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#1 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
If A and B are skew-symmetric matrices of same order, then $AB' + BA'$ is a/an:
A. symmetric matrix
B. skew-symmetric matrix
C. null matrix
D. identity matrix
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#2 Class 12 Mathematics Determinants 2026 Mcq 1M CBSE
If $A^2 = 4A + 3I$ and $A^{-1} = xA + yI$, then the value of $(x + y)$ is:
A. $-1$
B. $1$
C. $\dfrac{5}{3}$
D. $7$
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#3 Class 12 Mathematics Inverse Trigonometric Functions 2026 Mcq 1M CBSE
The domain of $f(x) = \cos^{-1}(2x - 5)$ is:
A. $[-1, 1]$
B. $[4, 6]$
C. $[-7, -3]$
D. $[2, 3]$
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#4 Class 12 Mathematics Continuity and Differentiability 2026 Long 4M CBSE
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows: $f(x) = \begin{case...
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#5 Class 12 Mathematics Application of Integrals 2026 Long 4M CBSE
A racing track is built around an elliptical ground whose equation is given by $9x^2 + 16y^2 = 144$. The width of the track is 3 m. Based on given information, answer the following questions: (i) Express y as a functi...
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#6 Class 12 Mathematics Probability 2026 Long 4M CBSE
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people ...
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#7 Class 12 Mathematics Three Dimensional Geometry 2026 Long 5M CBSE
A line passing through the points A$(1, 2, 3)$ and B$(5, 8, 11)$ intersects the line $\vec{r} = 4\hat{i} + \hat{j} + \lambda(5\hat{i} + 2\hat{j} + \hat{k})$. Find the co-ordinates of the point of intersection. Hence, ...
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#8 Class 12 Mathematics Inverse Trigonometric Functions 2026 Long 5M CBSE
Find the domain of $g(x) = \cos^{-1}(x^2 - 1)$. Hence, find the value of $x$ for which $g(x) = \dfrac{\pi}{3}$. Also, write the range of $\cos^{-1}x$ other than its principal branch.
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#9 Class 12 Mathematics Application of Derivatives 2026 Long 5M CBSE
A rectangle of perimeter 36 cm is revolved around one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
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#10 Class 12 Mathematics Application of Derivatives 2026 Long 5M CBSE
Find the sub intervals in which $f(x) = \cot^{-1}(\sin x + \cos x)$, $x \in (0, \pi)$ is increasing and decreasing.
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#11 Class 12 Mathematics Determinants 2026 Long 5M CBSE
Obtain the value of $\Delta = \begin{vmatrix} 1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z \end{vmatrix}$ in terms of $x$, y and z. Further, if $\Delta = 0$ and $x$, y, z are non-zero real numbers, prove that $x^{-1} + y...
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#12 Class 12 Mathematics Determinants 2026 Long 5M CBSE
If $P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{bmatrix}$, find $(QP)$ and hence solve the following system of equation...
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#13 Class 12 Mathematics Probability 2026 Short 3M CBSE
Mother, Father and Son line up at random for a family picture. Let events E : Son on one end and F : Father in the middle. Find $P(E/F)$.
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#14 Class 12 Mathematics Probability 2026 Short 3M CBSE
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when ...
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#15 Class 12 Mathematics Linear Programming 2026 Short 3M CBSE
Solve the following linear programming problem graphically: Maximize $Z = 10500x + 9000y$ Subject to constraints $x + y \le 50$ $2x + y \le 80$ $x, y \ge 0$
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#16 Class 12 Mathematics Differential Equations 2026 Short 3M CBSE
Find the general solution of the differential equation: $y\log y\,\dfrac{dx}{dy} + x = \dfrac{2}{y}$
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#17 Class 12 Mathematics Differential Equations 2026 Short 3M CBSE
Solve the following differential equation: $x\dfrac{dy}{dx} = y - x\sin^2\left(\dfrac{y}{x}\right)$, given that $y(1) = \dfrac{\pi}{6}$
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#18 Class 12 Mathematics Integrals 2026 Short 3M CBSE
If $\dfrac{d}{dx}\left(F(x)\right) = \dfrac{1}{e^x + 1}$, then find $F(x)$ given that $F(0) = \log\dfrac{1}{2}$.
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#19 Class 12 Mathematics Integrals 2026 Short 3M CBSE
Evaluate: $\displaystyle\int_{-\pi/6}^{\pi/2} \left(\sin x + \cos x \right)dx$
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#20 Class 12 Mathematics Integrals 2026 Short 3M CBSE
Evaluate: $\displaystyle\int_{\pi/12}^{5\pi/12} \frac{dx}{1 + \sqrt{\cot x}}$
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