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

1

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

2

The value of $ \sin(2\sin^{-1} 0.8) $ is

Topic: AMU MCA 2018

3

Let * be a binary operation on the set $R$ of real numbers defined by $ a * b = \frac{3ab}{7} $, then the identity elem…

Topic: AMU MCA 2018

4

Which statement is true for the line $\frac{x - 4}{8} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and plane having intercepts …

Topic: AMU MCA 2018

5

The function $(x^2 - 9)|x^2 - 7x + 12| + \cos(|x|)$ is not differentiable at

Topic: AMU MCA 2018

1

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

Topic: AMU MCA 2018

2

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

3

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

4

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

Topic: AMU MCA 2018

5

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

Topic: AMU MCA 2018

6

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

7

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

8

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

9

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

10

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