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NIMCET 2018 #1
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$$
\frac{d^{2}x}{dy^{2}} \; = \; ?
$$
$
(a) -\left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1}\left(\dfrac{dy}{dx}\right)^{-3}
$
$ (b) \left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-2}
$
$
(c) -\left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-3}
$
$
(d) \left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1}
$
NIMCET 2018 #2
If $\lim_{x\to\infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2$ then the values of a and b are:
NIMCET 2018 #3
NIMCET 2018 #4
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?
NIMCET 2018 #5
Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that $a^3+b^2+c^2-3abc$ is divisible by 3 is,
NIMCET 2018 #6
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 :
NIMCET 2018 #7
NIMCET 2018 #8
Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?
NIMCET 2018 #9
Suppose that m and n are fixed numbers such that the mth term of an HP is equal to n and the nth term is equal to m, (m ≠ n). Then the (m + n)th term is:
NIMCET 2018 #10
NIMCET 2018 #11
NIMCET 2018 #12
NIMCET 2018 #13
NIMCET 2018 #14
. Find 
NIMCET 2018 #15
NIMCET 2018 #16
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?
NIMCET 2018 #17
NIMCET 2018 #18
The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is
NIMCET 2018 #19
NIMCET 2018 #20
Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and
$Q = \{\theta : \sin\theta + \cos\theta = \sqrt{2}\sin\theta \}$ be two sets.
Then
NIMCET 2018 #21
isNIMCET 2018 #22
The circles whose equations are $x^2+y^2+c^2=2ax$ and $x^2+y^2+x^2-2by=0$ will touch one another externally, if
NIMCET 2018 #23
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
NIMCET 2018 #24
Equation of the common tangents with a positive slope to the circle $x^2+y^2-8x=0$ and$\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ is
NIMCET 2018 #25
isNIMCET 2018 #26
NIMCET 2018 #27
, then f(A)=NIMCET 2018 #28
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
NIMCET 2018 #29
NIMCET 2018 #30
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?
NIMCET 2018 #31
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
NIMCET 2018 #32
NIMCET 2018 #33
If $a_1, a_2,...a_n$ are positive real numbers whose product is a fixed number c, then the minimum of $a_1, a_2, ....2a_n$ is
NIMCET 2018 #34
isNIMCET 2018 #35
isNIMCET 2018 #36
be the roots f the equation 
and 
are the roots of the equation 
, then the value of r,NIMCET 2018 #37
NIMCET 2018 #38
, then the value of 
isNIMCET 2018 #39
NIMCET 2018 #40
NIMCET 2018 #41
does not exceedsNIMCET 2018 #42
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 
?
and and bisects the angle between and . Then which of the following gives possible values of and ?NIMCET 2018 #43
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?
NIMCET 2018 #44
NIMCET 2018 #45
NIMCET 2018 #46
NIMCET 2018 #47
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
NIMCET 2018 #48
A line passing through (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 -
NIMCET 2018 #49
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 ?