List of top Questions asked in VITEEE

The resistivity (\( \rho \)) of a semiconductor varies with temperature. Which of the following curves represents the correct behavior?

A long straight wire of circular cross-section (radius \( a \)) is carrying a steady current \( I \). The current \( I \) is uniformly distributed across this cross-section. The magnetic field is:

If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]

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

If \( f(x) = \cos^{-1 } \left( \frac{\sqrt{2x^2 + 1}}{x^2 + 1} \right) \), then the range of \( f(x) \) 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:

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

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:

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

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:

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:

Evaluate the integral: \[ \int_{-\pi}^{\pi} x^2 \sin(x) \, dx \]

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 and B are independent events of a random experiment if and only if:

Negation of the statement \( (p \land r) \rightarrow (r \lor q) \) is:

Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to