BISE Multan · Class 12 · Mathematics · 2026 · First Annual · Group 2

If $f(x)=\sin x+\cos x$ then $f\left({\displaystyle \frac{\pi }{4}}\right)=$

If $f(x)={\displaystyle \frac{1}{x+3}}$, $x\mathrm{\ne }-3$ then range of $f^{-1}(x)$ is:

${\displaystyle \frac{d}{dx}}(\sqrt{x})=$

If $y=e^{-ax}$ then ${\displaystyle \frac{d^{3}y}{d{x}^3}}$ is:

${\displaystyle \frac{d}{dx}}({\coth }^{-1}x)$ is:

If $y=e^{3x}$ then $y_3$ is:

$\int \sin 5xdx=$

$\int {\displaystyle \frac{1}{x+2}}dx=$

$\int (x^2-1{)}^{1\mathrm{/}2}xdx=$

$\int {\displaystyle \frac{1}{2x-1}}dx=$

The slop of the line parallel to $3x+4y+7=0$ is:

The vertical line through $(-3,6)$ is:

The distance of the point $(3,-7)$ from $x$-axis is:

The solution of $x+2y<6$ is:

$x^2=4ay$ is the equation of:

In hyperbola ${\displaystyle \frac{x^2}{a^2}}-{\displaystyle \frac{y^2}{b^2}}=1$

An parabola $y^2=4ax$

If $\underset{‾}{a}$ & $\underset{‾}{b}$ have the opposite direction then $\underset{‾}{a}\cdot \underset{‾}{b}=$

If ${\displaystyle \frac{\underset{‾}{a}\cdot \underset{‾}{b}}{ab}}=-{\displaystyle \frac{1}{2}}$ then $\theta$ is:

For three coplaner vectors $\underset{‾}{a},\underset{‾}{b}$ & $\underset{‾}{c}$ $\underset{‾}{a}\cdot \underset{‾}{b}\times c=$

Define even and odd function.

Find domain and range of $f$, if $f(x)=\sqrt{x^2-9}$

Prove that $\cos h^{2}x-\sin h^{2}x=1$

Evaluate ${\displaystyle \underset{x\to 0}{<mrow><mi>L</mi><mi>i</mi><mi>m</mi></mrow>}{\displaystyle \frac{\sin x^{\circ }}{x}}}$

Express in term of $e$:- ${\displaystyle \underset{x\to +\mathrm{\infty }}{<mrow><mi>L</mi><mi>i</mi><mi>m</mi></mrow>}{(1-{\displaystyle \frac{1}{n}})}^n}$

Find $y_2$ if $y=\sin 3x$

Find ${\displaystyle \frac{dy}{dx}}$, if $y=(<mi\; mathvariant="normal">\ell </mi><mi>n</mi>\tan hx)$

Find $f^{\mathrm{\prime }}(x)$ if $f(x)=<mi\; mathvariant="normal">\ell </mi><mi>n</mi>(e^x+e^{-x})$

Differentiate $y=a^x$, w.r.t '$x$'

Find ${\displaystyle \frac{dy}{dx}}$ if $x=y\sin y$

Prove that ${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{1}{1+x^2}}$, if $y={\tan }^{-1}x$

Differentiate $x^4+2x^3+x^2$, w.r.t '$x$'

Using differentials, find ${\displaystyle \frac{dy}{dx}}$ if $xy+x=4$

Evaluate $\int {\displaystyle \frac{3x+2}{\sqrt{x}}}dx$

Evaluate $\int {\tan }^{2}xdx$

Evaluate $\int {\displaystyle \frac{x+2}{\sqrt{x+3}}}dx$

Evaluate the definite integral ${\displaystyle {\int }_1^2(x^2+1)dx}$

Find the area bounded by the curve $y=x^3+3x^2$ and the $x$-axis from $x=-3$ to $x=0$

Solve the differential equation ${\displaystyle \frac{dy}{dx}}=-y$

Find the point three fifth of the way along the line segment from $A(-5,8)$ to $B(5,3)$

The $xy$-coordinate axes are rotated about the origin through the indicated angle. The new axes are $OX$ and $OY$. Find the $XY$-coordinates of the point $P$ with the given $xy$-coordinates $P(5,3)$; $\theta ={45}^{\circ }$.

Check whether the two lines $2x+y-3=0$ and $4x+2y+5=0$ are parallel or perpendicular.

Show that the lines $4x-3y-8=0$, $3x-4y-6=0$ and $x-y-2=0$ are concurrent.

Find the pair of straight lines represented by $2x^2+3xy-5y^2=0$

Define the linear inequality.

Graph the solution set of the following linear inequality in $xy$-plane $2x+1\ge 0$

Find an equation of the circle with centre at $(5,-2)$ and radius $4$.

Find the centre and radius of the circle $x^2+y^2+12x-10y=0$

Determine whether the point $P(-5,6)$ lies outside, on or inside the circle $x^2+y^2+4x-6y-12=0$

Find the focus and vertex of the parabola $y^2=8x$

Find an equation of the ellipse with vertices $(0,\pm 5)$, eccentricity ${\displaystyle \frac{3}{5}}$

Find the sum of the vectors $\overline{AB}$ and $\overline{CD}$ given the four points $A(1,-1)$, $B(2,0)$, $C(-1,3)$ and $D(-2,2)$

Find a vector whose magnitude is $4$ and is parallel to $2\underset{‾}{i}-3\underset{‾}{j}+6\underset{‾}{k}$

Find the constant $a$ so that the vectors $\underset{‾}{v}=\underset{‾}{i}-3\underset{‾}{j}+4\underset{‾}{k}$ and $\underset{‾}{w}=a\underset{‾}{i}+9\underset{‾}{j}-12\underset{‾}{k}$ are parallel.

Calculate the projection of $\underset{‾}{a}$ along $\underset{‾}{b}$ when $\underset{‾}{a}=\underset{‾}{i}-\underset{‾}{k}$, $\underset{‾}{b}=\underset{‾}{j}+\underset{‾}{k}$

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

Find the value of $3\underset{‾}{j}.\underset{‾}{k}\times \underset{‾}{i}$

Discuss the continuity of $f(x)$ at $x=-2$ if $f(x)=\{\begin{array}{ll}3x& \text{if }x\le -2\\ x^2-1& \text{if }-2<x<2\\ 3& \text{if }x\ge 2\end{array}$

Differentiate ${\sec }^{-1}\left({\displaystyle \frac{x^2+1}{x^2-1}}\right)$ w.r.t. '$x$'

Differentiate $(<mi\; mathvariant="normal">\ell </mi><mi>n</mi>x{)}^x$ w.r.t. '$x$'

Evaluate $\int {\tan }^{3}x\sec xdx$

Find the area between the $x$-axis and the curve $y=\sqrt{2ax-x^2}$, where $a>0$

Minimize $z=3x+y$ subject to the constraints $3x+5y\ge 15$; $x+3y\ge 9$, $x\ge 0$; $y\ge 0$

Find the centre and radius of the circle with the equation $4x^2+4y^2-8x+12y-25=0$

By means of slopes, show that the points $A(4,-5)$, $B(7,5)$ and $C(10,15)$ lie on the same line.

Find the centre, foci, eccentricity and vertices of the ellipse. $x^2+16x+4y^2-16y+76=0$

Prove that by vector method $\sin (\alpha -\beta )=\sin \alpha \cos \beta -\cos \alpha \sin \beta$