List of top Questions asked in VITEEE

A layer of oil with density $724\, kg/m^3$ floats on water of density $1000\, kg/m^3$. A block floats at the oil-water interface with $1/6$ of its volume in oil and $5/6$ of its volume in water, as shown in the figure. What is the density of the block?
The current in an $L-R$ circuit builds up to $\left(3 / 4^{\text {th }}\right)$ of its steady state value in $4$ seconds. The time constant of this circuit is
For a current carrying inductor, emf associated is 20mV. Now, current through it changes from 6A to 2A in 2s. The coefficient of mutual inductance is
Hologram is based on phenomenon of
The wavelength of an electron for transition from a state $n_1$ to $n_2$ is $\frac{ 9}{8R}$. Which of the following wavelengths is possible for a transition from $n_2$ to $n_1$.
In shown fig, the circular loop of wire is moved with velocity towards the infinite current carrying wire. Then
If $i_1 = 3 \, \sin \, \omega t$ and $i_2 = 4 \, \cos \, \omega t$, then $i_3$ is
The value of $ (1 + \omega - \omega^2)^7$ is
If $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is
The number of surjective functions from $A$ to $B$ where $A = \{1, 2, 3, 4 \}$ and $B = \{a, b\}$ is
If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is
If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}| $ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)
The value of $ (1 + \omega - \omega^2)^7$ is
The equation of one of the common tangents to the parabola $y^2 = 8x$ and $x^2 + y^2 - 12x + 4 = 0$ is
What is the area of a loop of the curve $r = a \sin^3 \theta$ ?
A tetrahedron has vertices at $O (0, 0, 0), A (1, 2, 1) B (2, 1, 3) $ and $C (-1, 1, 2)$. Then the angle between the faces $OAB$ and $ABC$ will be
If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ is
In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.
If $e^x = y + \sqrt{ 1 + y^2}$ , then the value of y is
If the nuclear radius of $^{27}Al$ is 3.6 Fermi, the approximate nuclear radius of $^{64}Cu$ in Fermi is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
Which of the following reactions is used to prepare isobutane ?
The masses of three copper wires are in the ratio $2 : 3 : 5$ and their lengths are in the ratio $5 : 3 : 2$ .Then, the ratio of their electrical resistances is
In a potentiometer experiment, the balancing length of a cell is $560\, cm$. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \,cm$.The internal resistance of a cell is
Two sources of equal emf are connected to a resistance $R$. The internal resistance of these sources are $r_1$ and $r_2 (r_1 > r_2 )$. If the potential difference across the source having internal resistance $r_2$ is zero, then