List of top Questions asked in VITEEE

An electron of mass $9.0 \times 10^{-31} kg$ under the action of a magnetic field moves in a circle of radius $2\, cm$ at a speed of $3 \times 10^6 \, m/s$ . If a proton of mass $1.8 \times 10^{27} \, kg$ was to move in a circle of same radius in the same magnetic field, then its speed will become

A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is

Two points masses, $m$ each carrying charges $-q$ and $+q$ are attached to the ends of a mass less rigid non-conducting wire of length $'L'$. When this arrangement is placed in a uniform electric field, then it deflects through an angle $i$. The minimum time needed by rod to align itself along the field is

Two polaroids are kept crossed to each other. If one of them is rotated an angle $60^{\circ}$, the percentage of incident light now transmitted through the system is

If a line segment OP makes angles of $ \frac{\pi}{4}$ and $\frac{\pi }{3}$ with X-axis and Y-axis, respectively. Then, the direction cosines are

If $N$ is a set of natural numbers, then under binary operation $a ?b =a + b, (N, ?)$ is

On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

The normal at the point $(at_1^2 ,\, 2at_1)$ on the parabola meets the parabola again in the point $(at_1^2 ,\, 2at_2)$ , then

The two lines $x = my + n, z = py + q$ and $x = m'y + n',\, z = p'y + q'$ are perpendicular to each other, if

If p, q, r are simple propositions with truth values T, F, T, then the truth value of $\left(\sim p \vee q\right) \wedge \sim r \Rightarrow p $ is

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is

The area bounded by the curves $y = cos\, x$ and $y = sin \,x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is

At $t = 0$, the function $f \left(t\right) = \frac{sin\,t}{t}$ has

If p : It rains today, q : I go to school, r : I shall meet my friends and s : I shall go for a movie, then which of the following is the proportion? If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

If $(2, 7, 3)$ is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6\,x -12\,y -2\,z + 20 = 0$, then the coordinates of the other end of the diameter are

If line $y = 2\,x + c$ is a normal to the ellipse $\frac{x^2}{9} + \frac{y^2}{16} = 1 $, then

If \[ \Delta_r = \begin{vmatrix} 2r - 1 & mC_r & 1 \\ m^2 - 1 & 2^m & m + 1 \\ \sin^2(m^2) & \sin^2(m) & \sin^2(m + 1) \end{vmatrix}, \] then the value of \[ \sum_{r=0}^{m} \Delta_r \text{ is:} \]

If \[ \Delta(x) = \begin{vmatrix} 1 & \cos{x} & 1 - \cos{x} \\ 1 + \sin{x} & \cos{x} & 1 + \sin{x} - \cos{x} \\ \sin{x} & \sin{x} & 1 \end{vmatrix}, \] then \[ \int_0^{\frac{\pi}{4}} \Delta(x) \, dx \text{ is equal to:} \]

Let \( f'(x) \) be differentiable for all \( x \). If \( f(1) = -2 \) and \[ f'(x) \geq 2 \quad \forall x \in [1, 6], \] then:

If \( (m,n) \) is an integer solution of \( \int_1^\infty \left( 1 + y^2 \right) dy \), then the expression for \( (m, n) \) in terms of \( (m+1, n+1) \) is?

The area in the first quadrant between \( x^2 + y^2 = 4 \) and \( y = \sin x \) is?

The area bounded by \( y = x \) and \( lines |x| = 1 \) is?

If \[ A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}, \] then \( A \cdot \text{(adj A)} \) is equal to:

If there is an error of \( k% \) in measuring the edge of a cube, then the percent error in estimating its volume is:

If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to: