A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area $C^2$. Then the locus of the middle point of the line is

1

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

2

If $ A=\left(\matrix{0&1&2\cr 1&2&3\cr 3&\alpha&1}\right) $, $ A^{-1}=\left(\matrix{\frac{1}{2}&-\frac{1}{2}&\frac{1}{…

Topic: AMU MCA 2018

3

A region in the $xy$-plane is bounded by the curve $y=\sqrt{25-x^2}$ and the line $y=0$. If the point $(a,a+1)$ lies in…

Topic: AMU MCA 2018

4

If four whole numbers taken at random are multiplied together, then the probability that the last digit in the product …

Topic: AMU MCA 2018

5

The graph $y^2+2xy+50|x|=625$ divides the plane into regions. Then, the area of bounded regions is

Topic: AMU MCA 2018

6

If $g(x)=x^2+x-2$ and $\frac{1}{2}(g \circ f)(x)=2x^2-5x+2$, then $f(x)$ is equal to

Topic: AMU MCA 2018

7

Let $R$ and $S$ be any two equivalence relations on a set $X$. Then which of the following is incorrect statement

Topic: AMU MCA 2018

8

The image of the point $ (1, -1, 1) $ in the plane $ x - 2y + 3z + 1 = 0 $ is

Topic: AMU MCA 2018

9

The shortest distance between the parabolas $ 2y^2 = 2x - 1 $, $ 2x^2 = 2y - 1 $ is

Topic: AMU MCA 2018

10

Let $ f(x) = x^3 + x $, then the equation $ \frac{2}{y - f(2)} + \frac{3}{y - f(3)} + \frac{4}{y - f(4)} = 0 $ has

Topic: AMU MCA 2018

1

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

2

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

3

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

4

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

5

The solution of the differential equation $\frac{dy}{dx}=\frac{2xy-y^2}{2xy-x^2}$ is

Topic: AMU MCA 2018

6

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

7

The solution of the inequality $|x^2-4x|

Topic: AMU MCA 2018

8

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

9

The coefficient of $x^{53}$ in the expansion $\sum_{m=0}^{100} {^{100}C_m}(x-3)^{100-m}\cdot2^m$ is

Topic: AMU MCA 2018

10

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