The coefficient of $x^{53}$ in the expansion $\sum_{m=0}^{100} {^{100}C_m}(x-3)^{100-m}\cdot2^m$ is
Previous 10 Questions — AMU MCA 2018
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A five-digit number divisible by $3$ is to be formed using the numbers $0,1,3,4$ and $5$ without repetition. The total …
Topic: AMU MCA 2018
The solution of the inequality $|x^2-4x|
Topic: AMU MCA 2018
Consider the following relations in the real numbers
$R_1={(x,y)\mid x^2+y^2\leq25}$
$R_2={(x,y)\mid y\geq\frac{4x^2}…
Topic: AMU MCA 2018
The solution of the differential equation
$\frac{dy}{dx}=\frac{2xy-y^2}{2xy-x^2}$ is
Topic: AMU MCA 2018
A ray of light passing through the point $(1,2)$ reflects on the $X$-axis at point $A$ and the reflected ray passes thr…
Topic: AMU MCA 2018
Let $A$ be an event that a family has children of both sexes and $B$ be the event that the family has atmost one boy. I…
Topic: AMU MCA 2018
If both roots of the equation $x^2-2(a-1)x+(2a+1)=0$ are positive, where $a$ is a real number, then
Topic: AMU MCA 2018
Let $a_1,a_2,a_3,\ldots,a_n$ be in A.P. If
$\frac{1}{a_1a_n}+\frac{1}{a_2a_{n-1}}+\ldots+\frac{1}{a_na_1}=\frac{K}{a_1+…
Topic: AMU MCA 2018
A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area $C^2…
Topic: AMU MCA 2018
If $A_i\ (i=1,2,\ldots,n)$ are $n$ independent events, with $P(A_i)=1-\frac{1}{2^i}$, then the probability that atleast…
Topic: AMU MCA 2018
Next 10 Questions — AMU MCA 2018
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A fair coin is tossed $n$ times. Let the random variable $X$ denote the number of times the head occurs. If $P[X=1],\ P…
Topic: AMU MCA 2018
The minimum value of $z=2x_1+3x_2$ subject to the constraints
$2x_1+7x_2\geq22,\ x_1+x_2\geq6,\ 5x_1+x_2\geq10$ and $x_…
Topic: AMU MCA 2018
$y=a\cos(\log x)+b\sin(\log x)$ is a solution of the differential equation
Topic: AMU MCA 2018
The amplitude of the complex number $1+\sin\alpha-i\cos\alpha$ is
Topic: AMU MCA 2018
The points $z_1=x+iy$ and $z_2=\frac{1}{-x+iy}$ in the complex plane lie on
Topic: AMU MCA 2018
The area of the region defined by $||x|-|y||\leq1$ and $x^2+y^2\leq1$ in the $xy$-plane is
Topic: AMU MCA 2018
The solution set of the inequality
$\log_{\sin(\pi/3)}(x^2-3x+2)\geq2$ is
Topic: AMU MCA 2018
If $S$ and $S'$ are the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{26}=1$, and $P$ is any point on it then range of…
Topic: AMU MCA 2018
The length of perpendicular from the point $\hat{i}+2\hat{j}+3\hat{k}$ to the line
$\frac{x-6}{3}=\frac{y-7}{2}=\frac{z…
Topic: AMU MCA 2018
Area of one loop formed by $|y|=|\sin x|$ is
Topic: AMU MCA 2018
