BITSAT 2025 Question Paper 28th May Shift 2 (Available): Download Solutions with Answer Key

The quadratic equation \( x^2 - 5x + k = 0 \) has equal roots. Find the value of \( k \).

• (A) \( 6 \)
• (B) \( \frac{25}{4} \)
• (C) \( \frac{9}{4} \)
• (D) \( 0 \)

If the sum of the first \( n \) terms of an arithmetic progression is given by \( S_n = 3n^2 + 5n \), find the first term \( a \) and common difference \( d \).

• (A) \( a=8, d=6 \)
• (B) \( a=8, d=3 \)
• (C) \( a=5, d=6 \)
• (D) \( a=3, d=5 \)

If \(\sin \theta = \frac{3}{5}\) and \(\theta\) lies in the first quadrant, find \(\cos \theta\).

• (A) \(\frac{4}{5}\)
• (B) \(\frac{3}{4}\)
• (C) \(\frac{5}{3}\)
• (D) \(\frac{5}{4}\)

How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?

• (A) 360
• (B) 720
• (C) 840
• (D) 1260

Find the equation of the circle which passes through the points \( (1,2) \), \( (4,3) \) and has its center on the line \( x + y = 5 \).

• (A) \( (x - 2)^2 + (y - 3)^2 = 5 \)
• (B) \( (x - 3)^2 + (y - 2)^2 = 2 \)
• (C) \( (x - 2.5)^2 + (y - 2.5)^2 = 2.5) \)
• (D) \( (x - 2)^2 + (y - 3)^2 = 2 \)

Find the equation of the tangent to the curve \( y = x^3 - 3x + 1 \) at the point where \( x = 2 \).

• (A) \( y = 9x - 19 \)
• (B) \( y = 9x - 15 \)
• (C) \( y = 13x - 23 \)
• (D) \( y = 15x - 25 \)

Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?

• (A) \(\frac{1}{6}\)
• (B) \(\frac{1}{9}\)
• (C) \(\frac{1}{12}\)
• (D) \(\frac{1}{18}\)

If \(\log_2 (x-1) + \log_2 (x-3) = 3\), find the value(s) of \( x \).

• (A) \(5\)
• (B) \(4\)
• (C) \(3\) and \(5\)
• (D) \(4\) and \(5\)

If \[ A = \begin{pmatrix} 2 & 3
1 & k \end{pmatrix} \]
and \(\det(A) = 7\), find the value of \( k \).

• (A) \(1\)
• (B) \(2\)
• (C) \(5\)
• (D) \(4\)

Find the sum of the infinite geometric series: \[ S = 8 + 4 + 2 + \cdots \]
if it converges.

• (A) \(14\)
• (B) \(16\)
• (C) \(18\)
• (D) \(20\)

A particle is projected vertically upward with an initial velocity of \( 20 \, m/s \). Calculate the maximum height reached by the particle.

• (A) \(20 \, m\)
• (B) \(15 \, m\)
• (C) \(10 \, m\)
• (D) \(25 \, m\)

How much heat is required to raise the temperature of \( 2 \, kg \) of water from \( 20^\circ C \) to \( 80^\circ C \)? (Specific heat capacity of water = \( 4200 \, J/kg^\circ C \))

• (A) \(504000 \, J\)
• (B) \(50400 \, J\)
• (C) \(126000 \, J\)
• (D) \(168000 \, J\)

A resistor of resistance \( 10\, \Omega \) is connected across a \( 20\, V \) battery. Calculate the current flowing through the resistor.

• (A) \(1\, A\)
• (B) \(2\, A\)
• (C) \(0.5\, A\)
• (D) \(4\, A\)

An object is placed \( 30\, cm \) in front of a convex lens of focal length \( 20\, cm \). Find the position of the image.

• (A) \(60\, cm\)
• (B) \(12\, cm\)
• (C) \(15\, cm\)
• (D) \(10\, cm\)

The rate constant \( k \) of a reaction doubles when the temperature is raised from 300 K to 310 K. Calculate the activation energy \( E_a \) of the reaction. (Use \( R = 8.314 \, J/mol\cdot K \))

• (A) \( 52 \, kJ/mol \)
• (B) \( 55 \, kJ/mol \)
• (C) \( 53 \, kJ/mol \)
• (D) \( 60 \, kJ/mol \)

Calculate the de Broglie wavelength of an electron moving with velocity \( 6 \times 10^6 \, m/s \). (Mass of electron \( m = 9.11 \times 10^{-31} \, kg \), Planck's constant \( h = 6.626 \times 10^{-34} \, Js \))

• (A) \(1.2 \times 10^{-10} \, m\)
• (B) \(1.1 \times 10^{-10} \, m\)
• (C) \(1.0 \times 10^{-10} \, m\)
• (D) \(0.9 \times 10^{-10} \, m\)

Which of the following molecules has a trigonal planar shape?

• (A) \( \mathrm{CH_4} \)
• (B) \( \mathrm{BF_3} \)
• (C) \( \mathrm{NH_3} \)
• (D) \( \mathrm{H_2O} \)

Choose the word which is closest in meaning to “Eloquent”.

• (A) Silent
• (B) Fluent
• (C) Awkward
• (D) Hesitant

Identify the part of the sentence that contains an error:

"Neither the manager nor the employees ___ willing to accept the new policy."

• (A) Neither the manager
• (B) nor the employees
• (C) willing
• (D) to accept the new policy

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."

Question: What is the main idea of the passage?

• (A) The economy is not affected by climate change.
• (B) Climate change is a minor issue.
• (C) Immediate action is needed to combat climate change.
• (D) Health is unrelated to climate change.

Choose the word which is most opposite in meaning to “Benevolent”.

• (A) Kind
• (B) Cruel
• (C) Generous
• (D) Compassionate

Choose the best alternative to improve the underlined part:

"She gave a beautiful speech, which everyone enjoyed it."

• (A) which everyone enjoyed
• (B) that everyone enjoyed
• (C) whom everyone enjoyed
• (D) who everyone enjoyed

Identify the part of the sentence which contains a grammatical error:

"Each of the students have submitted their assignments on time."

• (A) Each of the students
• (B) have submitted
• (C) their assignments
• (D) on time