NIMCET 2018 Previous Year Question Paper and Solution with PDF

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Previous Year Questions
NIMCET

NIMCET Previous Year Questions (PYQs)

The function

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 5NIMCET PYQ 2018

Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer than 20 minutes for the other. What is the probability that they meet?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 6NIMCET PYQ 2018

Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that

is divisible by 3 is,

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 7NIMCET PYQ 2018

A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a prize. The probability that they will not win a prize in a single trial is :

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

The total number of ways in which numbers can be choosed =25 x 25=625 The number of ways in which either players can choose same numbers = 25

Probability that they win a prize = 25/625 = 1/25

Thus, the probability that they will not win a prize in a single trial = 1 - 1/25 = 24/25

Qus : 8NIMCET PYQ 2018

The quadratic equation whose roots are

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 9NIMCET PYQ 2018

Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 10NIMCET PYQ 2018

Suppose that m and n are fixed numbers such that the mth term am is equal to n and nth term an is equal to m, (m≠n), the the value of (m+n)th term is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 11NIMCET PYQ 2018

If A is an invertible skew-symmetric matrix, then

is a

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 12NIMCET PYQ 2018

If the mean of the squares of first n natural numbers be 11, then n is equal to?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 13NIMCET PYQ 2018

The set of points, where

is differential in

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 14NIMCET PYQ 2018

is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 15NIMCET PYQ 2018

Let

be defined by

. Find

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 16NIMCET PYQ 2018

The slope of two-lines

differ by

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 17NIMCET PYQ 2018

If the radius of the circle changes at the rate of

, at what rate does the circle's area change when the radius is 10m?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 18NIMCET PYQ 2018

The point of intersection os circle

and the line

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 19NIMCET PYQ 2018

The number of solutions of the equation sinx + sin5x = sin3x lying in the interval

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 20NIMCET PYQ 2018

In an acute-angled ΔABC the least value of secA+secB+secC is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 21NIMCET PYQ 2018

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 22NIMCET PYQ 2018

then the value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 23NIMCET PYQ 2018

The circles whose equations are

and

will touch one another externally, if

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 24NIMCET PYQ 2018

The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where p≠q is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Straight Line

Qus : 25NIMCET PYQ 2018

Equation of the common tangents with a positive slope to the circle

and

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 26NIMCET PYQ 2018

The area enclosed between the curves

and

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 27NIMCET PYQ 2018

Equation of the line perpendicular to x-2y=1 and passing through (1,1) is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 28NIMCET PYQ 2018

and

, then f(A)=

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 29NIMCET PYQ 2018

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

First off all select 5 boxes out 6 boxes in which 5 big ball can fit then arrange these ball in these 5 boxes and then put remaining 4 ball in any remaining box.

So Ans is [(6C5)5!](4!) = 6!4! = 17280

Qus : 30NIMCET PYQ 2018

Which of the following function is the inverse of itself?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 31NIMCET PYQ 2018

A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 32NIMCET PYQ 2018

In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business. 8 students like both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 33NIMCET PYQ 2018

If A and B are two events and

, the A and B are two events which are

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 34NIMCET PYQ 2018

are positive real numbers whose product is a fixed number c, then the minimum of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 35NIMCET PYQ 2018

If a, b, c are the roots of the equation

, then the value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 36NIMCET PYQ 2018

The coefficient of

in the expansion of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 37NIMCET PYQ 2018

Let

and

be the roots f the equation

and

are the roots of the equation

, then the value of r,

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 38NIMCET PYQ 2018

How many natural numbers smaller than

can be formed using the digits 1 and 2 only?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 39NIMCET PYQ 2018

and

, then the value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 40NIMCET PYQ 2018

Differential coefficient of

with respect to

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 41NIMCET PYQ 2018

is continuous for

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 42NIMCET PYQ 2018

and

are unit vectors, then

does not exceeds

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 43NIMCET PYQ 2018

The vector

lies in the plane of the vector

and

and bisects the angle between

and

. Then which of the following gives possible values of

and

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 44NIMCET PYQ 2018

A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 45NIMCET PYQ 2018

The value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 46NIMCET PYQ 2018

, then value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 47NIMCET PYQ 2018

In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of

equal to?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 48NIMCET PYQ 2018

Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 49NIMCET PYQ 2018

A line passing through P(4, 2) meets the x and y-axis at P and Q respectively. If O is the origin, then the locus of the centre of the circumcircle of ΔOPQ is -

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 50NIMCET PYQ 2018

Let n be the number of different 5 digit numbers, divisible by 4 that can be formed with the digits 1,2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n ?

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

We have to make 5 digit no. And also divisible by 4 using digits (1,2,3,4,5,6) To be divisible by 4 last two digit of 5 digits no should be divisible by 4 so we choose last two digits st they are divisible by 4 and rest with remaining four digits. Last two digits only can be 12,16,24,32,36,52,56,64 as all are divisible by 4. So total no of ways= no ways of choosing first 3 digits* no ways of choosing last two digits Total= (4*3*2)*(8) =192

Abhijeet Kushwaha

Qus : 51NIMCET PYQ 2018

A cube is made up of 125 one cm. square cubes placed on a table. How many squares are visible only on three sides?

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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

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