BITSAT 2025 Question Paper 26th May Shift 1 (Available): Download Answer Key and Solution PDF

If \( \vec{a} = \hat{i} + 2\hat{j} - \hat{k} \), \( \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k} \), and \( \vec{c} = -\hat{i} + 3\hat{j} + 2\hat{k} \), find \( \vec{a} \cdot (\vec{b} \times \vec{c}) \).

• (1) \( 15 \)
• (2) \( -30 \)
• (3) \( 20 \)
• (4) \( -20

If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?

• (1) \( 166 \)
• (2) \( 216 \)
• (3) \( 234 \)
• (4) \( 252

From the top of a 60 m high building, the angles of depression to two points on the ground on the same side of the building are \( 30^\circ \) and \( 60^\circ \). What is the distance between the two points?

• (1) \( 40\sqrt{3} \, m \)
• (2) \( 20\sqrt{3} \, m \)
• (3) \( 60 \, m \)
• (4) \( 80 \, m

Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?

• (1) \( 12 \)
• (2) \( 16 \)
• (3) \( 14 \)
• (4) \( 10

Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).

• (1) \( 2500 \)
• (2) \( 2400 \)
• (3) \( 2600 \)
• (4) \( 2300

If \( \vec{p} = 3\hat{i} - \hat{j} + 2\hat{k} \), \( \vec{q} = \hat{i} + 4\hat{j} - \hat{k} \), and \( \vec{r} = 2\hat{i} - 3\hat{j} + 5\hat{k} \), find \( \vec{p} \cdot (\vec{q} \times \vec{r}) \).

• (1) \( 36 \)
• (2) \( -36 \)
• (3) \( 65 \)
• (4) \( -65 \)

If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?

• (1) \( 846 \)
• (2) \( 854 \)
• (3) \( 864 \)
• (4) \( 874 \)

Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?

• (1) \( 40 \)
• (2) \( 30 \)
• (3) \( 25 \)
• (4) \( 20 \)

From the top of a 50 m tall building, the angles of depression to two points on the ground are \( 45^\circ \) and \( 30^\circ \). Find the distance between the two points.

• (1) \( 20(\sqrt{3} - 1) \, m \)
• (2) \( 25(\sqrt{3} - 1) \, m \)
• (3) \( 30(\sqrt{3} - 1) \, m \)
• (4) \( 50(\sqrt{3} - 1) \, m \)

A projectile is launched with an initial velocity of \( 20 \, m/s \) at an angle of \( 30^\circ \) with the horizontal. What is the maximum height reached by the projectile?
(Take \( g = 10 \, m/s^2 \))

• (1) \( 5 \, m \)
• (2) \( 10 \, m \)
• (3) \( 15 \, m \)
• (4) \( 20 \, m \)

How much heat is required to raise the temperature of \( 2 \, kg \) of water from \( 25^\circ C \) to \( 75^\circ C \)? (Specific heat capacity of water \( c = 4200 \, J/kg^\circ C \))

• (1) \( 4.2 \times 10^5 \, J \)
• (2) \( 5.0 \times 10^5 \, J \)
• (3) \( 3.5 \times 10^5 \, J \)
• (4) \( 4.8 \times 10^5 \, J \)

Which of the following is the correct electronic configuration of \( \mathrm{Cr} \) (Chromium, atomic number 24)?

• (1) \( 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^4\,4s^2 \)
• (2) \( 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5\,4s^1 \)
• (3) \( 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6\,4s^0 \)
• (4) \( 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^3\,4s^3 \)

For the reaction \( A + B \to C \), the rate law is found to be \( rate = k[A]^2[B] \). If the concentration of \( A \) is doubled and \( B \) is halved, by what factor does the rate change?

• (1) \( 2 \)
• (2) \( \frac{1}{2} \)
• (3) \( 4 \)
• (4) \( 1 \)

In the reaction \( \mathrm{N_2(g)} + 3\mathrm{H_2(g)} \leftrightarrow 2\mathrm{NH_3(g)} \), if the equilibrium constant \( K_c = 4 \times 10^{-3} \) at a certain temperature, which of the following is true about the reaction at equilibrium?

• (1) Reactants are favored over products
• (2) Products are favored over reactants
• (3) Reactants and products are equally favored
• (4) Reaction does not reach equilibrium

In the electrolysis of molten \( \mathrm{NaCl} \), what is produced at the cathode?

• (1) Chlorine gas
• (2) Sodium metal
• (3) Hydrogen gas
• (4) Oxygen gas