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All Maths 12 papers

Class 12 · Past paper

Maths 12 past paper 2024

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

18 MCQs30 written questionsPractise this paper

Question index

1
If $f(x)=\sqrt{x+5}$ and $f(g(x))=3x$ then what is the value of $g(x)$?
MCQ1 marksannual
1
If $f(x)=\frac{3x+2}{2x-1}$, find $f^{-1}(x)$ and also show that $f^{-1}(f(x))=x$.
Part B4 marksannual
1
Let $f(x)=\begin{cases} px+2 & \text{if } 0 \leq x < 2 \\ 7-qx & \text{if } 2 \leq x < 4 \\ 2x+1 & \text{if } 4 \leq x < 6 \end{cases}$. Find $p$ and $q$ such that $f$ is continuou…
Part C8 marksannual
2
Without finding the inverse, what is the range of $f^{-1}(x)$, where $f(x)=3+\sqrt{x-2}$?

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

Find $\frac{dy}{dx}$ if $2y^3-3xy^2+2x^2y+5x=6$. Also find the value of $\frac{dy}{dx}$ at $(1,1)$.

Part B4 marksannual

2

A box with a square base and open top is to have a volume 32 cubic dm. Find the dimensions of the box that will require the least material.

Part C8 marksannual

3

Which of the following functions is continuous at $x=4$?

MCQ1 marksannual

3

Find the derivative of $y=(2\sqrt{x}+2)(x-\sqrt{x})$.

Part B4 marksannual

3

Evaluate $\int \frac{2x^2-x-7}{(x+2)^2(x^2+2x+5)} dx$.

Part C8 marksannual

4

If $x+y=\sin(x+y)$ then $\frac{dy}{dx}$ is equal to:

MCQ1 marksannual

4

Find the equation of tangent of an ellipse $\frac{x^2}{128}+\frac{y^2}{18}=1$ which are parallel to the line $3x+8y+1=0$. Also find the point of contact.

Part C8 marksannual

5

Minimum value of the function $f(x)=x^2+2x-3$ is:

MCQ1 marksannual

5

If $y=\cot(q \cot^{-1} x)$ then show that $(1+x^2)y_1 - q(1+y^2) = 0$.

Part B4 marksannual

6

If $f(x)=e^{\ln(\sin x)}$ then what is the value of $f'(\frac{\pi}{2})$?

MCQ1 marksannual

6

Evaluate $\lim_{\theta \to 0} \frac{\sec \theta - 1}{\theta \sec \theta}$.

Part B4 marksannual

6

A factory produces two items: ceiling lights and ceiling fans by using two machines A and B. Machine A has at most 120 hours available and machine B has a maximum of 144 hours avai…

Part C8 marksannual

7

What evaluates $\int_{0}^{\frac{\pi}{2}} \cos x (e^{\sin x}) dx$?

MCQ1 marksannual

7

Examine the function $x^3-6x^2+9x+3$ for extreme values.

Part B4 marksannual

7

Find the centre, foci, eccentricity, vertices and equation of directrices of the conic $9x^2-y^2-12x-2y+2=0$.

Part C8 marksannual

8

Which of the following options represents $f'(x)=\frac{x}{x^2+1}$ and $f(0)=1$?

MCQ1 marksannual

8

Use the differential to approximate value of $\sin 61^\circ$.

Part B4 marksannual

8

Evaluate $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \cos^2 \theta \cot^2 \theta d\theta$.

Part C8 marksannual

9

If $2\int_{0}^{2}(x-k)dx=1$ then what is the value of $k$?

MCQ1 marksannual

9

Find the area bounded by the curve $y=x^3-9x$ and the $x$-axis.

Part B4 marksannual

10

If the line $\pi x + \sqrt{2}y + \sqrt{7} = 0$ is perpendicular to the line $kx + 3y + 2 = 0$, then $k$ is:

MCQ1 marksannual

10

Find the area of the region bounded by $10x^2-xy-21y^2=0$ and $x+y+1=0$.

Part B4 marksannual

11

A line that cuts the $x$-axis at $(2,0)$ and $y$-axis at $(0,-4)$, has equation:

MCQ1 marksannual

11

Solve the differential equation $\frac{dy}{dx}=\frac{3}{4}x^3+x-3$ if $y=0$, when $x=2$.

Part B4 marksannual

12

What is the angle between pair of lines represented by $x^2+2xy-y^2=0$?

MCQ1 marksannual

12

Find the point $P$ on the line joining $A(1,4)$ and $B(5,6)$ that is twice as far from $A$ as $B$ is from $A$ and lies on the opposite side of $A$ as $B$ does.

Part B4 marksannual

13

If the lines $3x-y-2=0$, $5x+ay-3=0$ and $2x+y-2=0$ are concurrent then what is the value of $a$?

MCQ1 marksannual

13

The length of perpendicular from origin to the line is 8 units and angle of inclination is $30^\circ$. Find the slope and $y$-intercept of the line.

Part B4 marksannual

14

The ordered pair $(3,2)$ is **NOT** a solution of inequality:

MCQ1 marksannual

14

Integrate $\int \frac{x \sin^{-1} x}{\sqrt{1-x^2}} dx$.

Part B4 marksannual

15

What are the foci of an ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$?

MCQ1 marksannual

15

Find the equation of a circle passing through the point $(-2,-5)$ and touching the line $3x+4y-24=0$ at the point $(4,3)$.

Part B4 marksannual

16

Directrices of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are:

MCQ1 marksannual

16

Graph the feasible region of the following system of linear inequalities by shading and find the corner points: $3x+2y \geq 6, x+y \leq 4, x \geq 0, y \geq 0$.

Part B4 marksannual

17

What is the length of tangent from $(2,1)$ to the circle $3x^2+3y^2+6x-12y+1=0$?

MCQ1 marksannual

17

Graph the feasible region of the following system of linear inequalities by shading and find the corner points: $5x+7y \leq 35, x-2y \leq 4, x \geq 0, y \geq 0$.

Part B4 marksannual

18

Find the equation of parabola having Focus $(-3,4)$ and directrix $3x+2y-3=0$.

Part B4 marksannual

19

Prove that altitudes of a triangle are concurrent (by vector method).

Part B4 marksannual

20

What are the direction cosines of the vector $\sqrt{3}\hat{i}-\sqrt{3}\hat{j}+\sqrt{3}\hat{k}$?

MCQ1 marksannual

20

Find the value of $C$, when the line $5x+2y+C=0$ will touch the hyperbola $\frac{x^2}{4}-\frac{y^2}{9}=1$.

Part B4 marksannual

21

Find the points of intersection of the two conics $\frac{x^2}{18}+\frac{y^2}{8}=1$ and $\frac{x^2}{3}-\frac{y^2}{3}=1$.

Part B4 marksannual

22

If $\bar{u}=2\hat{i}+3\hat{j}+4\hat{k}$, $\bar{v}=\hat{i}+4\hat{j}+3\hat{k}$ and $\bar{w}=\hat{i}+7\hat{j}+\lambda\hat{k}$ represent the sides of a triangle, find the value of $\la…

Part B4 marksannual

23

Find the equation of an ellipse with foci $(\pm \sqrt{5}, 0)$ and passing through the point $(\frac{3}{2}, \sqrt{3})$.

Part B4 marksannual

24

Find the moment about $(1,1,1)$ of each of the concurrent forces $\hat{i}-2\hat{j}$, $3\hat{i}+2\hat{j}-\hat{k}$ and $5\hat{j}+2\hat{k}$ where $P(2,0,1)$ is the point of concurrenc…

Part B4 marksannual

Maths 12 Past Paper 2024 | Notely