List of top Questions asked in VITEEE- 2016

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

Direction: This question presents a sentence, part of which or all of which is underlined. Beneath the sentence you will find four ways of phrasing the underlined part. The first of these repeats the original; the other three are different. If you think the original is best, choose the first answer; otherwise choose one of the others. The administration discussed whether the number of students studying European languages was likely to decline when the senior lecturer retired.

Choose the best pronunciation of the word, Restaurant, from the following options.

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

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

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

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

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

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

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

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

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

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 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 \[ \sqrt{abc} = \text{?} \]

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