BISE Multan · Class 11 · Mathematics · 2026 · First Annual · Group 1 · New course

$(AB{)}^{\mathrm{\prime }}=$ _____ .

If ${\displaystyle \frac{3x}{(x-1)(x+2)}}={\displaystyle \frac{1}{x-1}}+{\displaystyle \frac{B}{x+2}}$, then $B=$ _____ .

If $5,5+\sqrt{2},5+2\sqrt{2},\dots$ is A.P, then its $4$th term will be:

If ${\displaystyle \frac{1}{3}},{\displaystyle \frac{1}{k+1}},{\displaystyle \frac{1}{11}}$ are in H.P., then $k=$ _____ .

$5\times {}^4{P}_4=$ _____ .

$5$ persons can be seated at a round table in how many ways?

If $(x-2)$ is a factor of $a{x}^2-12x+4$, then $a=$ _____ .

Distance between $(3,8)$ and $(5,6)$ is:

$\sin ({\displaystyle \frac{7\pi }{2}}+\theta )=$ _____ .

$f(x)=\cos x$ is an _____ function.

${\displaystyle \underset{x\to 0}{\lim }{e}^{1\mathrm{/}x}=}$ _____ , where $x<0$

If $f(x)=(x+1{)}^5$, then $f^{\mathrm{\prime }}(0)=$ _____ .

${\displaystyle \frac{1}{2\sqrt{x}}}$ is the derivative of _____ .

The projection of $6\underset{‾}{i}+2\underset{‾}{j}+\underset{‾}{k}$ along $\underset{‾}{i}$ is:

If $\alpha ,\beta$ and $\gamma$ are directional angles of a vector $\underset{‾}{u}$, then ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =$ _____ .

If $z=\sqrt{2}+i\sqrt{2}$, then $\mathrm{\mid }z\mathrm{\mid }=$ _____ .

If $\omega$ is a cube root of unity, then $1+{\omega }^6+{\omega }^{12}=$ _____ .

If each side of a cube has length $1m$, what will be its surface area?

The vertex of the parabola $f(x)=5x^2$ is:

What is the value of '$x$' if $\mid \begin{array}{cc}3& 2\\ x& 4\end{array}\mid =2$?

Separate into real and imaginary parts ${\displaystyle \frac{2-7i}{4+5i}}$

If $z_1=4+5i$ anc $z_2=\alpha -2i$, find real values of $\alpha$ such that $\mathrm{Re}(z_1{z}_2)=20$

Factorize $z^2-2iz-1$

Evaluate ${\left({\displaystyle \frac{-1+\sqrt{-3}}{2}}\right)}^7+{\left({\displaystyle \frac{-1-\sqrt{-3}}{2}}\right)}^7$

Given that $f(x)=\sqrt{2x+3}$, find $f(x-2)$

Find the domain and the range of the function $g(x)=5-x$

Solve the absolute value equation $\mathrm{\mid }{x}^2+1\mathrm{\mid }=5$

Solve ${\displaystyle \frac{x}{x+1}}+{\displaystyle \frac{x+1}{x}}={\displaystyle \frac{5}{2}}$; $x\mathrm{\ne }0$, $x\mathrm{\ne }-1$

If $A=[a_{ij}{]}_{3\times 4}$, then show that $I_{3}A=A$

Without expansion, show that $\left[\begin{array}{ccc}\mathrm{\ell }& m+n& 1\\ m& n+\mathrm{\ell }& 1\\ n& \mathrm{\ell }+m& 1\end{array}\right]=0$

If '$A$' is a square matrix of order '$3$' then show that $\mathrm{\mid }kA\mathrm{\mid }=k^3\mathrm{\mid }A\mathrm{\mid }$

Resolve ${\displaystyle \frac{7x+25}{(x+3)(x+4)}}$ into partial fractions.

Write down the first three terms of the sequence $a_{n+1}=4a_n-7$ and $a_1=3$

Which term of the A.P. $3,8,13,$ ----- is $123$?

Find $S_n$ for arithmetic series $a_1=40$, $n=20$, $d=-3$

Find G.M. between $-2i$ and $8i$.

Write $n(n-1)(n-2)\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}(n-r+1)$ in the factorial form.

In how many ways can $8$ keys be arranged in a circular key ring?

If ${}^{3n}{C}_2:{}^n{C}_2=15:1$, find $n$.

Use the remainder theorem to find the remainder when $x^3+5x^2+6$ is divided by $x+1$

When the polynomial $x^3+x^2+x+k$ is divided by $x+1$ the remainder is $7$. Find the value of $k$.

