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CBSE CLASS XII
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Mathematics
List of top Mathematics Questions asked in CBSE CLASS XII
If
\(A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix}\)
, then the value of \( I - A + A^2 - A^3 + \ldots \) is:
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Matrices
Given that
\(( A)^{-1} = \frac{1}{7}\)
\( \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix}\)
, matrix \( A \) is:
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Matrices
The integrating factor of the differential equation \( (x + 2y^2) \frac{dy}{dx} = y \, (y>0) \) is:}
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Differential equations
A vector perpendicular to the line \( \vec{r} = \hat{i} + \hat{j} - \hat{k} + \lambda (3\hat{i} - \hat{j}) \) is:
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Vectors
If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}| = 1 \), \( |\vec{b}| = 2 \), and \( \vec{a} \cdot \vec{b} = \sqrt{3} \), then the angle between \( 2\vec{a} \) and \( -\vec{b} \) is:
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Vectors
Assertion (A):
The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of \( Z = x + 2y \) occurs at infinite points.
Reason (R):
The optimal solution of a LPP having bounded feasible region must occur at corner points.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Linear Programming Problem and its Mathematical Formulation
Assertion (A):
The relation \( R = \{(x, y) : (x + y) \text{ is a prime number and } x, y \in \mathbb{N}\} \) is not a reflexive relation.
Reason (R):
The number \( 2n \) is composite for all natural numbers \( n \).
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Relations
Find the principal value of \( \tan^{-1}(1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) \).
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Trigonometric Identities
Show that \( f(x) = \frac{4 \sin x}{2 + \cos x} - x \) is an increasing function of \( x \) in \( \left[ 0, \frac{\pi}{2} \right] \).
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Differentiation
If \( x^y = e^{x-y} \), prove that
\(\frac{dy}{dx} = \frac{\log x}{(1 + \log x)^{2}}\)
.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Logarithmic Differentiation
Evaluate:
\[ I = \int_{-\frac{1}{2}}^{\frac{1}{2}} \cos x \cdot \log \left( \frac{1 - x}{1 + x} \right) dx \]
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Integration
Find the particular solution of the differential equation \( \frac{dy}{dx} = y \cot 2x \), given that \( y\left(\frac{\pi}{4}\right) = 2 \).
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Differential equations
A card from a well-shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Probability
A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Probability Distribution
Solve the following linear programming problem graphically:
Maximise
\[ Z = 2x + 3y \]
Subject to the constraints:
\[ x + y \leq 6 \] \[ x \geq 2 \] \[ y \leq 3 \] \[ x, y \geq 0 \]
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Linear Programming Problem and its Mathematical Formulation
Find:
\(\int e^x\)
\(\frac{1}{(1+x^2)^{3/2}}\)
+
\(\frac{x}{\sqrt{1+x^2}} dx .\)
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Integration
Use the product of matrices
\(\begin{bmatrix} 1 & 2 & -3 \\ 3 & 2 & -2 \\ 2 & -1 & 1 \end{bmatrix}\)
\(\begin{bmatrix} 0 & 1 & 2 \\ -7 & -7 & -7 \\ 7 & 5 & -4 \end{bmatrix}\)
to solve the following system of equations: \[ x + 2y - 3z = 6 \] \[ 3x + 2y - 2z = 3 \] \[ 2x - y + z = 2 \]
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Matrices
Let \( A = \mathbb{R} - \{5\} \) and \( B = \mathbb{R} - \{1\} \). Consider the function \( f : A \to B \), defined by
\(f(x) = \frac{x - 3}{x - 5}\)
. Show that \( f \) is one-one and onto.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Relations and functions
Check whether the relation \( S \) in the set of real numbers \( \mathbb{R} \), defined by
\(S = \{(a, b) : a - b + \sqrt{2}\)
\(\text{ is an irrational number}\)
, is reflexive, symmetric, or transitive.}
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Relations and functions
What rebate in price of the calculator should the store give to maximise the revenue?
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Maxima and Minima
Find the probability that exactly two of them are selected.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Probability
How far is the star \( V \) from star \( A \)?
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Vectors
Using integration, find the area bounded by the ellipse \( 9x^2 + 25y^2 = 225 \), the lines \( x = -2, x = 2 \), and the X-axis.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Integration
Find \( P(G \cap \overline{H}) \), where \( G \) is the event of Jaspreet's selection and \( \overline{H} \) denotes the event that Rohit is not selected.
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Probability
What is the probability that at least one of them is selected?
CBSE CLASS XII - 2024
CBSE CLASS XII
Mathematics
Probability
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