BISE Multan · Class 12 · Mathematics · 2026 · First Annual · Group 1

If $f(x)=\sqrt{x+5}$ then $f(-6)$ is:

${\mathrm{sech}}^{2}x=$

If $f(x)=(x^3+1{)}^6$ then $f^{\mathrm{\prime }}(-2)$ is:

${\displaystyle \frac{d}{dx}}(\sec x)$ at $x={\displaystyle \frac{\pi }{4}}$ is:

If $y=\sin x$ then:

The stationary values of $f(x)=x^2-x-2$ is:

${\displaystyle \frac{d}{dx}}\left({\cos }^{-1}{\displaystyle \frac{x}{a}}\right)=$

$\int (\cot x)dx=$

$\int (x^2+1)xdx=$

$\int \ln xdx=$

${\displaystyle {\int }_0^{\pi \mathrm{/}4}\cos xdx=}$

The slope of the line perpendicular to $3x-4y-3=0$ is:

The point of intersection of the three medians of a triangle is:

The point $(5,8)$ lies:

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

The equation of the tangent to the circle $x^2+y^2=25$ at $(5\cos \theta ,5\sin \theta )$ is:

The vertex of the parabola $y^2=-8(x-3)$ is:

The covertices of the ellipse ${\displaystyle \frac{x^2}{a^2}}+{\displaystyle \frac{y^2}{b^2}}=1$ with $b>a$:

The direction cosines of $\underset{‾}{v}=\underset{‾}{i}-3\underset{‾}{j}+4\underset{‾}{k}$ are:

The value of $3j\cdot k\times i$ is:

Define Identity Function. Give example.

Show that the equations $x=a\sec \theta$, $y=b\tan \theta$ represent the equation of hyperbola ${\displaystyle \frac{x^2}{a^2}}-{\displaystyle \frac{y^2}{b^2}}=1$

Let $f:R\to R$ be the function, $f(x)=2x+1$. Find $f^{-1}(-1)$

Evaluate ${\displaystyle \underset{x\to 2}{<mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow>}{\displaystyle \frac{\sqrt{x}-\sqrt{2}}{x-2}}}$

Express limit in term of '$e$' ${\displaystyle \underset{x\to \mathrm{\infty }}{<mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow>}{(1+{\displaystyle \frac{3}{x}})}^{2x}}$

Differentiate w.r. to '$x$' of ${\displaystyle \frac{x^2+1}{x^2-3}}$

Find ${\displaystyle \frac{dy}{dx}}$ if $y(x^2-1)=x\sqrt{x^2+4}$

Differentiate w.r. to variable involved, $x^2\sec 4x$

If $f(x)=<mi\; mathvariant="normal">\ell </mi><mi>n</mi>(x+\sqrt{x^2+1})$, what is $f^{\mathrm{\prime }}(x)$?

Calculate $y_2$, if $x^2+y^2+2gx+2fy+c=0$

Determine the intervals in which $f(x)$ is increasing or decreasing for the domain mentioned $f(x)=\sin x:x\in (-\pi ,\pi )$

The perimeter of a triangle is $20cm$. If one side is of length $8cm$, what are lengths of the other two sides for maximum area of triangle?

Find $dy$ in $y=\sqrt{x}$ when $x$ changes from $4$ to $4.41$.

Evaluate $\int x(\sqrt{x}+1)dx$, $(x>0)$

Evaluate $\int <mi\; mathvariant="normal">\ell </mi><mi>n</mi>xdx$

Find $\int x\cos xdx$

Evaluate $\int e^x(\cos x+\sin x)dx$

Evaluate ${\displaystyle {\int }_{\pi \mathrm{/}6}^{\pi \mathrm{/}3}\cos tdt}$

Solve the differential equation ${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{y}{x^2}}$, $(y>0)$

Find the midpoint of the line segment joining the two points $A(-8,3)$ and $B(2,-1)$

Find an equation of the line through $A(-6,5)$ having slope $7$.

Find the point of intersection of the lines. $x-2y+1=0$ and $2x-y+2=0$

Transform the equation $5x-12y+39=0$ into two-intercept form.

Check whether the point $(-7,6)$ lies above or below the line $4x+3y-9=0$

Graph the solution set of inequality $5x-4y\le 20$

Write the procedure for determining optimal solution.

Find the centre and radius of the circle $5x^2+5y^2+24x+36y+10=0$

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

Check the position of point $(5,6)$ with respect to circle $2x^2+2y^2+12x-8y+1=0$

Find vertex and directrix of the parabola $y^2=-8(x-3)$

Find the eccentricity of the hyperbola ${\displaystyle \frac{y^2}{16}}-{\displaystyle \frac{x^2}{49}}=1$

Find the vector from the point $A$ to the origin where $\overline{AB}=4\underset{‾}{i}-2\underset{‾}{j}$ and $B$ is the point $(-2,5)$

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

Determine whether the triple ${30}^{\circ }$, ${45}^{\circ }$, ${60}^{\circ }$ can be direction angle of the vector.

Find the angle between the vectors $\underset{‾}{u}=2\underset{‾}{i}-\underset{‾}{j}+\underset{‾}{k}$ and $\underset{‾}{v}=-\underset{‾}{i}+\underset{‾}{j}$

Find $\alpha$ so that vectors $\underset{‾}{u}=2\alpha \underset{‾}{i}+\underset{‾}{j}-\underset{‾}{k}$ and $\underset{‾}{v}=\underset{‾}{i}+\alpha \underset{‾}{j}+4\underset{‾}{k}$ are perpendicular.

If $\underset{‾}{a}\times \underset{‾}{b}=0$ and $\underset{‾}{a}\cdot \underset{‾}{b}=0$, what conclusion can be drawn about $\underset{‾}{a}$ or $\underset{‾}{b}$?

Evaluate the limit ${\displaystyle \underset{\theta \to 0}{<mrow><mi>L</mi><mi>i</mi><mi>m</mi></mrow>}{\displaystyle \frac{1-\cos p\theta }{1-\cos q\theta }}}$

Differentiate ${\displaystyle \frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}}$ w.r.t. "$x$"

If $x=\sin \theta$ and $y=sim(m\theta )$, show that $(1-x^2)y_2-x{y}_1+m^{2}y=0$

Evaluate $\int x^3{e}^{5x}dx$

Solve the differential equation $2x^{2}y{\displaystyle \frac{dy}{dx}}=x^2-1$

Maximize $f(x,y)=2x+5y$ subject to the constraints $2y-x\le 8$, $x-y\le 4$, $x\ge 0$, $y\ge 0$

Find equations of two parallel lines perpendicular to $2x-y+3=0$ and the product of $X$- and $Y$-intercepts of each is $3$.

Write equations of the tangents to the circle $x^2+y^2-4x+6y+9=0$ at the points on the circle whose ordinate is $-2$.

Find the centre, foci eccentricity and vertices of the given hyperbola $4y^2+12y-x^2+4x+1=0$

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