Prove that $\sin ({180}^{\circ }+\alpha )\sin ({90}^{\circ }-\alpha )=-\sin \alpha \cos \alpha$

Prove that $\sin ({45}^{\circ }+\alpha )={\displaystyle \frac{1}{\sqrt{2}}}(\sin \alpha +\cos \alpha )$

Express $\sin 5x+\sin 7x$ as a product.

Find the period of $6-4\cot ({\displaystyle \frac{7x}{4}}+{\displaystyle \frac{\pi }{4}})$

Find the maximum and minimum value of ${\displaystyle \frac{1}{7+3\cos (-2x)}}$

Evaluate $\underset{x\to 2}{<mrow><mi>L</mi><mi>i</mi><mi>m</mi></mrow>}\left({\displaystyle \frac{x^3-8}{x^2-5x+6}}\right)$

Evaluate $\underset{x\to 0}{<mrow><mi>L</mi><mi>i</mi><mi>m</mi></mrow>}{\displaystyle \frac{1-\cos 2x}{x^2}}$

Find the limit of the sequence $a_n={\displaystyle \frac{2n+3}{n+1}}$

Differentiate $y={\displaystyle \frac{3}{4}}{x}^4+{\displaystyle \frac{2}{3}}{x}^3+{\displaystyle \frac{1}{2}}{x}^2+2x+5$ w.r.t. $x$

Find the derivative of $y=(x^2+5)(x^3+7)$ w.r.t. $x$

Write steps to find derivative by definition.

The position of a car after $t$ hours is given by $s(t)=2t^3-3t^2+t$ (in kilometres) Find the average velocity over the interval $[1,4]$

Find $t$, so that $\mathrm{\mid }2\underset{‾}{i}+(t-1)\underset{‾}{j}+t\underset{‾}{k}\mathrm{\mid }=\sqrt{13}$

Find the direction cosines of $\underset{‾}{v}=4\underset{‾}{i}+2\underset{‾}{j}-5\underset{‾}{k}$

Find a real number $\alpha$, so that the vectors $\underset{‾}{u}=\alpha \underset{‾}{i}+2\alpha \underset{‾}{j}-\underset{‾}{k}$ and $\underset{‾}{v}=\underset{‾}{i}+\alpha \underset{‾}{j}+3\underset{‾}{k}$ are perpendicular.

If $\underset{‾}{u}=2\underset{‾}{i}-\underset{‾}{j}+\underset{‾}{k}$ and $\underset{‾}{v}=4\underset{‾}{i}+2\underset{‾}{j}-\underset{‾}{k}$, then find $\underset{‾}{u}\times \underset{‾}{v}$.

Find the square root of complex number $5+12i$

Solve the equation ${\displaystyle \frac{a}{ax-1}}+{\displaystyle \frac{b}{bx-1}}=a+b$; $x\mathrm{\ne }{\displaystyle \frac{1}{a}},{\displaystyle \frac{1}{b}}$

Solve the following systems of linear equations by Cramer's rule: $\begin{array}{rl}{\displaystyle 2x+y-z}& {\displaystyle =1}\\ {\displaystyle x-y+2z}& {\displaystyle =3}\\ {\displaystyle 3x+2y+z}& {\displaystyle =4}\end{array}\}$

Resolve ${\displaystyle \frac{2x^2+3x+3}{(x+1)(x^2+1)}}$ into partial fractions.

For what value of $n$, ${\displaystyle \frac{a^n+b^n}{a^{n+1}+b^{n+1}}}$ is the positive geometric mean between $a$ and $b$?

In how many ways can $8$ different books including $2$ on English be arranged on a shelf in such a way that the English books are never together?

If $\alpha ,\beta ,\gamma$ are the angles of $\mathrm{△}ABC$, prove that $\tan \alpha +\tan \beta +\tan \gamma =\tan \alpha \tan \beta \tan \gamma$

Find the values of $m$ and $n$, so that the function $f(x)=\{\begin{array}{ll}mx,& x<3,\\ n,& x=3,\\ -2x+9,& x>3\end{array}$ is continuous at $x=3$

Find the Co-ordinates of point of tangency and the equation of the tangent line for $f(x)=x^3-2x+1$ at $x=1$

If $\underset{‾}{a}+\underset{‾}{b}+\underset{‾}{c}=\underset{‾}{0}$, then prove that $\underset{‾}{a}\times \underset{‾}{b}=\underset{‾}{b}\times \underset{‾}{c}=\underset{‾}{c}\times \underset{‾}{a}$