List of top Questions asked in VITEEE

The sum of the first n terms of the series \[ 1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2 + 2.6^2 + \cdots \] {is} \[ \frac{n(n + 1)^2}{2} { when n is even. When n is odd the sum is} \]
Coin is tossed till heads is obtained what is expectation of no. of coin tosses
The middle term in the expansion of \[ (10x + x^{10})^{10} \] {is:}
The modulus of \( (1 + i\sqrt{3})(2 + 2i) \) / \( (\sqrt{3} - i) \) is:

The local minimum value of the function \[ f(x) = 3 + |x|, \quad x \in \mathbb{R} \] is:

The total number of 3-digit numbers, the sum of whose digits is even, is equal to:

The function \( f(x) \) is given by:

\[ f(x) = \begin{cases} x \lfloor x \rfloor & \text{if } 0 \leq x < 2 \\ (x - 1)x & \text{if } 2 \leq x < 3 \end{cases} \]

The function is:

The equation of the plane which bisects the angle between the planes \[ 3x - 6y + 2z + 5 = 0 \quad {and} \quad 4x - 12y + 3z - 3 = 0 { which contains the origin is:} \]
The solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]
In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

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.

What is the average marks obtained by these seven students in History? (rounded off to two digits)
An accurate clock shows 8 O'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 20:00 (8 O'clock in the evening)?
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 cost price of the suitcase purchased by Samir? I. Samir got a 25 percent concession on the labelled price. II. Samir sold the suitcase for Rs. 2000 with 25 percent profit on the labelled price.

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

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.
What is the total marks obtained by Meera in all the subjects?
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. \[ 5, 11, 24, 51, 106, \_ ? \]
Water sample is reported to be highly polluted if BOD (Biological Oxygen Demand) value of sample becomes:
Water is:
Lyophilic sols are more stable than lyophobic sols because:

The partial pressure of \( CH_3OH(g) \), \( CO(g) \), and \( H_2(g) \) in an equilibrium mixture for the reaction:

\[ CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g) \]

are 2.0, 1.0, and 0.1 atm respectively at \( 427^\circ C \). The value of \( K_p \) for the decomposition of \( CH_3OH \) to \( CO \) and \( H_2 \) is:

The polymer used for optical lenses is: