Question 1:

One of the principal solutions of √3 sec(x) = -2 is equal to:

1. π/4
2. 2π/3
3. π/6
4. 5π/6

Question 2:

Integrate the following function with respect to x:

∫ e^(3x) / (e^(3x) + 1) dx

1. (1/3) ln(e^(3x) + 1) + C
2. (1/3) ln(e^(3x) - 1) + C
3. (1/3) ln(e^(3x) + e^x) + C
4. (1/2) ln(e^(3x) + 1) + C

Question 3:

The general solution of:

(x dy/dx - y) sin(y/x) = x³ e^x is:

1. e^x (x - 1) + cos(y/x) + c = 0
2. x e^x + cos(y/x) + c = 0
3. e^x (x + 1) + cos(y/x) + c = 0
4. e^x x - cos(y/x) + c = 0

Question 4:

Find the area of the region bounded by the parabola:

y² = 4ax and its latus rectum.

1. a²/2
2. a²
3. a²/4
4. 8a²/3

Question 5:

If p ∧ q is False and p → q is False, then the truth values of p and q are:

1. True, True
2. True, False
3. False, True
4. False, False

The inverse of the matrix:

    [
        [1, 0, 0],
        [3, 3, 0],
        [5, 2, -1]
    ]
    

is:

1.             (-1/3) * [
                   [-3, 0, 0],
                   [3, 0, 0],
                   [9, 2, -3]
               ]
               

2.             (-1/3) * [
                   [-3, 0, 0],
                   [3, -1, 0],
                   [-9, -2, 3]
               ]
               

3.             (-1/3) * [
                   [3, 0, 0],
                   [3, -1, 0],
                   [-9, -2, 3]
               ]
               

4.             (-1/3) * [
                   [-3, 0, 0],
                   [-3, -1, 0],
                   [-9, -2, 3]
               ]
               

Question 7:

What is the equivalent logic gate when the output of an AND gate is passed through a NOT gate?

1. OR gate
2. NOR gate
3. NAND gate
4. XOR gate

Question 8:

In Young's double-slit experiment, if the distance between the slits is doubled while keeping the wavelength and the distance to the screen constant, the fringe spacing will:

1. Double
2. Halve
3. Remain the same
4. Quadruple

In a series LCR circuit connected to an AC source, at resonance, the current is maximum because:

1. The inductive reactance is maximum
2. The capacitive reactance cancels the inductive reactance
3. The resistance is zero
4. The reactances add up

Question 10:

Butter is an example of which type of colloid?

1. Liquid in solid
2. Solid in liquid
3. Liquid in liquid
4. Gas in liquid

Question 11:

Which of the following techniques is most suitable for determining the size and morphology of nanoparticles?

1. UV-Vis Spectroscopy
2. Transmission Electron Microscopy (TEM)
3. Fourier Transform Infrared Spectroscopy (FTIR)
4. Atomic Absorption Spectroscopy (AAS)

What is the pH of a 0.01 M hydrochloric acid (HCl) solution?

1. 2
2. 4
3. 7
4. 12

Also Check:

MHT CET Previous Year Question Papers

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