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#1 Class 12 Mathematics Differential Equations 2026 Short 3M CBSE

Find the particular solution of the differential equation $xy\dfrac{dy}{dx} = (x+2)(y+2)$, given that $y(1) = -1$.

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#2 Class 12 Mathematics Differential Equations 2026 Short 3M CBSE

Find the general solution of the following differential equation: $x^2\dfrac{dy}{dx} = x^2 + xy + y^2$

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#3 Class 12 Mathematics Integrals 2026 Short 3M CBSE

If $I_1 = \displaystyle\int_{-\pi/4}^{\pi/4} \frac{dx}{1 + \cos 2x}$ and $I_2 = \displaystyle\int_{-1/2}^{1/2} x \,dx$, then show that $I_1 - 4I_2 = 0$.

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#4 Class 12 Mathematics Integrals 2026 Short 3M CBSE

Find: $\displaystyle\int \frac{x^2}{(x^2+9)(x^2+16)}\,dx$

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#5 Class 12 Mathematics Integrals 2026 Short 3M CBSE

Find $\displaystyle\int \sqrt{\frac{x+2}{x-2}}\,dx$

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#6 Class 12 Mathematics Integrals 2026 Short 3M CBSE

Evaluate: $\displaystyle\int_{0}^{1} x\tan^{-1}x\,dx$

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#7 Class 12 Mathematics Inverse Trigonometric Functions 2026 Short 2M CBSE

Evaluate: $\tan\left(\sin^{-1}1 - \cos^{-1}\left(-\dfrac{1}{2}\right)\right)$

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#8 Class 12 Mathematics Inverse Trigonometric Functions 2026 Short 2M CBSE

Simplify: $\tan^{-1}\left(\dfrac{\cos 2x - \sin 2x}{\cos 2x + \sin 2x}\right)$, $0 < x < \dfrac{\pi}{4}$.

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#9 Class 12 Mathematics Vector Algebra 2026 Short 2M CBSE

Vectors $\vec{a} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{k}$ represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence find their lengths.

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#10 Class 12 Mathematics Vector Algebra 2026 Short 2M CBSE

Find the vector of magnitude 14 in the direction of $\vec{QP}$, where P and Q are the points $(1, 3, 2)$ and $(-1, 0, 8)$ respectively.

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#11 Class 12 Mathematics Application of Derivatives 2026 Short 2M CBSE

A room freshner bottle in the shape of an inverted cone sprays the perfume at regular intervals such that volume of the perfume in the bottle decreases at the steady rate of $1\ \text{mm}^3/\text{min}$. Find the rate ...

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#12 Class 12 Mathematics Continuity and Differentiability 2026 Short 2M CBSE

If $\sqrt{3}(x^2 + y^2) = 4xy$, then find $\dfrac{dy}{dx}$ at $\left(\dfrac{1}{2}, \dfrac{\sqrt{3}}{2}\right)$.

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#13 Class 12 Mathematics Continuity and Differentiability 2026 Short 2M CBSE

Check whether function $f(x)$ defined as $f(x) = \begin{cases} \dfrac{ x-3 }{2(x-3)}, & x < 3 \\[8pt] \dfrac{x-6}{6}, & x \ge 3 \end{cases}$ is continuous at $x = 3$ or not.

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#14 Class 12 Mathematics Three Dimensional Geometry 2026 Long 1M CBSE

Direction: Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes given below. Assertion (A): Lines given by $x = py + q$, $z = ry + s$ and $x ...

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#15 Class 12 Mathematics Probability 2026 Long 1M CBSE

Direction: Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes given below. Assertion (A): In an experiment of throwing an unbiased die, the...

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#16 Class 12 Mathematics Linear Programming 2026 Mcq 1M CBSE

The degree of an objective function of a linear programming problem is

A. $0$

B. $1$

C. $2$

D. Any natural number

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#17 Class 12 Mathematics Linear Programming 2026 Mcq 1M CBSE

The feasible region of a linear programming problem with objective function $Z = 5x + 7y$ is the shaded region shown in the graph, bounded by the corner points $(0, 0)$, $(0, 2)$, $(3, 4)$ and $(7, 0)$. The maximum va...

A. $8$

B. $29$

C. $35$

D. $43$

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#18 Class 12 Mathematics Three Dimensional Geometry 2026 Mcq 1M CBSE

The length of perpendicular drawn from point $(2, 5, 7)$ on line $\dfrac{x}{1} = \dfrac{y}{0} = \dfrac{z}{0}$ is

A. $2$

B. $5$

C. $\sqrt{74}$

D. $\sqrt{78}$

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#19 Class 12 Mathematics Vector Algebra 2026 Mcq 1M CBSE

If $ \vec{a} = 8$, $ \vec{b} = 3$ and $ \vec{a} \times \vec{b} = 12$, then the value of $ \vec{a}\cdot\vec{b} $ is

A. $6\sqrt{3}$

B. $8\sqrt{3}$

C. $12\sqrt{3}$

D. $3\sqrt{12}$

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#20 Class 12 Mathematics Vector Algebra 2026 Mcq 1M CBSE

The value of $m$ for which the points with position vectors $-\hat{i} - \hat{j} + 2\hat{k}$, $2\hat{i} + m\hat{j} + 5\hat{k}$ and $3\hat{i} + 11\hat{j} + 6\hat{k}$ are collinear, is

A. $8$

B. $-8$

C. $2$

D. $\dfrac{5}{2}$

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