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#1 Class 12 Mathematics Application of Derivatives 2026 Mcq 1M CBSE
For $f(x) = x + \dfrac{1}{x}$ $(x \ne 0)$
A. local maximum value is 2
B. local minimum value is $-2$
C. local maximum value is $-2$
D. local minimum value < local maximum value
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#2 Class 12 Mathematics Continuity and Differentiability 2026 Mcq 1M CBSE
If $e^{-x} + e^{-y} = 2$, then $\dfrac{dy}{dx}$ is
A. $e^{x-y}$
B. $e^{y-x}$
C. $-e^{x-y}$
D. $-e^{y-x}$
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#3 Class 12 Mathematics Determinants 2026 Mcq 1M CBSE
If $\begin{vmatrix} -1 & -2 & 5 \\ -2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = -86$, then the sum of all possible values of $a$ is
A. $4$
B. $5$
C. $-4$
D. $9$
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#4 Class 12 Mathematics Determinants 2026 Mcq 1M CBSE
For a square matrix A, $(3A)^{-1} = $
A. $3A^{-1}$
B. $9A^{-1}$
C. $\dfrac{1}{3}A^{-1}$
D. $\dfrac{1}{9}A^{-1}$
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#5 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
If $A = \begin{bmatrix} \cos x & -\sin x \\ \sin x & \cos x \end{bmatrix}$ and $A + A' = I$, then the value of $x \in \left[0, \dfrac{\pi}{2}\right]$ is
A. $0$
B. $\dfrac{\pi}{4}$
C. $\dfrac{\pi}{3}$
D. $\dfrac{\pi}{2}$
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#6 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
If $A = \begin{bmatrix} 1 & a & b \\ -1 & 2 & c \\ 0 & 5 & 3 \end{bmatrix}$ is a symmetric matrix, then the value of $3a + b + c$ is
A. $2$
B. $6$
C. $4$
D. $0$
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#7 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
If A and B are square matrices of same order, then which of the following statements is/are always true? (i) $(A + B)(A - B) = A^2 - B^2$ (ii) $AB = BA$ (iii) $(A + B)^2 = A^2 + AB + BA + B^2$ (iv) $AB = 0 \Rightarrow...
A. Only (i) and (iii)
B. Only (ii) and (iii)
C. Only (iii)
D. Only (iii) and (iv)
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#8 Class 12 Mathematics Relations and Functions 2026 Mcq 1M CBSE
A relation R on set $A = \{1, 2, 3\}$ defined as $R = \{(1, 1), (2, 2), (1, 2)\}$ is
A. Reflexive only
B. Reflexive and Transitive
C. Symmetric and Transitive
D. Transitive only
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#9 Class 12 Mathematics Application of Integrals 2026 Long 4M CBSE
Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by $C_1 : x^2 + y^2 = 64$. There is a circular pond...
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#10 Class 12 Mathematics Probability 2026 Long 4M CBSE
In an online jackpot, there is one first prize of ₹3,00,000, two second prizes of ₹2,00,000 each and three third prizes of ₹50,000 each. A total of 1,00,000 jackpot tickets each costing ₹100 were sold there by raising...
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#11 Class 12 Mathematics Application of Derivatives 2026 Long 4M CBSE
An online delivery company in a city has 5000 subscribers and collects annual subscription fees of ₹300 per subscriber for unlimited free deliveries. The company wishes to increase the annual subscription fee. It is p...
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#12 Class 12 Mathematics Three Dimensional Geometry 2026 Long 5M CBSE
Check whether the lines given by $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$ and $\dfrac{x-4}{5} = \dfrac{y-1}{2} = z$ are parallel or not. If parallel, find the distance between them, otherwise find their poin...
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#13 Class 12 Mathematics Continuity and Differentiability 2026 Long 5M CBSE
If $x = \cos t$, $y = \cos mt$, prove that $(1 - x^2)\dfrac{d^2y}{dx^2} - x\dfrac{dy}{dx} + m^2y = 0$.
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#14 Class 12 Mathematics Determinants 2026 Long 5M CBSE
If $\begin{bmatrix} 3 & -1 & \sin 3x \\ -7 & 4 & \cos 2x \\ -11 & 7 & 2 \end{bmatrix}$ is a singular matrix, then find all values of $x$ where $x \in \left[0, \dfrac{\pi}{2}\right]$.
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#15 Class 12 Mathematics Determinants 2026 Long 5M CBSE
If $A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix}$, find $A^{-1}$ and use it to solve the following system of equations: $-2y + z = 7$, $2x - y - z = 8$, $x - 2y = 10$
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#16 Class 12 Mathematics Relations and Functions 2026 Long 5M CBSE
A function $f : R - \left\{\dfrac{3}{5}\right\} \longrightarrow R - \left\{\dfrac{3}{5}\right\}$ is defined as $f(x) = \dfrac{3x+2}{5x-3}$. Show that $f$ is one-one and onto.
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#17 Class 12 Mathematics Relations and Functions 2026 Long 5M CBSE
A relation R is defined on Z, the set of integers, as $R = \{(x, y) : x - y \text{ is divisible by a prime number 'p'},\ x, y \in Z\}$. Check whether R is an equivalence relation or not.
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#18 Class 12 Mathematics Probability 2026 Short 3M CBSE
The probability of simultaneous occurrence of atleast one of the two events X and Y is $a$. If the probability that exactly one of the events X, Y occurs is $b$, prove that $P(X') + P(Y') = 2 - 2a + b$.
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#19 Class 12 Mathematics Probability 2026 Short 3M CBSE
Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is dra...
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#20 Class 12 Mathematics Linear Programming 2026 Short 3M CBSE
Solve the following linear programming problem graphically: Minimize $Z = 13x - 15y$ Subject to constraints $x + y \le 7$, $2x - 3y + 6 \ge 0$, $x \ge 0,\ y \ge 0$
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