CSIR NET Mathematical Science Mock Test - 7 - UGC NET MCQ
30 Questions MCQ Test CSIR NET Exam Mock Test Series 2025 - CSIR NET Mathematical Science Mock Test - 7
In an examination 80% candidates passed in English and 85% candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what per cent of candidates failed in both the subjects?
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
Direction: In this question a series given with one number missing. Choose the correct alternative from the given ones that will complete the series.
X50Z, T42V, P34R, L26N,____.
In a class of 52 students the number of boys is two less than the number of girls. Average weight of the boys is 42 kg. while the average weight of all the 52 students is 40 kg Approximately what is the average weight of the girls?
Average age of seven persons in a group is 30 years, the average age of five persons of this group is 31 years. What is the average age of the other two persons in the group?
If an article is sold for a gain of 7% instead of selling it at a loss of 13%, a trader gets Rs.1080 more. What is the selling price of the article, when the article is sold at a profit of 25%?
A shopkeeper expects a gain of 20 % on his cost price. If in a week his sale is of Rs. 540, then what is his profit?
is-
Let w be the wronskian of two linearly independent solutions of ODE 
Then for all t, there exist a constant 
such that w(t)
If A is Skew-Hermitian matrix, then iA is—
A is Skew-Hermitian 
is Hermitian.If A is a square matrix, and A2 = A, then A is—
Let In be an Identity matrix of order n, then—
is—
If A is a singular matrix, then its characteristic root are—
If A and B are Symmetric matrices, then AB are Symmetric iff—
is—
,
is
If W1 and W2 are subspaces of vector space v and W1 is the subspace spanned by vectors α1, ....., αn If α1 ,........αn ,∈ W2 then
are scalar
such that 
for all 
Then
is invertible function with self-inverse, hence 
is both one 
one and ontoLet 
and 
be two linearly independent solutions of the differential equation 
satisfying 
and 
Then the
wronskian of 
and 
at 
i. e. 
is equal to
where 
where 
Interval
we have
and 
and 
which contradicts the statement that 
and 
are distinct. Thus, the sequence 
have atmost one limit.Let 〈Fn〉 is a sequence of measurable functions (on the some domain).
is a measurable function and in then inf gk is a measurable function too and so 
is also measurable.If f is bounded and measurable on closed interval [a, b]
(A) 
(B) 
exist for almost all 
(C) 
almost everywhere in [a, b]
(D) 
almost everywhere in [a, b]
is of bounded variation, then so 
exist for almost all x in [a, b]
such that 
, set
almost everywhere
almost everywhere in [a, b]
almost everywhere in [a, b]Given collection C of open intervals of the form 
If 〈 fn 〉 is a sequence of mappings of a countable set D into a metric space Y such that for each x ∈ D the closure of the set {fn(x) : 0 ≤ n < ∞} is compact.
By the sequential compactness of the closure of 
we can pick a subsequence 
of 
such that 
converges. Choose a subsequence 
of 
such that 
converges. Continuing this, we obtain a subsequence 
convergent on 
. Consider the 'diagonal' sequence 
a subsequence of 
and 
converges.Consider the quadratic forms q and p given by—
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