NIMCET 2013 Previous Year Question Paper and Solution with PDF

NIMCET Previous Year Questions (PYQs) – 2013 – Page 1 of 12

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Previous Year Questions

Qus : 1

A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & - 2 & 4 \end{matrix}]

and

6 A^{- 1} = A^{2} + c A + d I

, where

A^{- 1}

is A- inverse, I is the identify matrix, then (c, d) is

Video Solution Discussion

Qus : 2

Let

\vec{a} = \hat{j} - \hat{k}

and

\vec{c} = \hat{i} - \hat{j} - \hat{k}

. Then the vector

\vec{b}

satisfying

(\vec{a} \times \vec{b}) + \vec{c} = 0

and

\vec{a} . \vec{b} = 3

Video Solution Discussion

Qus : 3

Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240 elements respectively, given that each pair of sets has 15 elements in common. Each triple of sets has 3 elements in common and

A \cap B \cap C \cap D = ϕ

Video Solution Discussion

Qus : 4

If the straight line ax + by + c = 0 always passes through (1, –2), then a, b, c are in

Video Solution Discussion

Qus : 5

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is

Video Solution Discussion

Qus : 6

I_{n} = \int_{0}^{π / 4} t a n^{n} θ d θ

, then

I_{8} + I_{6}

equals

Video Solution Discussion

Qus : 7

Let

Δ A B C

be a triangle whose area is

10 \sqrt{3}

units with side lengths

| A B | = 8

units and

| A C | = 5

units. Find possible values of the angle A

Video Solution Discussion

Qus : 8

Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C – 2 times in 3 attempts. They fire a volley. The probability that the target is hit at least two times. Is

Video Solution Discussion

Qus : 9

The value of the integral

\int_{0}^{π / 2} \frac{\sqrt{s i n x}}{\sqrt{s i n x} + \sqrt{c o s x}} d x

Video Solution Discussion

Qus : 10

ω

is a cube root of unity, then find the value of determinant

| \begin{matrix} 1 + ω & ω^{2} & - ω \\ 1 + ω^{2} & ω & - ω^{2} \\ ω^{2} + ω & ω & - ω^{2} \end{matrix} |

Video Solution Discussion

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