List of top Mathematics Questions asked in VITEEE

If \( f(x) = \cos^{-1 } \left( \frac{\sqrt{2x^2 + 1}}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
The range of \( 2 \left| \sin x + \cos x \right| - \sqrt{2} \) is:
If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: 
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:
Let \( f(x) \) be a polynomial function satisfying \[ f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right). \] If \( f(4) = 65 \) and \( I_1, I_2, I_3 \) are in GP, then \( f'(I_1), f'(I_2), f'(I_3) \) are in:
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:
Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$
The integral \( I = \int_{\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x + \frac{\pi}{4}}{2 - \cos 2x} \, dx \) is equal to:
The maximum area of a right-angled triangle with hypotenuse \( h \) is: (a) \( \frac{h^2}{2\sqrt{2}} \)
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
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:
The solution of the differential equation: \[ x^4 \frac{dy}{dx} + x^3 y + \csc(xy) = 0 \] is equal to:
A and B are independent events of a random experiment if and only if:
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?
If the solution of \[ \left( 1 + 2e^\frac{x}{y} \right) dx + 2e^\frac{x}{y} \left( 1 - \frac{x}{y} \right) dy = 0 \] is \[ x + \lambda y e^\frac{x}{y} = c \quad \text{(where \(c\) is an arbitrary constant), then \( \lambda \) is:} \]
In four schools \( B_1, B_2, B_3, B_4 \), the number of students is given as follows: \[ B_1 = 12, \quad B_2 = 20, \quad B_3 = 13, \quad B_4 = 17 \] A student is selected at random from any of the schools. The probability that the student is from school \( B_2 \) is:
The probability distribution of a random variable is given below: \[\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X = x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(X = x) & 0 & K & 2K & 2K & 3K & K^2 & 2K^2 & 7K^2 + K \\ \hline \end{array}\]

Find \( P(0<X<5) \).

The coefficient of \( x^{50} \) in \( (1 + x)^{101} (1 - x + x^2)^{100} \) is:
The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:
If \( z_r = \cos \frac{r\alpha}{n^2} + i \sin \frac{r\alpha}{n^2} \), where \( r = 1, 2, 3, ..., n \), then the value of \( \lim_{n \to \infty} z_1 z_2 z_3 ... z_n \) is:
Evaluate the limit: \[ L = \lim_{x \to 0} \frac{35^x - 7^x - 5^x + 1}{(e^x - e^{-x}) \ln(1 - 3x)} \]
The length of the perpendicular from the point \( (1, -2, 5) \) on the line passing through \( (1, 2, 4) \) and parallel to the line given by \( x + y - z = 0 \) and \( x - 2y + 3z - 5 = 0 \) is:
The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
The area bounded by \( y - 1 = |x| \) and \( y + 1 = |x| \) is: (a) \( \frac{1}{2} \)