For any three sets $A, B$ and $C$ the set $(A \cup B \cup C)\cap (A \cap B' \cap C')' \cap C'$ is equal to

1

Let $P={\theta;\ \sin\theta - \cos\theta = \sqrt{2}\cos\theta}$ and $Q={\theta;\ \sin\theta + \cos\theta = \sqrt{2}\sin…

Topic: AMU MCA 2017

2

The function $f(x)=x-[x]$ where $[,]$ denotes the greatest integer function is

Topic: AMU MCA 2017

3

If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

Topic: AMU MCA 2017

4

The range of the function $f(x)=\frac{2+x}{2-x},\ x\ne2$ is

Topic: AMU MCA 2017

5

If $\sin(\alpha+\beta)=1,\ \sin(\alpha-\beta)=\frac{1}{2},\ \alpha,\beta\in\left[0,\frac{\pi}{2}\right]$ then the value…

Topic: AMU MCA 2017

6

Using the information from the figure, $\cos^{-1} x$ is equal to

Topic: AMU MCA 2017

7

Let $f(x)$ be a function defined by $f(x)=\begin{cases}4x-5,\ x\le2 \ x-\lambda,\ x>2 \end{cases}$ If $\lim_{x\to2} f(x…

Topic: AMU MCA 2017

8

The tangent of the angle between the lines whose intercepts on the axes are respectively $a,-b$ and $b,-a$ is

Topic: AMU MCA 2017

9

The equation of the circle whose radius is $5$ and which touches the circle $x^2+y^2-2x-4y-20=0$ externally at the poin…

Topic: AMU MCA 2017

10

The variance of $20$ observations is $5$. If each observation is multiplied by $2$, then the variance of the resulting …

Topic: AMU MCA 2017