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NIMCET 2018 #1151
$$ \frac{d^{2}x}{dy^{2}} \; = \; ? $$

$ (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 #1152
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 #1153
The function  is
NIMCET 2018 #1154
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 #1155
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 #1156
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 #1157
The quadratic equation whose roots are  is
NIMCET 2018 #1158
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 #1159
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 #1160
If A is an invertible skew-symmetric matrix, then  is a
NIMCET 2018 #1161
If the mean of the squares of first n natural numbers be 11, then n is equal to?
NIMCET 2018 #1162
The set of points, where $f(x)=\frac{x}{1+|x|}$  is differentiable in 
NIMCET 2018 #1163
 is equal to

NIMCET 2018 #1164
Let be defined by . Find 
NIMCET 2018 #1165
The slope of two-lines $6x^2-xy-2y^2=0$ differ by
NIMCET 2018 #1166
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 #1167
The point of intersection os circle $x^2+y^2+10x-12y+51=0$ and the line $3y+x=3$ is
NIMCET 2018 #1168
The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is
NIMCET 2018 #1169
In an acute-angled ΔABC the least value of secA+secB+secC is
NIMCET 2018 #1170
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 #1171
If  then the value of  is
NIMCET 2018 #1172
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 #1173
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 #1174
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 #1175
The area enclosed between the curves  and  is
NIMCET 2018 #1176
Equation of the line perpendicular to x-2y=1 and passing through (1,1) is
NIMCET 2018 #1177
If   and , then f(A)=

NIMCET 2018 #1178
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 #1179
Which of the following function is the inverse of itself?
NIMCET 2018 #1180
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 #1181
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 #1182
If A and B are two events and , the A and B are two events which are
NIMCET 2018 #1183
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 #1184
If a, b, c are the roots of the equation , then the value of  is
NIMCET 2018 #1185
The coefficient of  in the expansion of is
NIMCET 2018 #1186
Let  and  be the roots f the equation  and  are the roots of the equation , then the value of r,
NIMCET 2018 #1187
How many natural numbers smaller than  can be formed using the digits 1 and 2 only?
NIMCET 2018 #1188
If  and , then the value of  is


NIMCET 2018 #1189
Differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ to
NIMCET 2018 #1190
 is continuous for
NIMCET 2018 #1191
If , and  are unit vectors, then  does not exceeds
NIMCET 2018 #1192
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 ?
NIMCET 2018 #1193
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 #1194
The value of  is
NIMCET 2018 #1195
If , then value of 
NIMCET 2018 #1196
In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of  equal to?

NIMCET 2018 #1197
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 #1198
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 #1199
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 ?