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CBSE CLASS XII
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Mathematics
List of top Mathematics Questions asked in CBSE CLASS XII
Find:
\[ \int \frac{e^{4x} - 1}{e^{4x} + 1} \, dx. \]
CBSE CLASS XII
Mathematics
Integration
If \( f(x) = |\tan 2x| \), then find the value of \( f'(x) \) at \( x = \frac{\pi}{3} \).
CBSE CLASS XII
Mathematics
Differentiation
Find the domain of the function \( f(x) = \sin^{-1
(x^2 - 4) \). Also, find its range.}
CBSE CLASS XII
Mathematics
Domain of a Relation
Assertion (A):
For two non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( \vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a} \).
Reason (R):
For two non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( \vec{a} \times \vec{b} = -\vec{b} \times \vec{a} \).
CBSE CLASS XII
Mathematics
Vector Algebra
If a line makes an angle of \( 30^\circ \) with the positive direction of \( x \)-axis, \( 120^\circ \) with the positive direction of \( y \)-axis, then the angle which it makes with the positive direction of \( z \)-axis is:
CBSE CLASS XII
Mathematics
Trigonometric Ratios
Assertion (A):
For any symmetric matrix \( A \), \( B'A B \) is a skew-symmetric matrix.
Reason (R):
A square matrix \( P \) is skew-symmetric if \( P' = -P \).
CBSE CLASS XII
Mathematics
Matrix
The unit vector perpendicular to both vectors \( \hat{i} + \hat{k} \) and \( \hat{i} - \hat{k} \) is:
CBSE CLASS XII
Mathematics
Vector Algebra
Direction ratios of a vector parallel to the line \( \frac{x - 1}{2} = -y = \frac{2z + 1}{6} \) are:
CBSE CLASS XII
Mathematics
Circles
Let \( E \) be an event of a sample space \( S \) of an experiment, then \( P(S | E) \) is:
CBSE CLASS XII
Mathematics
Conditional Probability
The degree of the differential equation \( (y'')^2 + (y')^3 = x \sin(y') \) is:
CBSE CLASS XII
Mathematics
Differential Equations
If \( A = [a_{ij}] \) be a \( 3 \times 3 \) matrix, where \( a_{ij} = i - 3j \), then which of the following is \textbf{false
?}
CBSE CLASS XII
Mathematics
Matrix
The derivative of \( \tan^{-1}(x^2) \) w.r.t. \( x \) is:
CBSE CLASS XII
Mathematics
Trigonometric Ratios
The differential equation \( \frac{dy}{dx} = F(x, y) \) will not be a homogeneous differential equation, if \( F(x, y) \) is:
CBSE CLASS XII
Mathematics
Differential Equations
The common region determined by all the constraints of a linear programming problem is called:
CBSE CLASS XII
Mathematics
Linear Programming Problem and its Mathematical Formulation
For any two vectors \( \vec{a} \) and \( \vec{b} \), which of the following statements is always true?
CBSE CLASS XII
Mathematics
Vectors
The coordinates of the foot of the perpendicular drawn from the point \( (0, 1, 2) \) on the \( x \)-axis are given by:
CBSE CLASS XII
Mathematics
Properties of Lines
The function \( f(x) = x^3 - 3x^2 + 12x - 18 \) is:
CBSE CLASS XII
Mathematics
Functions
\( \int_{0}^{\pi/2} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \) is equal to:
CBSE CLASS XII
Mathematics
Some Properties of Definite Integrals
If \( \begin{vmatrix} -a & b & c
a & -b & c
a & b & -c \end{vmatrix} = kabc \), then the value of \( k \) is:
CBSE CLASS XII
Mathematics
Determinants
Let \( f : \mathbb{R}_+ \to [-5, \infty) \) be defined as \( f(x) = 9x^2 + 6x - 5 \), where \( \mathbb{R}_+ \) is the set of all non-negative real numbers. Then, \( f \) is:
CBSE CLASS XII
Mathematics
Functions
If the sum of all the elements of a \( 3 \times 3 \) scalar matrix is 9, then the product of all its elements is:
CBSE CLASS XII
Mathematics
Matrix
If \( A = \begin{bmatrix} -1 & a & 2 \\ 1 & 2 & x \\ 3 & 1 & 1 \end{bmatrix} \) and \( A^{-1} = \begin{bmatrix} 1 & -1 & 1 \\ -8 & 7 & -5 \\ b & y & 3 \end{bmatrix} \), find the value of \((a + x) - (b + y)\).
CBSE CLASS XII
Mathematics
Matrix
Evaluate:
\[ \int_{-2}^{2} \frac{x^3 + |x| + 1}{x^2 + 4|x| + 4} \, dx. \]
CBSE CLASS XII
Mathematics
Some Properties of Definite Integrals
Find:
\[ \int \frac{(3 \cos x - 2) \sin x}{5 - \sin^2 x - 4 \cos x} \, dx. \]
CBSE CLASS XII
Mathematics
Integration
Using integration, find the area of the ellipse:
\[ \frac{x^2}{16} + \frac{y^2}{4} = 1, \]
included between the lines \(x = -2\) and \(x = 2\).
CBSE CLASS XII
Mathematics
Integration
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