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Maths 11 Past Paper 2024 | Notely

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All Maths 11 papers

Class 11 · Past paper

Maths 11 past paper 2024

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

19 MCQs32 written questionsPractise this paper

Question index

1
What is the period of $3 \sin\left(\frac{x}{5}\right)$?
MCQ1 marksannual
1
Simplify $z = \frac{(3+i)^3}{3-i}$ in the form $a+ib$ where $i=\sqrt{-1}$ and find the value of $|z|$.
Part B4 marksannual
1
Find inverse of the matrix $\begin{bmatrix} 1 & 1 & 2 \\ 3 & -1 & 1 \\ -1 & 3 & 4 \end{bmatrix}$.
Part C8 marksannual
2
What is the value of $\sin^{-1}\left(-\frac{1}{2}\right)$?

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 row rank of $\begin{bmatrix} 1 & 2 & 3 & 2 \\ 4 & 2 & 1 & 3 \\ 5 & 2 & -1 & 2 \end{bmatrix}$.

Part B4 marksannual

2

If $\underline{a} = -10\underline{i} + 2\underline{j} + 4\underline{k}$ and $\underline{b} = \underline{i} - \underline{j} + 2\underline{k}$ then find a unit vector orthogonal to $…

Part C8 marksannual

3

What is the multiplicative inverse of $-i$?

MCQ1 marksannual

3

Solve the system of linear equations: \begin{aligned} (3-2i)x + (1+2i)y - 1 &= 0 \\ (3+2i)x - (1-2i)y - 1 &= 0 \end{aligned}

Part B4 marksannual

3

Use Gauss Jordan method to solve the system of linear equations: $x - 2y + z = 3; \quad 3x + 5y = 11; \quad 4y + 3z = 13$.

Part C8 marksannual

4

The real part of $\frac{1+7i}{3-4i}$ is:

MCQ1 marksannual

4

If $4^{\text{th}}$ and $10^{\text{th}}$ terms of a HP are $\frac{2}{15}$ and $\frac{2}{33}$ respectively, then find its $23^{\text{rd}}$ term.

Part B4 marksannual

4

If $y = \frac{1}{2(1!)}\left(\frac{1}{6}\right) + \frac{1.3}{4(2!)}\left(\frac{1}{6}\right)^2 + \frac{1.3.5}{8(3!)}\left(\frac{1}{6}\right)^3 + \dots$ then verify that $5y^2 + 10y…

Part C8 marksannual

5

If $A$ is a $2 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, then the order of $AB$ is:

MCQ1 marksannual

5

If $A = \begin{bmatrix} 5 & 9 & 2 \\ 4 & 8 & 1 \\ 3 & 7 & 0 \end{bmatrix}$, then show that $(A+A')$ is symmetric.

Part B4 marksannual

5

Find point of intersection of the functions $f(x) = -x + 6$ and $g(x) = x^2 - 4x + 6$ graphically.

Part C8 marksannual

6

If $A = \begin{bmatrix} i & 0 & 0 \\ 0 & i & 0 \\ 0 & 0 & i \end{bmatrix}$, then which one in the options is $A^3$?

MCQ1 marksannual

6

For what value of $p$, vectors $3p\underline{i} + 11\underline{j} - 5\underline{k}$ and $2p\underline{i} + p\underline{j} + 2\underline{k}$ are mutually perpendicular?

Part B4 marksannual

6

Find general solution of a trigonometric equation $3 \cos x + 3 = 2 \sin^2 x$.

Part C8 marksannual

7

Find the volume of a tetrahedron with vertices $A(1,2,2), B(2,1,1), C(3,3,4)$ and $D(0,1,5)$.

Part B4 marksannual

7

Find maximum and minimum values of a function $f(x, y) = 2x + 3y$ subject to the constraints $x + 2y \leq 10, \quad 3x + y \leq 9, \quad 9x + 8y \leq 72, \quad x \geq 0, y \geq 0$.

Part C8 marksannual

8

What is the value of the determinant $\begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix}$?

MCQ1 marksannual

8

Insert four A.Ms between 5 and 25.

Part B4 marksannual

8

Sketch the graph of $y = 2 \cos \frac{\theta}{2}$; $-\pi \leq \theta \leq \pi$.

Part C8 marksannual

9

What is the sum of the first 3 terms of the sequence $a_n = 2n$?

