Let $\frac{\sin(\theta-\alpha)}{\sin(\theta-\beta)}=\frac{a}{b},\ \frac{\cos(\theta-\alpha)}{\cos(\theta-\beta)}=\frac{c}{d}$. Then the value of $\cos(\alpha-\beta)$ equals

1

The equation $|x|+\left|\frac{x}{x-1}\right|=\frac{x^2}{|x-1|}$ will be always true for $x$, belonging to

Topic: AMU MCA 2018

2

Let $0

Topic: AMU MCA 2018

3

The distance of point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ with the plane $x-y+z=5$…

Topic: AMU MCA 2018

4

The area bounded by the curve $y=\begin{cases} x^{1/\ln x}, & x\ne1 \ e, & x=1 \end{cases}$ and $y=|x-e|$ is

Topic: AMU MCA 2018

5

If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$, then $\sin x$ is equal to

Topic: AMU MCA 2018

6

If $\lim_{x\to0}|x|^{[\cos x]}=l$, where $[.]$ denotes the greatest integer function, then the value of $l$ is

Topic: AMU MCA 2018

7

The unit vector which is orthogonal to the vector $\hat{i}+\hat{j}+\hat{k}$ and is coplanar with vectors $\hat{i}+2\hat…

Topic: AMU MCA 2018

8

Let $\alpha_n$ be the $n$th term of an AP, whose first term is $a$ and common difference is $d$. If for some positive i…

Topic: AMU MCA 2018

9

Area of one loop formed by $|y|=|\sin x|$ is

Topic: AMU MCA 2018

10

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

1

If $R$ is the set of real numbers and $f:R\to R$ is a function defined by $f(x)=\sin x$, then $f^{-1}([-1,1])$ is

Topic: AMU MCA 2018

2

If $A=\left[\matrix{k&l\cr m&n}\right]$ and $kn\ne lm$, then the value of $A^2-(k+n)A+(kn-lm)I$ equals

Topic: AMU MCA 2018

3

If $a,b,c$ are the integers between $1$ and $9$ and $a51,\ b41,\ c31$ are three-digit numbers and the value of determin…

Topic: AMU MCA 2018

4

If $\int_{0}^{\infty}[3e^{-x}],dx=l$, where $[.]$ denotes the greatest integer function, then the value of $l$ is

Topic: AMU MCA 2018

5

If $A$ and $B$ are disjoint sets, then $B\cap A'$ where $A'$ is complement of $A$ is equal to

Topic: AMU MCA 2018

6

Which of the following is an incorrect statement?

Topic: AMU MCA 2018

7

The angle between the line $x-2y+z=0=x+2y-2z$ and the plane $5x-2y-z+17=0$ is

Topic: AMU MCA 2018