List of top Mathematics Questions asked in VITEEE

If the eccentricity of the hyperbola $x^{2}-y^{2} cos ec^{2} \alpha=25 is \sqrt{5}$ times the eccentricity of the ellipse $x^{2} cos ec^{2} \alpha+y^{2}=5, then \alpha$ is equal to :

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 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

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

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

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.

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

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 $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is

The value of $ (1 + \omega - \omega^2)^7$ is

If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ 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

What is the area of a loop of the curve $r = a \sin^3 \theta$ ?

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

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

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

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 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

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

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 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