MCQ1 marksannual

9

If $2^{\text{nd}}$ and $6^{\text{th}}$ terms of a GP are 3 and $\frac{3}{4}$ respectively, find its $16^{\text{th}}$ term.

Part B4 marksannual

10

The sum of the series $\sum_{r=1}^n (2r-1)^2$ is:

MCQ1 marksannual

10

Sum to $n$-terms the series $1.5 + 2.6 + 3.7 + 4.8 + \dots$.

Part B4 marksannual

11

In how many ways 5 persons can be seated at a round table?

MCQ1 marksannual

11

How many 7-digit different numbers can be formed from the digits 5, 5, 6, 6, 9, 9, 9 using all of them, and how many of them are greater than 9,950,000?

Part B4 marksannual

12

What is the probability of drawing a King from a well shuffled pack of 52 playing cards?

MCQ1 marksannual

12

Prove that $1+4+7+\dots+(3n-2) = \frac{n(3n-1)}{2}$ by using mathematical induction.

Part B4 marksannual

13

What is the coefficient of $3^{rd}$ term in the expansion of $\left(x-\frac{1}{x}\right)^8$?

MCQ1 marksannual

13

For a real valued function $f(x) = \frac{5x-2}{x+2}, x \neq -2$ find $f^{-1}(x)$ and determine its domain and range.

Part B4 marksannual

14

Which one in the given options is true if $2^n > 2(n+1)$ for all $n \in \mathbb{Z}^+$?

MCQ1 marksannual

14

If $\cos \alpha = \frac{3}{5}, \sin \beta = \frac{5}{13}$ with $\frac{\pi}{2} < \beta < \pi$ and $\frac{3\pi}{2} < \alpha < 2\pi$, then find the value of $\sin(\alpha+\beta)$.

Part B4 marksannual

15

The graph of $y=x^4$ is symmetrical about:

MCQ1 marksannual

15

State number of diagonals of an $n$-sided polygon and find number of diagonals of a nine sided polygon.

Part B4 marksannual

16

($-1, -1$) is a solution of the inequality:

MCQ1 marksannual

16

Prove that $\sin 2\theta + \sin 4\theta + \sin 6\theta + \sin 8\theta = 4 \sin 5\theta \cos 2\theta \cos \theta$.

Part B4 marksannual

17

Which of the following options equates $\cos 196^\circ$?

MCQ1 marksannual

17

Find the equation of a parabola $y = ax^2 + bx + c$ that cuts $x$-axis at points $(-4,0), (4,0)$ and passes through a point $(0,8)$.

Part B4 marksannual

18

If $\cos \beta = \frac{3}{4}$, then value of $\cos 2\beta$ is:

MCQ1 marksannual

18

A pair of fair dice is thrown. The number of dots on the top are added. What is the probability of getting a sum greater than 9 or a sum divisible by 5?

Part B4 marksannual

19

Area of a triangle $\triangle ABC$ (with usual notations) where $a=2, b=3, \gamma=30^\circ$ is:

MCQ1 marksannual

19

Verify that $\cos^4 \theta = \frac{1}{8}(3 + 2 \cos 2\theta + \cos 4\theta)$.

Part B4 marksannual

20

What is the shadow length of a $\sqrt{3} \text{ m}$ high tree if the sun's elevation angle is $45^\circ$?

MCQ1 marksannual

20

Solve triangle $ABC$ with $\alpha = 31^\circ 5'$, $\beta = 50^\circ 55'$ and $c = 13 \text{ cm}$ using usual notations.

Part B4 marksannual

21

Find radii of the escribed circles of triangle $ABC$ opposite to the largest and smallest sides given that $a=13, b=10$ and $c=7$ (using usual notations).

Part B4 marksannual

22

Without drawing, guess the graph of $y = \sin \frac{\theta}{6}$ and find its period, frequency and amplitude.

Part B4 marksannual

23

Verify that $2S = 8R \cos \frac{\alpha}{2} \sin \frac{\beta}{2} \cos \frac{\gamma}{2}$, where $S$ is the area of a triangle, $R$ is the circumradius, and $\alpha$, $\beta$, $\gamma…

Part B4 marksannual

24

Verify that $\tan^{-1} \frac{3}{4} - \tan^{-1} \frac{4}{3} + 2 \tan^{-1} \frac{1}{7} = 0$.

Part B4 marksannual