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All Maths 12 papers

Class 12 · Past paper

Maths 12 past paper 2023

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

20 MCQs20 written questionsPractise this paper

Question index

1
For what value of $a$ the vectors $2\underline{i}+4\underline{j}-5\underline{k}$ and $-4\underline{i}-8\underline{j}+a\underline{k}$ are parallel?
MCQ1 marksannual
1
Let $f(x)=x^{2}+2$ and $g(x)=x+1$ then: (a) Find $g \circ f(x)$ (b) Find $x$ for which $f \circ g(x)=11$
Part B4 marksannual
1
Let $f(x)= \begin{cases}2-x, & 0 \leq x<1 \\ k, & x=1 \\ 2x-1, & 1<x \leq 2\end{cases}$ then: a. What are domain and range of $f(x)$? b. Find the value of $k$ for which $f(x)$ is c…
Part C8 marksannual
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.

What is the value of $f(-1)$ if $f^{-1}(x)=\frac{8-x}{2}$?

MCQ1 marksannual

2

For the function $f(x)= \begin{cases}3x+4, & 0 \leq x<3 \\ 16-x, & 3 \leq x<12 \\ x, & 12 \leq x<14\end{cases}$ (a) Explain whether $\lim_{x \rightarrow 3} f(x)$ exists (b) Discuss…

Part B4 marksannual

2

A box has square base and the sum of one side of the base and height of the box is 12. If the length of one side of box is $x$ cm: a. Express volume $V$ of the box in terms of $x$.…

Part C8 marksannual

3

What is the value of $\lim_{x \rightarrow 0} \frac{1-\cos x}{x^{2}}$?

MCQ1 marksannual

3

If $x=a \cos^{3} \theta, y=b \sin^{3} \theta$ show that $a \frac{dy}{dx}+b \tan \theta=0$ (Chain Rule)

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3

For a curve $f(x)=x^{2}-2x, x \in [-1,3]$: a. Find $\int_{-1}^{3} f(x) dx$. b. Sketch the graph of $f(x)$ and shade the area bounded by $x$-axis and the curve $f(x)$. c. Find the a…

Part C8 marksannual

4

Which of the following is equal to $y_{2}$ if $xy=2$?

MCQ1 marksannual

4

If $e^{x}+e^{y}=e^{x+y}$ then find the value of $\frac{dy}{dx}$ at $(1,1)$

Part B4 marksannual

4

If the sides of a triangle $\triangle ABC$ are $7x-y-10=0$, $10x+y-41=0$, and $3x+2y+3=0$ then: a. Find the vertices $A, B, C$ of the triangle. b. Find the equations of altitudes o…

Part C8 marksannual

5

What is the value of $\frac{d}{dx}[f \circ g(x)]$ if $f(x)=e^{x}$ and $g(x)=\sin x$?

MCQ1 marksannual

5

Show that $\cos(x+h)=\cos x-h \sin x-\frac{h^{2}}{2!} \cos x+\frac{h^{3}}{3!} \sin x+\dots$

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5

A car detailing company performs two types of detailing: deluxe and ordinary. The deluxe detailing requires 1 hour inspection and 3 hours maintenance time. While an ordinary detail…

Part C8 marksannual

6

Which of the following is the derivative of $x^{x}$ w.r.t. $x$?

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6

Find two positive integers whose sum is 9 and product of one with square of the other is maximum.

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6

Find the centre, foci, eccentricity, vertices and directrices of the given conic $9x^{2}-y^{2}-36x-6y+18=0$.

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7

The derivative of an odd function is always:

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7

The side of a cube is measured to be 20 cm with a maximum error of 0.12 cm in its measurement. Find the maximum error in the calculated volume of the cube.

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8

Which of the following is equal to $\int(\csc^{2} x-1) dx$?

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8

Evaluate $\int \frac{\cos x}{\sin x \cdot \ln \sin x} dx$

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9

For what value of $x$ the function $f(x)=x^{2}-3x+7$ has a **critical point**?

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9

Find the equation of the curve for which $\frac{dy}{dx}+\frac{2xy}{2y+1}=x$. The curve passes through the point $(2,1)$

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10

If $\int_{a}^{\frac{\pi}{4}} \cos 2x \, dx = \frac{1}{2}$ then what should be the value of $a$?

MCQ1 marksannual

11

Which of the following is the evaluation of $\int \frac{e^{x}}{e^{x}-3} dx$?

MCQ1 marksannual

11

If $\int_{-3}^{3}(x^{3}+kx^{2}) dx=54$ find the value of $k$.

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12

The slope and $y$-intercept of the line $2x+y-3=0$ are:

MCQ1 marksannual

12

Find the area of a triangle with one vertex as point of intersection of the lines $x+y-5=0$ and $2x-y+2=0$, and points $(2,-3)$ and $(3,4)$ are other two vertices.

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13

Perpendicular distance of the line $x+2y+4=0$ from the point $(1,0)$ is:

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13

Find the equation of a circle concentric with the circle $x^{2}+y^{2}-8x+4=0$ and is tangent to the line $x+2y+6=0$.

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14

If line $l_1$ is making angle $45°$ with the $x$-axis, what is the slope?

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15

Which one is the solution of inequality $-20 > -2x$?

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15

Verify that $\underline{a}$ and $\underline{b}$ are perpendicular to $\underline{b} \times \underline{a}$ where $\underline{a}=3\underline{i}-\underline{j}+5\underline{k}$ and $\un…

Part B4 marksannual

16

If $y^{2}-y=\sin x$ then which one is equal to $\frac{dy}{dx}$?

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16

Prove that in any triangle $\triangle ABC$, $b=c \cos A+a \cos C$.

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17

What is the length of latus rectum of parabola $(x+1)^{2}=8y+8$?

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18

What is the centre of ellipse $\frac{(2x+1)^{2}}{9}+\frac{(y-1)^{2}}{5}=1$?

MCQ1 marksannual

19

If $\theta$ is the angle between two vectors $\underline{a}$ and $\underline{b}$, and $\sin \theta=\frac{1}{2}$, $|\underline{a}|=|\underline{b}|=\sqrt{2}$ then what is the value o…

MCQ1 marksannual

20

When a force $\underline{F}=3\underline{i}+2\underline{j}-4\underline{k}$ is applied to an object a displacement $\underline{d}=4\underline{i}+\alpha\underline{j}+4\underline{k}$ o…

MCQ1 marksannual

Maths 12 Past Paper 2023 | Notely