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VITEEE
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Mathematics
List of top Mathematics Questions asked in VITEEE
If \( |\mathbf{a}| = 3 \), \( |\mathbf{b}| = 4 \), then the value of \( \lambda \) for which \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{a} - \lambda \mathbf{b} \) is:
VITEEE - 2023
VITEEE
Mathematics
Sequences and Series
The determinant of the matrix:
is:
VITEEE - 2023
VITEEE
Mathematics
Sequences and Series
The derivative of
\[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \]
with respect to
\[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \]
is equal to:
VITEEE - 2023
VITEEE
Mathematics
inequalities
The lines
\[ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 \]
are perpendicular to a common line for:
VITEEE - 2023
VITEEE
Mathematics
sets
If the function
\[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \]
is continuous at \( x = 2 \) and \( x = 4 \), then the values of \( a \) and \( b \) are:
VITEEE - 2023
VITEEE
Mathematics
Graphical Method of Analysis
The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2, respectively. Find \( P(X = 1) \).
VITEEE - 2023
VITEEE
Mathematics
Graphical Method of Analysis
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that:
\[ a b = \frac{a}{b + 1} \]
which of the following is true?
VITEEE - 2023
VITEEE
Mathematics
inequalities
Find the missing number in the sequence:
\[ 285, 253, 221, 189, ? \]
VITEEE - 2023
VITEEE
Mathematics
Sequences and Series
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:
VITEEE - 2023
VITEEE
Mathematics
Graphical Method of Analysis
The domain of the function
\[ f(x) = \frac{1}{\sqrt{9 - x^2}} \]
is:
VITEEE - 2023
VITEEE
Mathematics
Graphical Method of Analysis
The number of distinct real roots of the equation:
\[ x^7 - 7x - 2 = 0 \]
is:
VITEEE - 2023
VITEEE
Mathematics
Differential equations
Evaluate:
\[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]
VITEEE - 2023
VITEEE
Mathematics
Permutations
What is the percentage drop in the production of Ludo from 1992 to 1994?
VITEEE - 2023
VITEEE
Mathematics
Probability
The number of nonzero terms in the expansion of
\[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \]
is:
VITEEE - 2023
VITEEE
Mathematics
inequalities
The sum of the series
\[ \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots \]
up to 15 terms is:
VITEEE - 2023
VITEEE
Mathematics
inequalities
If
\[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \]
then
\( \frac{dy}{dx} \)
is:
VITEEE - 2023
VITEEE
Mathematics
inequalities
The particular solution of
\[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \]
is:
VITEEE - 2023
VITEEE
Mathematics
Probability
The angle between the two lines:
\[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \]
is:
VITEEE - 2023
VITEEE
Mathematics
Probability
If
\[ \sin x + \cos x = \frac{1}{5} \]
then
\( \tan 2x \)
is:
VITEEE - 2023
VITEEE
Mathematics
Differential equations
The equation of the circle with centre (0,2) and radius 2 is
\[ x^2 + y^2 - my = 0. \]
The value of \( m \) is:
VITEEE - 2023
VITEEE
Mathematics
inequalities
Evaluate the integral:
\[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
VITEEE - 2023
VITEEE
Mathematics
inequalities
The minimum value of the function
\[ y = x^4 - 2x^2 + 1 \]
in the interval
\( \left[\frac{1}{2}, 2 \right] \)
is:
VITEEE - 2023
VITEEE
Mathematics
Differential equations
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
VITEEE - 2023
VITEEE
Mathematics
sets
If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:
VITEEE - 2023
VITEEE
Mathematics
Tangents and Normals
Evaluate the definite integral:
\[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]
VITEEE - 2023
VITEEE
Mathematics
inequalities
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