List of top Mathematics Questions asked in VITEEE

The solution of the differential equation \[ (1 + y^2) + (x - e^{\tan^{-1}y}) \frac{dy}{dx} = 0 \] is

The probability of India winning a test match against Australia is $\frac{1}{2}$ assuming independence from match to match. The probability that in a match series India�s second win occurs at third test match is

If $g(x)$ is a polynomial satisfying $g (x) g(y) = g(x) + g(y) + g(xy) - 2 $ for all real $x$ and $y$ and $g (2) = 5$ then $\Lt_{x \to 3} g(x)$ 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

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

The equation of one of the common tangents to the parabola $y^2 = 8x$ and $x^2 + y^2 - 12x + 4 = 0$ is

The number of surjective functions from $A$ to $B$ where $A = \{1, 2, 3, 4 \}$ and $B = \{a, b\}$ is

The value of $ (1 + \omega - \omega^2)^7$ 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 $\vec{a} + \vec{b} + \vec{c} = 0$)

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 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

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

The matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 1 \end{pmatrix} \), then adj \( (A) \) is equal to

Using Rolle’s theorem, the equation \( a_0x^n + a_1x^{n-1} + \dots + a_n = 0 \) has at least one root between 0 and 1 if,

The solution of \( \frac{d^2x}{dy^2} = k \), where \( k \) is a non-zero constant, vanishes when \( y = 0 \) and tends to finite limit as \( y \to \infty \), is

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

From a city population, the probability of selecting a male or smoker is \( \frac{7}{10} \), a male smoker is \( \frac{2}{5} \) and a male, if a smoker is already selected, is \( \frac{3}{5} \). Then, the probability of

If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is

Which of the following inequality is true for \( x>0 \)?

The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is