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#1 Class 12 Mathematics Vector Algebra 2026 Mcq 1M CBSE
The value of $p$ for which vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $2\hat{i} - p\hat{j} + \hat{k}$ are perpendicular to each other is
A. $0$
B. $1$
C. $\dfrac{5}{2}$
D. $-\dfrac{5}{2}$
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#2 Class 12 Mathematics Differential Equations 2026 Mcq 1M CBSE
The order and degree of the differential equation $\dfrac{d}{dx}\left(e^{y}\right) = 0$ respectively are
A. $0, 1$
B. $1, 1$
C. $2, 1$
D. $1$, not defined
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#3 Class 12 Mathematics Differential Equations 2026 Mcq 1M CBSE
The integrating factor of differential equation $R\dfrac{dx}{dy} + Px = Q$ where P, Q, R are functions of $y$ is
A. $e^{\int \frac{P}{Q}dy}$
B. $e^{\int P\,dy}$
C. $e^{\int \frac{P}{R}dy}$
D. $e^{\int \frac{P}{R}dx}$
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#4 Class 12 Mathematics Application of Integrals 2026 Mcq 1M CBSE
The area bounded by the curve $y = x x $, $x$-axis and the ordinates $x = -1$ and $x = 1$ is given by
A. $0$
B. $\dfrac{1}{3}$
C. $\dfrac{2}{3}$
D. $\dfrac{4}{3}$
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#5 Class 12 Mathematics Integrals 2026 Mcq 1M CBSE
The value of $\displaystyle\int_{-1}^{1} \frac{x^3}{x^2 + 2 x + 1}\,dx$ is
A. $0$
B. $\log 2$
C. $2\log 2$
D. $\dfrac{1}{2}\log 2$
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#6 Class 12 Mathematics Integrals 2026 Mcq 1M CBSE
If $\displaystyle\int \frac{3ax}{b^2 + c^2x^2}\,dx = A\log\left b^2 + c^2x^2\right + K$, then the value of A is
A. $3a$
B. $\dfrac{3a}{2b^2}$
C. $\dfrac{3a}{b^2c^2}$
D. $\dfrac{3a}{2c^2}$
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#7 Class 12 Mathematics Application of Derivatives 2026 Mcq 1M CBSE
The least value of $f(x) = x^3 - 12x$, $x \in [0, 3]$ is
A. $-16$
B. $-9$
C. $0$
D. $16$
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#8 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric?
A. $AB$
B. $AB + BA$
C. $(A + B)^2$
D. $A - B$
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#9 Class 12 Mathematics Determinants 2026 Mcq 1M CBSE
One of the values of $x$ for which $\begin{vmatrix} \cos x & \sin x \\ -\cos x & \sin x \end{vmatrix} = 1$ is
A. $0$
B. $\dfrac{\pi}{4}$
C. $\dfrac{\pi}{3}$
D. $\dfrac{\pi}{2}$
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#10 Class 12 Mathematics Determinants 2026 Mcq 1M CBSE
If $\Delta_1 = \begin{vmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{vmatrix}$ and $\Delta_2 = \begin{vmatrix} 0 & 2 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 6 \end{vmatrix}$, then
A. $\Delta_1 = 2\Delta_2$
B. $\Delta_2 = -2\Delta_1$
C. $\Delta_1 = \Delta_2$
D. $\Delta_2 = -\Delta_1$
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#11 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
Which of the following properties is/are true for two matrices of suitable orders? (i) $(A + B)' = A' + B'$ (ii) $(A - B)' = B' - A'$ (iii) $(AB)' = A'B'$ (iv) $(kAB)' = kB'A'$ ($k$ is a scalar)
A. (i) only
B. (i), (ii) and (iii)
C. (i) and (ii)
D. (i) and (iv)
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#12 Class 12 Mathematics Matrices 2026 Mcq 1M CBSE
Which of the following cannot be the order of a row-matrix?
A. $2 \times 1$
B. $1 \times 2$
C. $1 \times 1$
D. $1 \times n$
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#13 Class 12 Mathematics Inverse Trigonometric Functions 2026 Mcq 1M CBSE
If $2\cos^{-1}x = y$, then
A. $0 \le y \le \pi$
B. $-\pi \le y \le \pi$
C. $0 \le y \le 2\pi$
D. $-\pi \le y \le 0$
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#14 Class 12 History Rebels and the Raj 2026 Long 4M CBSE
Read the passage — "What the Sepoys Thought" (Arzi/petition of rebel sepoys, 1857): "A century ago the British arrived in Hindostan... Our forefathers have always served them... By the mercy of God and with our assist...
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#15 Class 12 History Peasants Zamindars and the State 2026 Long 4M CBSE
Read the passage — "Trade between hill tribes and the plains, c. 1595" (Abu'l Fazl, describing trade in suba of Awadh): "From the northern mountains quantities of goods are carried on the backs of men, of stout ponies...
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#16 Class 12 History Peasants Zamindars and the State 2026 Long 4M CBSE
Read the passage — "How Buddhist texts were prepared and preserved": "The Buddha (and other teachers) taught orally – through discussion and debate. None of the Buddha's speeches were written down during his lifetime....
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#17 Class 12 History Colonialism and the Countryside 2026 Long 4M CBSE
Read the passage — "The Malabar Coast" (Periplus of the Erythraean Sea, 1st century CE): "They send large ships to these market-towns on account of the great quantity and bulk of pepper and malabathrum. There are impo...
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#18 Class 12 History Framing the Constitution – The Beginning of a New Era 2026 Long 4M CBSE
Read the passage — "Framing the Constitution": "The Indian Constitution, which came into effect on 26 January, 1950, has the dubious distinction of being the longest in the world. But its length and complexity are per...
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#19 Class 12 History Kinship, Caste and Class – Early Societies 2026 Long 4M CBSE
Read the passage — "How Silver Came to India" (Giovanni Careri, based on Bernier's account): "All the Gold and Silver, which circulates throughout the World at last Centres here. It is well known that as much of it co...
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#20 Class 12 History Thinkers Beliefs and Buildings 2026 Long 4M CBSE
Read the passage — "Verses from the Upanishads" (Chhandogya Upanishad, c. 6th century BCE): "The nature of the self: This self of mine within the heart, is smaller than paddy or barley or mustard or millet or the kern...
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