List of top Questions asked in BITSAT- 2022

The number of different seven-digit numbers that can be written using only the digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is:
A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its sides are:
A six-faced die is a biased one. It is three times more likely to show an odd number than an even number. It is thrown twice. The probability that the sum of the numbers in two throws is even is:
The number of ways of arranging the letters of the word HAVANA so that V and N do not appear together is:
Let \(a, b\) be the solutions of \(x^2 + px + 1 = 0\) and \(c, d\) be the solution of \(x^2 + qx + 1 = 0\). If \((a - c)(b - c)\) and \((a + d)(b + d)\) are the solution of \(x^2 + ax + \beta = 0\), then \(\beta\) is equal to:
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:
In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of the AP is equal to the middle term of the GP, then the middle term of the entire sequence is:
A house subtends a right angle at the window of the opposite house and the angle of elevation of the window from the bottom of the first house is 60°. If the distance between the two houses is 6m, then the height of the first house is:
A spherical balloon is filled with \( 4500\pi \) cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of \( 72\pi \) cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:
If the sum of the coefficients in the expansion of \( (x + y)^n \) is 1024, then the value of the greatest coefficient in the expansion is:
If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:
Given \[ \frac{dy}{dx} \tan x = y \sec^2 x + \sin x, \quad {find the general solution:} \]
The area of the region bounded by the parabola \( (y - 2)^2 = (x - 1) \), the tangent to the parabola at the point \( (2, 3) \), and the X-axis is:
For each parabola \( y = x^2 + px + q \), meeting the coordinate axes at three distinct points, if circles are drawn through these points, then the family of circles must pass through:
If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of  \( \lambda \) such that the given system of equations has no solution is:

X reacts with chlorine (\({Cl}_2\)) under boiling conditions to form Benzotrichloride, which further reacts with \(H_3O^+\) to form Y. Identify X and Y.
\[ \textbf{X} \xrightarrow{{Cl}_2, \text{Boiling}} \textbf{Benzotrichloride} \xrightarrow{H_3O^+} \textbf{Y} \]
The number of \( 3{C} - 2{e}^- \) bonds present in diborane is:
The reaction of \( {C}_6{H}_5 {CH=CHCH}_3 \) with HBr produces:
Which of the following compounds is thermodynamically the most stable?
Glucose reacts with \( X \) number of molecules of phenylhydrazine to yield osazone. The value of \( X \) is:

Match the species in Column I with their types in Column II. 

A certain metal sulphide, M\(_2\)S\(_2\), is used extensively as a high temperature lubricant. If M\(_2\)S\(_2\) is 40.06 % by mass sulphur, the atomic mass of metal M is:

0.20 g of an organic compound gave 0.12 g of AgBr. By using Carius method, the % of bromine in the compound will be: