MHT-CET
Q. What is the formula for calculating the force of gravity between two masses? (2021)
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A.
F = ma
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B.
F = G(m1m2)/r²
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C.
F = mv
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D.
F = mgh
Solution
The formula for gravitational force is F = G(m1m2)/r², where G is the gravitational constant.
Correct Answer: B — F = G(m1m2)/r²
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Q. What is the formula for calculating the number of moles? (2023) 2023
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A.
Mass/Volume
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B.
Mass/Molar Mass
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C.
Volume/Mass
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D.
Molar Mass/Volume
Solution
The number of moles is calculated using the formula: Moles = Mass / Molar Mass.
Correct Answer: B — Mass/Molar Mass
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Q. What is the formula for the average power consumed in an AC circuit with a phase angle φ? (2020)
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A.
P = VI
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B.
P = VI cos(φ)
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C.
P = VI sin(φ)
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D.
P = V²/R
Solution
The average power P in an AC circuit is given by P = VI cos(φ), where φ is the phase angle.
Correct Answer: B — P = VI cos(φ)
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Q. What is the formula for the complex formed between iron(III) and thiocyanate? (2021)
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A.
[Fe(SCN)3]
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B.
[Fe(SCN)2]
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C.
[Fe(SCN)6]3+
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D.
[Fe(SCN)4]2-
Solution
The complex formed is [Fe(SCN)3] as iron(III) can bond with three thiocyanate ions.
Correct Answer: A — [Fe(SCN)3]
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Q. What is the formula for the resonant frequency of an RLC circuit? (2021)
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A.
f = 1/(2π√(LC))
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B.
f = R/(2πL)
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C.
f = 1/(2πRC)
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D.
f = 2π√(LC)
Solution
The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).
Correct Answer: A — f = 1/(2π√(LC))
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Q. What is the freezing point depression of a solution containing 1 mol of NaCl in 1 kg of water? (Kf for water = 1.86 °C kg/mol) (2023)
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A.
1.86 °C
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B.
3.72 °C
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C.
2.00 °C
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D.
0.93 °C
Solution
Freezing point depression (ΔTf) = i * Kf * m. For NaCl, i = 2 (dissociates into Na+ and Cl-). m = 1 mol/kg. ΔTf = 2 * 1.86 °C kg/mol * 1 = 3.72 °C.
Correct Answer: B — 3.72 °C
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Q. What is the frequency of a pendulum that completes 30 oscillations in 60 seconds? (2017)
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A.
0.5 Hz
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B.
1 Hz
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C.
2 Hz
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D.
3 Hz
Solution
Frequency f = number of oscillations / time = 30 / 60 = 0.5 Hz.
Correct Answer: B — 1 Hz
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Q. What is the frequency of a sound wave with a period of 0.01 seconds? (2014)
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A.
100 Hz
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B.
200 Hz
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C.
50 Hz
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D.
10 Hz
Solution
Frequency = 1/Period = 1/0.01 s = 100 Hz.
Correct Answer: A — 100 Hz
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Q. What is the frequency of a tuning fork that vibrates 256 times in 2 seconds? (2019)
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A.
128 Hz
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B.
256 Hz
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C.
512 Hz
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D.
64 Hz
Solution
Frequency (f) = Number of vibrations / Time = 256 / 2 = 128 Hz.
Correct Answer: A — 128 Hz
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Q. What is the frequency of a wave with a period of 0.01 s? (2020)
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A.
100 Hz
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B.
50 Hz
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C.
200 Hz
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D.
10 Hz
Solution
Frequency f = 1/T = 1/0.01 s = 100 Hz.
Correct Answer: A — 100 Hz
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Q. What is the frequency of a wave with a period of 0.1 s? (2020)
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A.
10 Hz
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B.
5 Hz
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C.
20 Hz
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D.
15 Hz
Solution
Frequency f = 1/T = 1/0.1 s = 10 Hz.
Correct Answer: A — 10 Hz
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Q. What is the frequency of a wave with a period of 0.2 seconds?
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A.
5 Hz
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B.
10 Hz
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C.
20 Hz
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D.
50 Hz
Solution
Frequency (f) is the reciprocal of the period (T). Therefore, f = 1/T = 1/0.2 s = 5 Hz.
Correct Answer: B — 10 Hz
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Q. What is the frequency of a wave with a period of 0.5 seconds? (2019)
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A.
2 Hz
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B.
1 Hz
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C.
0.5 Hz
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D.
4 Hz
Solution
Frequency (f) = 1/Period (T) = 1/0.5 s = 2 Hz.
Correct Answer: A — 2 Hz
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Q. What is the frequency of a wave with a speed of 300 m/s and a wavelength of 3 m? (2023)
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A.
100 Hz
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B.
150 Hz
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C.
200 Hz
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D.
250 Hz
Solution
Frequency (f) = speed (v) / wavelength (λ) = 300 m/s / 3 m = 100 Hz.
Correct Answer: B — 150 Hz
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Q. What is the frequency of a wave with a wavelength of 2 m and a speed of 340 m/s?
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A.
170 Hz
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B.
340 Hz
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C.
85 Hz
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D.
420 Hz
Solution
Frequency (f) is given by the formula f = speed / wavelength. Here, f = 340 m/s / 2 m = 170 Hz.
Correct Answer: A — 170 Hz
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Q. What is the functional group of alcohols? (2020)
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A.
-OH
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B.
-COOH
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C.
-CHO
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D.
-NH2
Solution
The functional group of alcohols is the hydroxyl group (-OH).
Correct Answer: A — -OH
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Q. What is the functional group of aldehydes?
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A.
-OH
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B.
-CHO
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C.
-C=O
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D.
-COOH
Solution
The functional group of aldehydes is -CHO.
Correct Answer: B — -CHO
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Q. What is the functional group of phenols? (2019) 2019
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A.
-OH
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B.
-COOH
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C.
-CHO
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D.
-NH2
Solution
Phenols contain a hydroxyl group (-OH) directly attached to an aromatic ring.
Correct Answer: A — -OH
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Q. What is the functional group present in alcohols? (2023) 2023
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A.
Aldehyde
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B.
Ketone
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C.
Hydroxyl
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D.
Carboxylic acid
Solution
Alcohols contain a hydroxyl (-OH) functional group.
Correct Answer: C — Hydroxyl
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Q. What is the functional group present in phenols? (2021)
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A.
-OH
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B.
-COOH
-
C.
-CHO
-
D.
-NH2
Solution
Phenols contain a hydroxyl group (-OH) directly attached to an aromatic hydrocarbon group.
Correct Answer: A — -OH
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Q. What is the functional group present in phenols? (2021) 2021
-
A.
-OH
-
B.
-COOH
-
C.
-CHO
-
D.
-NH2
Solution
Phenols contain a hydroxyl group (-OH) directly attached to an aromatic hydrocarbon group.
Correct Answer: A — -OH
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Q. What is the general formula for secondary amines? (2021) 2021
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A.
RNH2
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B.
R2NH
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C.
R3N
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D.
RNH
Solution
The general formula for secondary amines is R2NH, where R represents an alkyl or aryl group.
Correct Answer: B — R2NH
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Q. What is the general solution of the equation y' = 4y + 3?
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A.
y = Ce^(4x) - 3/4
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B.
y = Ce^(4x) + 3/4
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C.
y = 3e^(4x)
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D.
y = Ce^(3x) + 4
Solution
The integrating factor is e^(-4x). The solution is y = Ce^(4x) + 3/4.
Correct Answer: B — y = Ce^(4x) + 3/4
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Q. What is the general solution of the equation y'' - 3y' + 2y = 0?
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A.
y = C1 e^(x) + C2 e^(2x)
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B.
y = C1 e^(2x) + C2 e^(x)
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C.
y = C1 e^(3x) + C2 e^(0)
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D.
y = C1 e^(0) + C2 e^(3x)
Solution
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. Thus, the general solution is y = C1 e^(2x) + C2 e^(x).
Correct Answer: B — y = C1 e^(2x) + C2 e^(x)
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Q. What is the geometry of a molecule with two bonding pairs and no lone pairs on the central atom? (2023)
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A.
Linear
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B.
Trigonal planar
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C.
Tetrahedral
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D.
Bent
Solution
The geometry is linear when there are two bonding pairs and no lone pairs on the central atom.
Correct Answer: A — Linear
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Q. What is the geometry of the complex ion [Ag(NH3)2]+? (2019) 2019
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A.
Tetrahedral
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B.
Square planar
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C.
Octahedral
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D.
Linear
Solution
The complex [Ag(NH3)2]+ has a linear geometry due to the presence of two ligands around the silver ion.
Correct Answer: D — Linear
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Q. What is the gravitational potential energy of a 10 kg mass at a height of 10 m?
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A.
100 J
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B.
200 J
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C.
500 J
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D.
1000 J
Solution
Gravitational potential energy (PE) is given by PE = mgh. Here, PE = 10 kg * 9.81 m/s² * 10 m = 981 J.
Correct Answer: D — 1000 J
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Q. What is the gravitational potential energy of a 10 kg object at a height of 5 m? (g = 9.8 m/s²)
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A.
49 J
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B.
98 J
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C.
245 J
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D.
490 J
Solution
Gravitational potential energy (PE) is given by PE = mgh. Here, m = 10 kg, g = 9.8 m/s², and h = 5 m. PE = 10 * 9.8 * 5 = 490 J.
Correct Answer: B — 98 J
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Q. What is the gravitational potential energy of a 2 kg object at a height of 10 m? (2023)
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A.
20 J
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B.
15 J
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C.
10 J
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D.
25 J
Solution
Gravitational potential energy (PE) = mgh = 2 kg × 9.8 m/s² × 10 m = 196 J.
Correct Answer: A — 20 J
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Q. What is the group number of Alkali metals in the periodic table? (2023)
Solution
Alkali metals are located in group 1 of the periodic table.
Correct Answer: A — 1
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