BISE Multan · Class 11 · Mathematics · 2025 · First Annual · Group 1

The period of $\sin 3x$ is:

The greatest side of the triangle will be in front of the $\underset{‾}{}$.

If in triangle $\mathrm{\Delta }ABC$ $\alpha ={30}^{\circ }$, $\beta ={60}^{\circ }$ and $a=3$ then $b=\underset{‾}{}$

${\sin }^{-1}(1)+{\sin }^{-1}(-1)=\underset{‾}{}$

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

If $p$ is a prime number, then $\sqrt{p}$ is a $\underset{‾}{}$ number.

$(-i{)}^{17}$ is equal to:

The set of natural numbers is not a group under:

The rank of the matrix $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ is:

If $A$ is a square matrix of order $4\times 4$ then $\mathrm{\mid }kA\mathrm{\mid }=\underset{‾}{}$

A quadratic equation in $x$, $a{x}^2+bx+c=0$ with $a,b,c\in \mathbb{R}$ becomes linear if $a=\underset{‾}{}$

Three cube roots of $8$ are:

If $1=A(x+1)+B(x-1)$ then:

A sequence is a function whose domain is a subset of the set of $\underset{‾}{}$ numbers.

The sum upto ${10}^{th}$ term of the A.P, $-7+(-4)+(-1)+---$ is:

The factorial notation was introduced by Christian Kramp in $\underset{‾}{}$.

The number of terms in the expansion of $(a+x{)}^{11}$ are:

The area of the sector of circular region with radius $r$ is:

$\sin {98}^{\circ }=\underset{‾}{}$

The value of $\tan 4\theta \cos 4\theta$ is:

Find the multiplicative inverse of $(1,0)$.

Show that $\mathrm{\forall }{z}_1,z_2\in c$, $\overline{z_1\cdot z_2}=\overline{z_1}\cdot \overline{z_2}$

Give any two properties of binary operation $\dot{\times }$.

Define Groupoid and give an example.

If $A=\left[\begin{array}{cc}1& 2\\ a& b\end{array}\right]$ and $A^2=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$ then find the values of $a$ and $b$.

Define cofactor of an element.

Without expansion, verify that $\mid \begin{array}{ccc}\alpha & \beta +\gamma & 1\\ \beta & \gamma +\alpha & 1\\ \gamma & \alpha +\beta & 1\end{array}\mid =0$.

Define Skew-symmetric matrix.

Give the names of methods for finding the solution of quadratic equation.

Find three cube roots of unity.

State Remainder theorem.

Define Synthetic division.

Define improper fraction with an example.

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

Write only partial fraction form of $\frac{2x^4-3x^3-4x}{(x^3+2{)}^2(x+1{)}^2}$

Find $a_7$ in the sequence $2,6,11,17,\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}$

Which term of A.P $5,2,-1,\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}$ is $-85$?

Find A.M between $1-x+x^2$ and $1+x+x^2$

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

Evaluate ${}^{16}{P}_4$

How many arrangements of the letters of MATHEMATICS, taken all the worlds together?

Find $n$ if ${}^n{C}_5={}^n{C}_4$

Find fifth term in the expansion of ${(\frac{3}{2}x-\frac{1}{3x})}^{11}$

Expand upto three terms of $(4-3x{)}^{1\mathrm{/}2}$

Convert ${21.256}^{\circ }$ to $D^{\circ }{M}^{\mathrm{\prime }}{S}^{\mathrm{\prime }\mathrm{\prime }}$ form.

What is the length of the arc intercepted on a circle of radius $14cms$ by the arms of a central angle of ${45}^{\circ }$?

Prove that $\frac{\sin \theta }{1+\cos \theta }+\cot \theta =\mathrm{cosec}\theta$

Define allied angles.

If $\alpha ,\beta ,\gamma$ are angles of a triangle $ABC$, then prove that $\cos \left(\frac{\alpha +\beta }{2}\right)=\sin \frac{\gamma }{2}$

Prove that $1+\tan \alpha \cdot \tan 2\alpha =\sec 2\alpha$

Find the period of $\sin x$.

A kite flying at a height of $67.2m$ is attached to a fully stretched string inclined at an angle of ${55}^{\circ }$ to the horizontal. Find the length of the string.

State sine law of triangle.

Find the side $a$ in a triangle $ABC$ in which $b=95$, $c=34$, $\alpha ={52}^{\circ }$

Show that $r_2=S.\tan \frac{\beta }{2}$

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

Find the general solution of the equation $\sin x+\cos x=0$

Find the inverse of $A=\left[\begin{array}{ccc}2& 1& 0\\ 1& 1& 0\\ 2& -3& 5\end{array}\right]$

If $\alpha ,\beta$ are the roots of $5x^2-x-2=0$, form the equation whose roots are $\frac{3}{\alpha }$ and $\frac{3}{\beta }$

Resolve $\frac{x^2+1}{x^3+1}$ into partial fraction.

Find "$n$" so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ may be A.M between $a$ and $b$.

There are $10$ girls and $20$ boys in a class. Half of the boys and half of the girls have blue eyes. Find the probability that one student chosen as monitor in either a boy or has blue eyes.

Prove by mathematical induction $1^2+3^2+5^2\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}+(2n-1)=n\frac{(4n^2-1)}{3}$

If $\tan \theta =\frac{8}{15}$ and the terminal arm of the angle is in $III$ quadrant, find the values of the other trigonometric functions of $\theta$.

Prove the identity $\sqrt{\frac{1+\sin \alpha }{1-\sin \alpha }}=\frac{\sin \frac{\alpha }{2}+\cos \frac{\alpha }{2}}{\sin \frac{\alpha }{2}-\cos \frac{\alpha }{2}}$

Prove $r_1+r_2+r_3-r=4R$

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