BISE Multan · Class 11 · Mathematics · 2025 · Second Annual · Group 2

${}^n{C}_0=:$

An algebraic expression consisting of two terms is called:

The value of $\sin \left(\frac{7\pi }{2}\right)$ is:

$\cos {315}^{\circ }=:$

$\sin \theta =:$

The domain of $\sin x$ is:

The area of the triangle $ABC$ with $b=4$, $c=2$, $\alpha ={30}^{\circ }$ is:

$r_3=:$

The reference angle of $\cos x=\frac{1}{2}$ is:

${\cos }^{-1}\left(\frac{-1}{2}\right)=:$

$\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}$ is the Polar representation of:

If ‘$n$’ is prime number then $\sqrt{n}$ is:

If $a,b\in G$ then $(ab{)}^{-1}=:$

$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ is adjoint of Matrix:

$\mid \begin{array}{ccc}1& 2& 3x\\ 2& 3& 6x\\ 3& 5& 9x\end{array}\mid =:$

The value of $(1+\omega -{\omega }^2)(1-\omega +{\omega }^2)$ is:

The solution of $x^2-y^2=5$ is:

An equation which is true for all values of variable is called:

With usual notation $A\times H=:$

H.M between $a$ & $b$ is:

Simplify: $(0,3)(0,5)$

Factorize: $9a^2+16b^2$

Write down the power set of $\{a,\{b,c\}\}$.

Give the definitions of Tautology and Absurdity.

Define Rank of Matrix. Give one example.

Solve the system of Linear equations $\begin{array}{r}3x-5y=1\\ -2x+y=-3\end{array}$

If $A=\left[\begin{array}{ccc}1& -1& 2\\ 0& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}2& 3& 0\\ 1& 2& -1\end{array}\right]$ then show that $(A+B{)}^t=A^t+B^t$

If $A=\left[\begin{array}{cc}2& 1\\ 6& 3\end{array}\right]$ then find $A^{-1}$

Evaluate: $(-1+\sqrt{-3}{)}^5+(-1-\sqrt{-3}{)}^5$

Solve the equation $x^3+x^2+x+1=0$

Find the numerical value of $k$ if the polynomial $x^3+k{x}^2-7x+6$ has remainder of $-4$, when divided by $(x+2)$.

Define Reciprocal Equation.

Differentiate between proper and improper rational fractions.

Resolve into partial fraction $\frac{1}{x^2-1}$

Define irreducible quadratic factor.

How many terms of the series $-7+(-5)+(-3)+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}$ amount to $65$?

Find the $5^{th}$ term of G.P $3,6,12,\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}$

Insert three G.M's between $1$ and $16$.

Define geometric progression.

Find the probability of an event that does not occur.

Define impossible and certain events.

Evaluate ${}^{20}{C}_{17}$.

Show that $n!>2^n-1$ for integral values of $n\ge 4$.

Expand in descending powers of $x$ for $(x^2+x-1{)}^3$.

What is sexagesimal system of measurement of angles?

Find $\theta$ when $\mathrm{\ell }=1.5cm$, $r=2.5cm$

Find $x$, if ${\tan }^2{45}^{\circ }-{\cos }^2{60}^{\circ }=x\sin {45}^{\circ }\cos {45}^{\circ }\tan {60}^{\circ }$

State fundamental law of trigonometry.

If $\alpha ,\beta ,\gamma$ are the angles of a triangle $ABC$, then prove that $\tan (\alpha +\beta )+\tan \gamma =0$.

Prove that $\cot \alpha -\tan \alpha =2\cot 2\alpha$

Find period of $\mathrm{cosec}\theta$.

At the top of a cliff $80m$ high, the angle of depression of a boat is ${12}^{\circ }$. How far is the boat from the cliff?

With usual notation, prove that $\sin \frac{\alpha }{2}=\sqrt{\frac{(s-b)(s-c)}{bc}}$ where $s=\frac{a+b+c}{2}$

Find area of the triangle $ABC$, in which $a=18$, $b=24$, $c=30$

Prove that $(r_1+r_2)\tan \frac{\gamma }{2}=c$

Show that $\cos (2{\sin }^{-1}x)=1-2x^2$

Find the solutions of $\sec x=-2$ which lie in $[0,2\pi ]$

Find the rank of $\left[\begin{array}{cccc}1& -1& 2& 1\\ 2& -6& 5& 1\\ 3& 5& 4& -3\end{array}\right]$

Use synthetic division to find the value of $p$ and $q$ if $x+1$ and $x-2$ are the factors of $x^3+p{x}^2+qx+6$.

Resolve $\frac{x^2-2x+3}{x^4+x^2+1}$ into partial fractions.

If $A,G,H$ are arithmetic geometric and harmonic means then show that $A>G>H$ if $a,b$ are any distinct positive real numbers and $G=\sqrt{ab}$

Find the values of $n$ and $r$ when ${}^{n-1}{C}_{r-1}:{}^n{C}_r:{}^{n+1}{C}_{r+1}=3:6:11$.

If $x$ is so small that its square and higher powers can be neglected, then show that $\frac{\sqrt{4+x}}{(1-3{)}^3}\approx 2+\frac{25}{4}x$

If $\cot \theta =\frac{15}{8}$ and the terminal arm of the angle is not in quard – $I$, find the values of $\cos \theta$ and $\mathrm{cosec}\theta$.

Express the following as a product of $\cos A+\cos 3A+\cos 5A+\cos 7A$.

Prove that in an equilateral triangle $r:R:r_1=1:2:3$

Prove that ${\sin }^{-1}\frac{1}{\sqrt{5}}+{\cot }^{-1}3=\frac{\pi }{4}$