List of top Mathematics Questions asked in VITEEE

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

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

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

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

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

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

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

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

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

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

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

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

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 value of \( \sin^{-1} \left( \frac{1}{\sqrt{5}} \right) + \cot^{-1}(3) \) is

If \( a = \cos 2\alpha + \sin 2\alpha, b = \cos 2\beta + \sin 2\beta, c = \cos 2\gamma + \sin 2\gamma \) and \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma = 1 \), then \[ \sqrt{abc} = \text{?} \]

Consider the objective function \( Z = 40x + 50y \). The minimum number of constraints that are required to maximize \( Z \) are

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 mean of a binomial distribution is 25, then its standard deviation lies in the interval

The value of \( \cos \left( \cos^{-1} \left( \frac{1}{3} \right) \right) \) is equal to

If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is

The normal at the point \( (t_1, t_2) \) on the parabola, cuts the parabola again at the point whose parameter is

What is the area of a loop of the curve \( y = \sin 30^\circ \)?

The distance moved by the particle in time \( t \) is given by \[ s = t^3 - 12t^2 + 6t + 8 \] At the instant, when its acceleration is zero, its velocity is