For what value of $\alpha$ the vectors $2\mathbf{i} + \alpha\mathbf{j} + 5\mathbf{k}$ and $3\mathbf{i} + \mathbf{j} + 2\mathbf{k}$ are orthogonal?

How many 4 digit numbers can be formed using digits $0, 2, 3, 4$, if each number starts from 2?

The distance between lines $2x-5y+13=0$ and $4x-10y+12=0$ is;

What is the sum of $1-x+x^2-x^3+...$? where $|x|\ge1$

If $f(x)=\frac{1}{x}$, find $f^{-1}(1)=?$

The relation $r=\{(0, 3), (1, 5), (2, 7), (3, 9)\}$ is generated by:

Find $K$ so that one root of $2Kx^2-20x+21=0$ exceeds the order by 2.

The number of diagonals of 12-sides polygon is;

If $y=\tan^{-1}(\sec{x}-\tan{x})$; then $\frac{dy}{dx}$ is equal to

If first term of an H.P is $\frac{1}{3}$ and third term is $-1$, then $a_6=?$

The derivative of $2x^3$, with respect $ln{x^2}$ is;

The locus of the points in the plane satisfying the equation $|Z-1|=4$ is:

What is the coefficient of $a^2b^2$ in the expansion $(a+b)^4$?

Which of the following is true about universal set:

How many two digit numbers leaves remainder 1. when divided by 5?

The product of slopes of lines represented by $x^2-xy-y^2=0$ is;

The numbers $(a-b)^2, a^2+b^2, (a+b)^2$ are in

The sum of squares of two conjugate complex numbers is always:

If A is subset of B then B is super set of A, this condition holds for which option?

$\lim_{x \to 0} {\frac{e^{\tan{x}-1}}{10^x}}=?$

The equation of the line through the intersection of $x-y-4=0$ and $7x+y+2=0$ is;

$[\mathbf{i} \,\,\, \mathbf{j} \,\,\, \mathbf{k}]$

The line $mx+y+1=0$ is tangent to parabola $y^2=-6x$ if

$2\cos{45^o}\cos{15^o}=$?

$\int e^x (1 + \tan{x} + \tan^2{x}) \, dx=?$

The equation of tangent to conic $x^2+5xy-4y^2+4=0$, at $y=-1$

$\sin({\tan^{-1}(-1)})=?$

If $f(x) = \begin{cases} 1 - mx & \text{if } x < 1 \\ x^2 & \text{if } x \ge 1 \end{cases}$ is continuous at $x=1$, then $m=?$

$1+2+3+4+5+....+100$

$\sum_{t=4}^{10} (2 - t)=?$

The sum of three cube roots of $-125$ is;

The value of $(\frac{-1-\sqrt{3}i}{-1-\sqrt{3}i})^8$

The transform $5x^2-6xy+5y^2-8=0$, in to ellipse $4x^2+y^2=4$ angle required.

$f(x)=x+1, g(x)=x^2$, then $fog(0)=?$

The middle term in the expansion of $(\frac{a}{x}+\frac{x}{a})^{10}$ is;

Which one could be solution of $\tan{\theta}=-\frac{\sqrt{3}}{3}?$

The range of $\sin{x}-3\cos{x}$ is;

The length of latus-rectum of parabola $2x^2-4x-8y+9$

$\tan{2\beta}+\sec{2\beta}$=?

Find two numbers whose A.M is 34 and G.M is 16;

The value of $\lim_{x \to y} {\frac{\sin{x}-\sin{y}}{x^3-y^3}}=?$

For what value of $x$ the polynomial $x^2-4x$ equal to zero?

The polynomial function $y=2+x+3x^2+8x^3$ has ________ values;

The point on the parabola $(x-2)^2=3(y+3)$ closest foci;

A force $3\mathbf{i} + 2\mathbf{j} -4\mathbf{k}$ is applied at the point $(1, -1, 2)$ then moment about $(2, -1, 3)$ is;

The domain of $y=\tan{x} +\cos{x}$ is;

Find the number of triangles which can be formed by joining the angular points of 8 sides as vertices;

The area enclosed by the curve $y=\sin{x}$, from $x=0 \, to \, x=\frac{\pi}{2}$ is;

Two air planes leave a field at same time. One flies $30^o$ East of North at 60 km/h the other $60^o$ East of South at 80 km/h. How far apart are they at the end of two hours?

The expansion $\frac{1}{4-x}$ is valid if,

If $X {\begin{pmatrix} 5 & 2 \\ -2 & 1 \end{pmatrix}}={\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}}$, the matrix X is;

The $n^{th}$ term of sequence $0,1,0,1,0,1,0,...$ can be written as;

The equation of hyperbola whose foci are $(0, \pm \sqrt{65})$ and $e=\frac{\sqrt{65}}{4}$, is;

Which one is feasible solution of $2x+y \ge 2$?

If $y^3-2xy^2+x^2y+3x=0$, then $\frac{dy}{dx}=?$

The differential equation $ydy+xdx=0$ represents, family of;

For what value of $K$; $7,K,\frac{1}{7}$ are in G.P?

The Period of $-\cos(2x-1)$

The circles $x^2+y^2+2x-2y-7=0$ and $x^2+y^2-6x+4y+9=0$

The centroid of triangle with vertices $A(3, 1), B(-2, -4), C(1, 1)$

$\tan{\frac{\alpha}{2}}=?$

The point of inflection of in the graph of $f(x)=1-x^3$ is

The product of distances from the foci of $\frac{x^2}{128}-\frac{y^2}{18}=1$ any tangent to it is;

The rank of matrix $\begin{bmatrix} 0 & 1 & 0 & 4 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{bmatrix}$ is;

If $f(x)=\cos{x}$ for all $x$, then the average value of on interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$

For what value of $k$, the $(2, k)$ lies below the line $2x+y-6=0$?

The reciprocal of the complex number $\cos{\theta}-i\sin{\theta}$ is;

Using Binomial theorem, the approximate value of $(9.9)^3$ is;

The eccentricity of conic $xy=4$ is;

The equation of normal to $x^2=16y$ at $(8, 4)$ is;

$\int_{0}^{3} |x-1| \, dx=?$

The truth value of the statement "if a triangle has four angles then Lahore is capital of Pakistan" is:

Choose proper fraction

Two dice are thrown simultaneously, what is the probability that the sum of numbers of top is 5

Which of the following is true?

Two excavators dig $10m^3$ of each in first day $15m^3$ in second day, $20m^3$ in the third day and so on, how much they will both dig by the $9^{th}$ day?

$171.888^o =$?

$lx^2+mx+c=0$ only has one root if;

An ellipse has major axis along y-axis then its equation is;