List of top Questions asked in BITSAT

If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
Find the derivative of \( y = \sin(x^2) \) with respect to \( x \).
Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?
If $$ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix} $$ and $\det(A) = 7$, find the value of $ k $.
Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$
A box contains 5 red balls and 4 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green, given that the first ball drawn was red?
The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
What is the value of \(\int \frac{1}{x^2 + 1} \, dx\)?
Find the equation of the tangent to the curve \(y = x^2\) at the point (1,1).
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is the value of \( \sin \theta \cos \theta \)?
Identify the next number in the series: 2, 6, 12, 20, ?
Rearrange the following parts to form a meaningful sentence:
P. technological advancement
Q. has led to
R. in many fields
S. a significant leap
Choose the word most opposite in meaning to "Candid":
Which number comes next in the series? 3, 6, 11, 18, 27, ?
Choose the word opposite in meaning to: "Benevolent"
Read the passage and answer the question:
"Climate change is one of the biggest challenges facing humanity. It affects the environment, economy, and health. Immediate action is required to reduce greenhouse gas emissions."
What is the main idea of the passage?
In a certain code, "CAT" is written as "DBU." How is "DOG" written in that code?
Choose the correct word to complete the sentence: “She was so tired that she could ......... keep her eyes open.”

Statement: All flowers are beautiful. Some beautiful things are fragile.
Conclusion I: Some flowers are fragile. 
Conclusion II: All beautiful things are flowers.

Choose the word closest in meaning to 'Candid'.
Identify the part of the sentence that contains an error:
He did not knew that the train had already left.

Choose the correct meaning of the idiom “to throw in the towel”