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Maths 12 Past Paper 2025 | Notely

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All Maths 12 papers

Class 12 · Past paper

Maths 12 past paper 2025

42 published questions in this index. The full practice view lets you work through them and track your own attempts.

19 MCQs23 written questionsPractise this paper

Question index

1
$\lim_{x \rightarrow \infty} \frac{(1+2x)^{2}-1}{x}=$
MCQ1 marksannual
1
Evaluate: $\lim_{\theta \rightarrow 0} \frac{1-\cos \theta}{\sin^{2} \theta}$
Part B4 marksannual
1
The growth of bacteria is given by the function of time ($t$) (in hours) $f(t)=500 e^{0.25 t}$, then find: **a.** Initial number of bacteria at $t=0$ **b.** Number of bacteria afte…
Part C8 marksannual
2
$\lim_{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{\frac{x}{2}}=$

This is a skimmable index, not a replacement for the study surface. Open the practice view to answer questions and use the linked study material.

MCQ1 marksannual

2

If $f(x, y)=3 x^{3}+7 x^{2} y+x y^{2}+5 y^{3}$, then find: **a.** Degree of homogeneous function **b.** Verify Euler's theorem for $f(x, y)$

Part B4 marksannual

3

$\frac{d}{dx}\left(e^{x}+2e^{-2x}\right)=$

MCQ1 marksannual

3

Find the value of '$k$' if $f(x)$ is continuous at $x=1$: $f(x)= \begin{cases}\frac{3 x^{2}-3}{x-1}, & x \neq 1 \\ 2(k-1) x, & x=1\end{cases}$

Part B4 marksannual

4

If $\frac{dy}{dx}=\frac{3}{2}x^{\frac{1}{2}}-2x$, then $\frac{d^{2}y}{dx^{2}}=$

MCQ1 marksannual

4

If line $x-2y+\ell=0$ is tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$, then find: **a.** Value of $\ell$ **b.** Equation of tangent **c.** Length of latus rectum

Part B4 marksannual

4

Evaluate: $\int \frac{2x-1}{x^3-x^2-2x} dx$

Part C8 marksannual

5

If $y=\frac{1}{8} \sin 2 x$, then the value of $\frac{d^{4} y}{d x^{4}}$ is:

MCQ1 marksannual

5

If $y=3\theta^{3}-\theta^{\frac{-3}{2}}$ and $u=2\theta^{2}-\theta^{\frac{-1}{2}}$, then find $\frac{dy}{du}$

Part B4 marksannual

5

Evaluate: $\int \frac{dx}{4x^3 - x}$

Part C8 marksannual

6

If $\vec{r}(t)=\left(1+t^{2}\right) \hat{i}+\sin t \hat{j}+\cos 2 t \hat{k}$, then $\lim _{t \rightarrow 0} \vec{r}(t)=$

MCQ1 marksannual

6

Compute two iterations up to 4 decimal places of $f(x)=x^{3}-5x+1$ by using **Newton-Raphson's method** with initial start $x_{0}=0.5$

Part B4 marksannual

7

If $\vec{r}(t)=t^{2} \hat{i}-2 t \hat{j}$, then $\vec{v}(t)=$

MCQ1 marksannual

7

If $\vec{r}(t)=t^{3} \hat{i}+e^{-2 t} \hat{j}+\sin 2 t \hat{k}$ is position vector of a moving particle at time $t$, then find:\n**a.** Velocity vector $\vec{v}(t)$\n**b.** Acceler…

Part B4 marksannual

8

$\int \frac{\cos x}{\sin x} dx=$

MCQ1 marksannual

8

Find the equation of line passing through the point of intersection of lines $x+y=3$ and $x-y=1$ and parallel to line $x-3y=2$ and write it in slope intercept form.

Part B4 marksannual

9

If $2 \int_{0}^{2} x \, dx = 3k - 2$, then the value of '$k$' is:

MCQ1 marksannual

9

Evaluate: $\int(3t+1)(t-1) dt$

Part B4 marksannual

10

If $A(5,-5), B(-2,0)$ and $C(0,2)$ are vertices of a triangle then its centroid is:

MCQ1 marksannual

10

Find the equation of the circle passing through the points $(4,0)$, $(0,5)$ and $(0,0)$

Part B4 marksannual

11

If $4x - 2y = 3$, then the slope of the line is:

MCQ1 marksannual

11

Find the solution of differential equation $\frac{dy}{dx}=1+e^{x}y+y+e^{x}$

Part B4 marksannual

12

The equation of circle with centre $(-1,-1)$ and radius 2 is:

MCQ1 marksannual

12

Find the area under the graph of $f(x)=3x^{2}-2x$ over the interval $[1,3]$

Part B4 marksannual

13

If $x^{2}+y^{2}+4x+4y=0$ is an equation of circle then its radius is:

MCQ1 marksannual

13

Find the extreme values of $f(x)=\frac{1}{3}x^{3}-x^{2}-3x+6$

Part B4 marksannual

14

If $3x^{2}-2xy-8y^{2}=0$ is a 2nd degree homogeneous equation then find: **a.** Pair of straight lines **b.** Angle between these lines

Part B4 marksannual

15

If $\frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)^{2}+y=3 x$ is a differential equation, then its order and degree respectively are:

MCQ1 marksannual

15

Find the area of a triangle if its vertices are $A(5,4), B(2,1)$ and $C(7,3)$

Part B4 marksannual

16

If $\frac{1}{x} \frac{dy}{dx} = 2$, then the solution $y(x)$ of the differential equation is:

MCQ1 marksannual

16

Evaluate $\int x^{2} \cos x \, dx$ using integration by parts method

Part B4 marksannual

17

If $f(x, y)=x^{2}+3 y$, then $\frac{\partial f}{\partial x}(1,1)=$

MCQ1 marksannual

17

Find the equation of tangent and normal to parabola $x^{2}=8y-8$ at $x=4$

Part B4 marksannual

18

If $f(x, y)=e^{x+y}$, then $\frac{\partial f}{\partial y}(1,0)$ is:

MCQ1 marksannual

18

Find $\frac{dy}{dx}$, if $y=(2x+3)^{\frac{3}{2}}$ by first principle

Part B4 marksannual

19

If $f(x)=x^{3}-2x+1$ and $x_{0}=0$, then $f^{\prime}(x_{0})$ is:

MCQ1 marksannual

19

Evaluate $\int \frac{e^{x} dx}{e^{2x}+1}$ by substitution method

Part B4 marksannual

20

The value of $\Delta x$ to approximate $\int_{0}^{2}\left(x^{2}+1\right) dx$ for $n=4$ sub-intervals by **Trapezoidal Rule** is:

MCQ1 marksannual

20

If $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ is an equation of hyperbola then find: **a.** Centre **b.** Vertices **c.** Foci **d.** Equation of asymptotes

Part B4 marksannual