List of top Questions asked in VITEEE

Let \( R \) be a relation on the set \( \mathbb{N} \) defined by \[ \{(x, y) \mid x, y \in \mathbb{N}, \, 2x + y = 41\}. \] {Then, \( R \) is:}
The solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]

The value of the definite integral

\[ \int_0^{\frac{\pi}{2}} \log(\tan x) \, dx \]

is:

The relationship between \( a \) and \( b \) so that the function \( f(x) \) defined by

\[ f(x) = \begin{cases} ax + 1, & \text{if } x \leq 3 \\ bx + 3, & \text{if } x > 3 \end{cases} \]

is continuous at \( x = 3 \), is:

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \] is:

A parabola has the origin as its focus and the line \( x = 2 \)  as the directrix. Then the vertex of the parabola is at:

The variance of the data \( 2, 4, 6, 8, 10 \) is:

The point \( (t^2 + 2t + 5, 2t^2 + t - 2) \) { lies on the line} \( x + y = 2 \) { for:}
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. \[ 5, 11, 24, 51, 106, \_ ? \]

Two statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. 
Statements: 1. All utensils are spoons. 
2. All bowls are spoons. 
Conclusions: I. No utensil is a bowl. II. Some utensils are bowls. III. No spoon is a utensil.

How many students have got 60% or more marks in all the subjects?

What is the total marks obtained by Meera in all the subjects?
What is the average marks obtained by these seven students in History? (rounded off to two digits)
Kailash faces towards north. Turnings to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his right. He then turns to the right again and walks 55 metres. Finally, he turns to the right and moves 40 metres. In which direction is he now from his starting point?
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is:
What was the ratio between the ages of P and Q four years ago? I. The ratio between the present ages of P and Q is 3 : 4. II. The ratio between the present ages of Q and R is 4 : 5.
Carboxylic acids are more acidic than phenol and alcohol because of:
The polymer used for optical lenses is:
The value of van der Waals constant ' a ' for gases \( {O}_2 \), \( {N}_2 \), \( {NH}_3 \), and \( {CH}_4 \) are 1.360, 1.390, 4.170, and 2.253 L\(^2\)atm/mol\(^2\) respectively. The gas which can most easily be liquefied is:
Water is:

The limiting equivalent conductivity of NaCl, KCl, and KBr are \( 126.5 \), \( 150.0 \), and \( 151.5 \) S cm\(^2\) eq\(^{-1}\), respectively. The limiting equivalent ionic conductivity for Br\(^{-}\) is \( 78 \) S cm\(^2\) eq\(^{-1}\). The limiting equivalent ionic conductivity for Na\(^+\) ions would be:

Water sample is reported to be highly polluted if BOD (Biological Oxygen Demand) value of sample becomes:
The correct order of thermal stability of hydroxides is:
The order of increasing sizes of atomic radii among the elements O, S, Se, and As is:

The shape of \([ \text{Cu}(\text{NH}_3)_4 ]^{2+}\) is: