List of top Mathematics Questions asked in VITEEE

The solution of the differential equation: \[ x^4 \frac{dy}{dx} + x^3 y + \csc(xy) = 0 \] is equal to:
Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$
If  \(f(x) = \frac{\log(\pi + x)}{\log(e + x) }\), then the function is:
If \( f(x) = \ln \left( \frac{x^2 + e}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
If the two lines \( l_1: \frac{x - 2}{3} = \frac{y + 1}{-2} = \frac{z - 2}{0} \) and \( l_2: \frac{x - 1}{1} = \frac{y + 3}{\alpha} = \frac{z + 5}{2} \) are perpendicular, then the angle between the lines \( l_2 \) and \( l_3: \frac{x - 1}{-3} = \frac{y - 2}{-2} = \frac{z - 0}{4} \) is:
Let the vectors \( \overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k} \) and \( \overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k} \) be two sides of a triangle ABC. If \( G \) is the centroid of \( \triangle ABC \), then \( \frac{22}{7} |\overrightarrow{AG}|^2 + 5 = \): (a) 25
The area bounded by \( y - 1 = |x| \) and \( y + 1 = |x| \) is: (a) \( \frac{1}{2} \)
If \( f(x) \) is continuous and \( \int_0^9 f(x) \, dx = 4 \), then the value of the integral \( \int_0^3 x \cdot f(x^2) \, dx \) is: (a) 2
The maximum area of a right-angled triangle with hypotenuse \( h \) is: (a) \( \frac{h^2}{2\sqrt{2}} \)
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is:
If \( A \) and \( B \) are the two real values of \( k \) for which the system of equations \( x + 2y + z = 1 \), \( x + 3y + 4z = k \), \( x + 5y + 10z = k^2 \) is consistent, then \( A + B = \): (a) 3
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?
The derivative of  \(\sin^2\)\(( \cot^{-1} {\sqrt {( \frac{1 + x}{1 - x}} })\) with respect to \( x \) is equal to: (a) 0
 
Let \( f(x) \) be defined as: \[f(x) = \begin{cases} 3 - x, & x<-3 \\ 6, & -3 \leq x \leq 3 \\ 3 + x, & x>3 \end{cases}\]
Let \( \alpha \) be the number of points of discontinuity of \( f(x) \) and \( \beta \) be the number of points where \( f(x) \) is not differentiable. Then, \( \alpha + \beta \) is:
If \( f(x) \) defined as given below, is continuous on \( R \), then the value of \( a + b \) is equal to: % Function Definition \[f(x) = \begin{cases} \sin x, & x \leq 0 \\ x^2 + a, & 0<x<1 \\ bx + 3, & 1 \leq x \leq 3 \\ -3, & x>3 \end{cases}\]
A, P, B are \( 3 \times 3 \) matrices. If \( |B| = 5 \), \( | BA^T | = 15 \), \( | P^T AP | = -27 \), then one of the values of \( | P | \) is:
Let \( n(A) = m \) and \( n(B) = n \), if the number of subsets of \( A \) is 56 more than that of subsets of \( B \), then \( m + n \) is equal to:
The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:
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:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
For which toy category has there been a continuous increase in production over the years?
Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:
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:

If 

and $(A + B)^2 = A^2 + B^2$ then $x + y$ is: