List of top Mathematics Questions asked in VITEEE

$\quad\int_{0}^{1} \left[f \left(x\right)g'' \left(x\right)-f''\left(x\right)g \left(x\right)\right]$ dx is equal to : [Given f(0) = g(0) = 0]

The area bounded by f (x) $=x^{2}, 0 \le x \le 1, g\left(x\right)=x+2,1\le x\le2$ and x- axis is

Let A be the centre of the circle $x^{2}+y^{2}-2x-4y-20=0,$ and B( 1,7) andD(4,-2) are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadri 1 ateral A BCD is-

A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve $y^{2}=4x+5.$ Then the point of contact is

Equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos\, \theta represents$

Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is

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 logical expression \( X \), in its simplest form for the truth table \[ \begin{array}{|c|c|c|} \hline A & B & X \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array} \] is

If \( f(a + b - x) = f(x), \) then \( \int_a^b f(x) \, dx \) 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

The domain and range of the function \( f(x) = 2 - |x - 5| \) is

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

\[ \int x^2 (x^4 + 1)^{3/4} \, dx \text{ is equal to } \]

If \( y = 2^x \), then \[ \frac{dy}{dx} \, \text{at} \, x = e \, \text{is} \]

The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is

The solution of the equation \[ \sin^2\theta + \cos^2\theta = 1 \] lies in the interval

If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is

While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability that the missing cards to be of different colours is

A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is

The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is

Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is

The number of common tangents to the circles \( x^2 + y^2 = 16 \) and \( x^2 + y^2 - 6x = 0 \) is

Which of the following is INCORRECT for the hyperbola \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)?

If \( a = 1 \), \( b = 2 \), \( c = 3 \), and \( d = 4 \), then \[ abc = d \]