ISC Mathematics 2024 Question Paper with Answers
All 46 questions of the ISC Mathematics 2024 Question Paper, in printed order. Open a question to read it in full and see its answer.
- Q1(i) Let $L$ be a set of all straight lines in a plane. The relation $R$ on $L$ defined as 'perpendicular to' is: 1 mark · MCQ
- Q1(ii) The order and the degree of differential equation… 1 mark · MCQ
- Q1(iii) Let $A$ be a non-empty set. Statement 1: Identity relation on $A$ is Reflexive. Statement 2: Every Reflexive relation on $A$ is… 1 mark · MCQ
- Q1(iv) The graph of the function $f$ is shown below. Of the following options, at what values of $x$ is the function $f$ NOT… 1 mark · MCQ
- Q1(v) The value of… 1 mark · MCQ
- Q1(vi) The value of $\int_1^{\sqrt{3}} \frac{dx}{1 + x^2}$ is: 1 mark · MCQ
- Q1(vii) Let the matrices $A = \begin{bmatrix} -3 & 2 \\ -5 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -2 \\ 5 & -3 \end{bmatrix}$ be… 1 mark · Assertion-reason
- Q1(viii) If $\int (\cot x - \operatorname{cosec}^2 x)e^x dx = e^x f(x) + c$ then $f(x)$ will be: 1 mark · MCQ
- Q1(ix) In which one of the following intervals is the function $f(x) = x^3 - 12x$ increasing? 1 mark · MCQ
- Q1(x) If $A$ and $B$ are symmetric matrices of the same order, then $AB - BA$ is: 1 mark · MCQ
- Q1(xi) Find the derivative of $y = \log x + \frac{1}{x}$ with respect to $x$. 1 mark · Short answer
- Q1(xii) Teena is practising for an upcoming Rifle Shooting tournament. The probability of her shooting the target in the $1^{\text{st}}$… 1 mark · Short answer
- Q1(xiii) Which one of the following graphs is a function of $x$? Graph A Graph B 1 mark · Short answer
- Q1(xiv) Evaluate: $\int_0^6 |x + 3| dx$ 1 mark · Short answer
- Q1(xv) Given that $\frac{1}{y} + \frac{1}{x} = \frac{1}{12}$ and $y$ decreases at a rate of $1\text{ cm s}^{-1}$, find the rate of… 1 mark · Short answer
- Q2(i) Let $f: \mathbb{R} - \left\{-\frac{1}{3}\right\} \to \mathbb{R} - \{0\}$ be defined as $f(x) = \frac{5}{3x + 1}$ is invertible… 2 marks · Short answer
- Q2(ii) If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = \frac{2x - 7}{4}$, show that $f(x)$ is one - one and onto. 2 marks · Derivation
- Q3 Find the value of the determinant given below, without expanding it at any stage… 2 marks · Numerical
- Q4(i) Determine the value of $k$ for which the following function is continuous at $x = 3$… 2 marks · Numerical
- Q4(ii) Find a point on the curve $y = (x - 2)^2$ at which the tangent is parallel to the line joining the chord through the points… 2 marks · Numerical
- Q5 Evaluate: $\int_0^{2\pi} \frac{1}{1 + e^{\sin x}} dx$ 2 marks · Short answer
- Q6 Evaluate: $P(A \cup B)$ if $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$ 2 marks · Numerical
- Q7 If $y = 3\cos(\log x) + 4\sin(\log x)$, show that $x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + y = 0$ 4 marks · Derivation
- Q8(i) Solve for $x$: $\sin^{-1}\left(\frac{x}{2}\right) + \cos^{-1} x = \frac{\pi}{6}$ 4 marks · Numerical
- Q8(ii) If $\sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \pi$, show that $x^2 - y^2 - z^2 + 2yz\sqrt{1 - x^2} = 0$ 4 marks · Derivation
- Q9(i) Evaluate: $\int x^2 \cos x dx$ 4 marks · Short answer
- Q9(ii) Evaluate: $\int \frac{x + 7}{x^2 + 4x + 7} dx$ 4 marks · Short answer
- Q10 A jewellery seller has precious gems in white and red colour which he has put in three boxes. The distribution of these gems is… 4 marks · Numerical
- Q11 A furniture factory uses three types of wood namely, teakwood, rosewood and satinwood for manufacturing three types of furniture… 6 marks · Short answer
- Q12(i) Mrs. Roy designs a window in her son’s study room so that the room gets maximum sunlight. She designs the window in the shape of… 6 marks · Numerical
- Q12(ii) Sumit has bought a closed cylindrical dustbin. The radius of the dustbin is '$r$' cm and height is '$h$' cm. It has a volume of… 6 marks · Short answer
- Q13(i) Solve the following differential equation: $2y e^{x/y} dx + (y - 2x e^{x/y}) dy = 0$, given $x = 0$ and $y = 1$ 6 marks · Short answer
- Q12(iii) Solve the following differential equation: $x(x^2 - 1)\frac{dy}{dx} = 1$, $y = 0$, given $x = 2$ 6 marks · Short answer
- Q14 A primary school teacher wants to teach the concept of 'larger number' to the students of Class II. To teach this concept, he… 6 marks · Short answer
- Q15 In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. If… 5 marks · Short answer
- Q16(i) If $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ where $\vec{a}$, $\vec{b}$ and $\vec{c}$ are non-zero vectors, then prove… 2 marks · Derivation
- Q16(ii) If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a} \times \vec{b}| = \vec{a} \cdot \vec{b}$, find the angle… 2 marks · Numerical
- Q17 A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points… 4 marks · Short answer
- Q18(i) Using integration, find the area bounded by the curve $y^2 = 4ax$ and the line $x = a$ 4 marks · Numerical
- Q18(ii) Using integration, find the area of the region bounded by the curve $y^2 = 4x$ and $x^2 = 4y$ 4 marks · Numerical
- Q19 In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. A company… 5 marks · Short answer
- Q20(i) The Average Cost function associated with producing and marketing $x$ units of an item is given by $AC = x + 5 + \frac{36}{x}$… 2 marks · Short answer
- Q20(ii) A monopolist’s demand function is $x = 60 - \frac{p}{5}$. At what level of output will marginal revenue be zero? 2 marks · Numerical
- Q21(i) XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on… 4 marks · Short answer
- Q21(ii) The line of regression of marks in Statistics ($X$) and marks in Accountancy ($Y$) for a class of 50 students is… 4 marks · Short answer
- Q22 Aman has ₹ 1500 to purchase rice and wheat for his grocery shop. Each sack of rice and wheat costs ₹ 180 and ₹ 120 respectively… 4 marks · Short answer