it is FALSE.
. Then 
is bounded and entire and hence constant and so 
is constant. So, it is FALSE.
hence we can construct a unique Green's function.
which satisfies the boundary condition 
satisfies the boundary condition 
and 
at the point 
is
Let 
be family of curves with 
as 3 parameters (arbitrary) if 
is the solution of 
Then order of 
is
The collection C of open intervals of the form (1/n , 2/n ), n = 2 , 3,...... is an open
covering of the open interval (0, 1)
Let m be a countable additive measure defined on all sets in σ-algebra M.
and 
are mutually disjoint sets. By definition of countable additive measure, 
we have 
If f is an extended real-valued function whose domain is measurable. The following are equivalent, for each real number, α
(A) Set {x : f(x) > α} is measurable
(B) Set {x : f(x) ≥ α} is measurable
(C) Set {x : f(x) < α} is measurable
(D) Set {x : f(x) ≤ α} is measurable
then the value of 
:
For a bivariate data set (xi, yi), i = 1, 2, …, n, suppose the least squares regression lines are—
Equation 1: 5x – 8y + 14 = 0
Equation 2: 2x – 5y + 11 = 0
Then which of the following statements are true?
Let A and B be two disjoint nonempty subsets of R2 such that A ∪ B is open in R2. Then—
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