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#1 Class 12 Mathematics Integrals 2026 Short 3M CBSE
Find: $\displaystyle\int \frac{x+2}{\sqrt{9x - x^2}}\,dx$
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#2 Class 12 Mathematics Three Dimensional Geometry 2026 Short 2M CBSE
Find the co-ordinates of the point on the line $\vec{r} = -\hat{j} + 3\hat{k} + \lambda(2\hat{i} - 2\hat{j} + \hat{k})$ such that the sum of co-ordinates is 3.
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#3 Class 12 Mathematics Vector Algebra 2026 Short 2M CBSE
If $\vec{AB} = \hat{j} + \hat{k}$ and $\vec{AC} = 3\hat{i} - \hat{j} + 4\hat{k}$ represent the two vectors along the sides AB and AC of $\triangle ABC$, prove that the median $\vec{AD} = \dfrac{\vec{AB} + \vec{AC}}{2}...
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#4 Class 12 Mathematics Application of Derivatives 2026 Short 2M CBSE
If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.
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#5 Class 12 Mathematics Application of Derivatives 2026 Short 2M CBSE
Find the absolute maximum value of $f(x) = \cos x + \sin^2 x$, $x \in [0, \pi]$
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#6 Class 12 Mathematics Continuity and Differentiability 2026 Short 2M CBSE
If $x = a\sin^3 t$, $y = b\cos^3 t$, then find $\dfrac{dy}{dx}$ at $t = \dfrac{\pi}{4}$.
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#7 Class 12 Mathematics Relations and Functions 2026 Short 2M CBSE
Check whether $f : Z \times Z \to Z \times Z$ (where Z is the set of integers) defined as $f(x, y) = (2y, 3x)$ is injective or not.
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#8 Class 12 Mathematics Relations and Functions 2026 Short 2M CBSE
Check whether $f : R - \{3\} \to R$ defined as $f(x) = \dfrac{x-2}{x-3}$ is onto or not.
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#9 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): A line can have direction cosines $<1, 1, 1>$ Rea...
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#10 Class 12 Mathematics Vector Algebra 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. For two vectors $\vec{a}$ and $\vec{b}$: Assertion (A): $ \vec{a...
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#11 Class 12 Mathematics Probability 2026 Mcq 1M CBSE
For two events A and B such that $P(A) \ne 0$ and $P(B) \ne 1$, $P(A'/B') = $
A. $1 - P(A/B)$
B. $1 - P(A'/B)$
C. $\dfrac{1 - P(A \cap B)}{P(B')}$
D. $\dfrac{1 - P(A \cup B)}{P(B')}$
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#12 Class 12 Mathematics Linear Programming 2026 Mcq 1M CBSE
For the feasible region shown in the graph, bounded by the lines with intercepts $(0,5),(5,0)$ and $(0,3),(9,0)$, the non-trivial constraints of the linear programming problem are
A. $x + y \le 5$, $x + 3y \le 9$
B. $x + y \le 5$, $x + 3y \ge 9$
C. $x + y \ge 5$, $x + 3y \le 9$
D. $x + y \ge 5$, $3x + y \le 9$
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#13 Class 12 Mathematics Linear Programming 2026 Mcq 1M CBSE
In a linear programming problem, the linear function which has to be maximized or minimized is called
A. a feasible function
B. an objective function
C. an optimal function
D. a constraint
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#14 Class 12 Mathematics Three Dimensional Geometry 2026 Mcq 1M CBSE
Direction cosines of the line given by equations $\dfrac{2x-1}{4} = \dfrac{1-y}{3} = \dfrac{-z}{6}$ are
A. $2, -3, -6$
B. $\dfrac{2}{7}, \dfrac{-3}{7}, \dfrac{-6}{7}$
C. $\dfrac{2}{7}, \dfrac{-3}{7}, \dfrac{6}{7}$
D. $\dfrac{4}{\sqrt{61}}, \dfrac{-3}{\sqrt{61}}, \dfrac{-6}{\sqrt{61}}$
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#15 Class 12 Mathematics Three Dimensional Geometry 2026 Mcq 1M CBSE
Vector of magnitude 3 making equal angles with $x$ and $y$ axes and perpendicular to $z$ axis is
A. $\hat{i} + 2\sqrt{2}\hat{j}$
B. $3\hat{k}$
C. $\dfrac{3\sqrt{2}}{2}\hat{i} + \dfrac{3\sqrt{2}}{2}\hat{j}$
D. $\sqrt{3}\hat{i} + \sqrt{3}\hat{j} + \sqrt{3}\hat{k}$
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#16 Class 12 Mathematics Vector Algebra 2026 Mcq 1M CBSE
If $ \vec{a} = 5$ and $-2 \le \lambda \le 1$, then the sum of greatest and the smallest value of $ \lambda\vec{a} $ is
A. $-5$
B. $5$
C. $10$
D. $15$
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#17 Class 12 Mathematics Differential Equations 2026 Mcq 1M CBSE
The integrating factor of the differential equation $2x\dfrac{dy}{dx} - y = 3$ is
A. $\sqrt{x}$
B. $\dfrac{1}{\sqrt{x}}$
C. $e^{x}$
D. $e^{-x}$
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#18 Class 12 Mathematics Differential Equations 2026 Mcq 1M CBSE
The general solution of the differential equation $\dfrac{dy}{dx} = \dfrac{\sqrt{y}}{\sqrt{x}}$ is
A. $\log\sqrt{y} = \log\sqrt{x} + C$
B. $\sqrt{y} + \sqrt{x} = C$
C. $\sqrt{y} - \sqrt{x} = C$
D. $\log\sqrt{y} + \log\sqrt{x} = C$
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#19 Class 12 Mathematics Application of Integrals 2026 Mcq 1M CBSE
Which of the following expressions will give the area of region bounded by the curve $y = x^2$ and line $y = 16$?
A. $\displaystyle\int_{0}^{4} x^2\,dx$
B. $2\displaystyle\int_{0}^{4} x^2\,dx$
C. $\displaystyle\int_{0}^{16} \sqrt{y}\,dy$
D. $2\displaystyle\int_{0}^{16} \sqrt{y}\,dy$
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#20 Class 12 Mathematics Integrals 2026 Mcq 1M CBSE
If $\displaystyle\int_{0}^{2a} \frac{1}{1 + 4x^2}\,dx = \frac{\pi}{6}$, then the value of $a$ is
A. $\dfrac{\sqrt{3}}{4}$
B. $\dfrac{\sqrt{3}}{2}$
C. $\sqrt{3}$
D. $2\sqrt{3}$
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