Mathematics Previous Year Questions — Last 3 Years (2024–2026)

640 Mathematics previous-year questions spanning 2024–2026.

Mathematics 2026 · Functions

If the domain of the function $f(x) = \cos^{-1}\left(\frac{2x - 5}{11 - 3x}\right) + \sin^{-1}(2x^2 - 3x + 1)$ is the interval $[\alpha, \beta]$ , then $\alpha + 2\beta$ is equal to :

Mathematics 2026 · Area Under Curves

The area of the region, inside the ellipse $x^{2} + 4y^{2} = 4$ and outside the region bounded by the curves $y = |x| - 1$ and $y = 1 - |x|$ , is:

Mathematics 2026 · Sets and Relations

The number of relations, defined on the set $\{a, b, c, d\}$ , which are both reflexive and symmetric, is equal to:

Mathematics 2026 · Straight Lines

Let a point A lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines $L_{1}$ and $L_{2}$ respectively, is:

Mathematics 2026 · Vector Algebra

Let $\vec{a} = -\hat{i} + 2\hat{j} + 2\hat{k}$ , $\vec{b} = 8\hat{i} + 7\hat{j} - 3\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a} \times \vec{c} = \vec{b}$ . If $\vec{c}. (\hat{i} + \hat{j} + \hat{k}) = 4$ , then $|\vec{a} + \vec{c}|^2$ is equal to:

Mathematics 2026 · Sequences and Series

Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ..... be a G.P. of increasing positive terms such that $a_{2} \cdot a_{3} \cdot a_{4} = 64$ and $a_{1} + a_{3} + a_{5} = \frac{813}{7}$ . Then $a_{3} + a_{5} + a_{7}$ is equal to :

Mathematics 2026 · Vector Algebra

Let $\vec{c}$ and $\vec{d}$ be vectors such that $|\vec{c}+\vec{d}|=\sqrt{29}$ and $\vec{c}\times(2\hat{i}+3\hat{j}+4\hat{k})=(2\hat{i}+3\hat{j}+4\hat{k})\times\vec{d}$ . If $\lambda_{1},\lambda_{2}(\lambda_{1}>\lambda_{2})$ are the possible values of $(\vec{c}+\vec{d}).(-7\hat{i}+2\hat{j}+3\hat{k})$ , then the equation $K^{2}x^{2}+(K^{2}-5K+\lambda_{1})xy+\left(3K+\frac{\lambda_{2}}{2}\right)y^{2}-8x+12y+\lambda_{2}=0$ represents a circle, for k equal to:

Mathematics 2026 · Differential Equations

Let $y = y(x)$ be the solution curve of the differential equation $(1 + x^2)dy + (y - \tan^{-1}x)dx = 0$ , $y(0) = 1$ . Then the value of $y(1)$ is:

Mathematics 2026 · Permutations and Combinations

The number of strictly increasing functions $f$ from the set $\{1, 2, 3, 4, 5, 6\}$ to the set $\{1, 2, 3, \ldots, 9\}$ such that $f(i) \neq i$ for $1 \leq i \leq 6$ , is equal to:

Mathematics 2026 · Limits, Continuity and Differentiability

Let $f: R \to (0, \infty)$ be a twice differentiable function such that $f(3) = 18$ , $f'(3) = 0$ and $f''(3) = 4$ . Then $\lim_{x \to 1} \left( \log_{e} \left( \frac{f(2 + x)}{f(3)} \right)^{\frac{18}{(x-1)^2}} \right)$ is equal to:

Mathematics 2026 · Conic Sections

Let the foci of hyperbola coincide with the foci of the ellipse $\frac{x^2}{36} +\frac{y^2}{16} = 1$ . If the eccentricity of the hyperbola is 5, then the length of its latus rectum is:

Mathematics 2026 · Definite Integration

The value of $\int_{-\pi/6}^{\pi/6}\left(\frac{\pi+4x^{11}}{1-\sin(|x|+\pi/6)}\right)dx$ is equal to

Mathematics 2026 · Statistics and Probability

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, $x > y$, be 8 and 16 respectively. Two numbers are chosen from $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is:

Mathematics 2026 · Three Dimensional Geometry

Let $(\alpha, \beta, \gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point (5, 4, 2) on the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \lambda(2\hat{i} + 3\hat{j} - \hat{k})$ . Then the length of the projection of the vector $\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ on the vector $6\hat{i}+2\hat{j}+3\hat{k}$ is :

Mathematics 2026 · Circles

Let PQ and MN be two straight lines touching the circle $x^{2} + y^{2} - 4x - 6y - 3 = 0$ at the points A and B respectively. Let O be the centre of the circle and $\angle AOB = \pi/3$ . Then the locus of the point of intersection of the lines PQ and MN is:

Mathematics 2026 · Binomial Theorem

If the coefficient of x in the expansion of $(ax^{2} + bx + c)(1 - 2x)^{26}$ is -56 and the coefficients of $x^{2}$ and $x^{3}$ are both zero, then $a + b + c$ is equal to

Mathematics 2026 · Complex Numbers and Quadratic Equations

If $x^{2} + x + 1 = 0$ , then the value of $\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)^{4}+\left(\mathrm{x}^{2}+\frac{1}{\mathrm{x}^{2}}\right)^{4}+\left(\mathrm{x}^{3}+\frac{1}{\mathrm{x}^{3}}\right)^{4}+\ldots+\left(\mathrm{x}^{25}+\frac{1}{\mathrm{x}^{25}}\right)^{4}$ is :

Mathematics 2026 · Trigonometric Functions

The value of $\csc 10^{\circ} - \sqrt{3} \sec 10^{\circ}$ is equal to:

Mathematics 2026 · Quadratic Equations

The sum of all the roots of the equation $(x-1)^{2}-5|x-1|+6=0$ , is:

Mathematics 2026 · Parabola

Let O be the vertex of the parabola $x^{2}=4y$ and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2: 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is:
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