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Sample Mock Test CET
15 questions · Physics, Chemistry, Maths · tap an option to check your answer
Physics
Q1. A small signal voltage V(t) = 0 sin(ωt) is applied across an ideal capacitor C. Which of the following statements is true?
Answer: A
For an AC circuit containing capacitor only, the phase difference between current and voltage is \( \frac{\pi}{2} \) (i.e. 90°). In this case current is ahead of voltage by \( \frac{\pi}{2} \). Hence, the power is given by \( P = V I \cos(\phi) \) where \( \phi = \) phase difference. Therefore, \( P = V I \cos(90°) = 0 \).
For an AC circuit containing capacitor only, the phase difference between current and voltage is \( \frac{\pi}{2} \) (i.e. 90°). In this case current is ahead of voltage by \( \frac{\pi}{2} \). Hence, the power is given by \( P = V I \cos(\phi) \) where \( \phi = \) phase difference. Therefore, \( P = V I \cos(90°) = 0 \).
Q2. If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
Answer: C
Surface tension (S) is defined as Force [F] per unit Length [L].
Therefore, the dimensional formula of surface tension is [MLT][L]^{-1} = [MLT^{-2}].
We also know that:
1. Energy (E) = Force × Displacement = [MLT^{-2}] [L] = [ML^{2}T^{-2}]
2. Velocity (v) = Displacement/Time = [L][T^{-1}]
Thus, substituting the dimensions into the surface tension gives:
S = Force / Length = [MLT^{-2}] / [L] = [MLT^{-2}].
Using E, v, and T as fundamental quantities gives us the formula [E v T^{-2}].
Surface tension (S) is defined as Force [F] per unit Length [L].
Therefore, the dimensional formula of surface tension is [MLT][L]^{-1} = [MLT^{-2}].
We also know that:
1. Energy (E) = Force × Displacement = [MLT^{-2}] [L] = [ML^{2}T^{-2}]
2. Velocity (v) = Displacement/Time = [L][T^{-1}]
Thus, substituting the dimensions into the surface tension gives:
S = Force / Length = [MLT^{-2}] / [L] = [MLT^{-2}].
Using E, v, and T as fundamental quantities gives us the formula [E v T^{-2}].
Q3. For the circuit given below, the Kirchhoff’s loop rule for the loop BCDEB is given by the equation
Answer: B
Applying KVL rule in loop BCDEB, we get the equation as \( R I + E - R_2 I_2 - R_3 I_3 = 0 \)
Applying KVL rule in loop BCDEB, we get the equation as \( R I + E - R_2 I_2 - R_3 I_3 = 0 \)
Q4. The escape velocity from the surface of the earth is \(v_e\). The escape velocity from the surface of a planet whose mass and radius are three times those of the earth, will be what?
Answer: A
Since escape velocity is proportional to \(\sqrt{\frac{M}{R}}\), for a planet with mass \(M_p = 3M_e\) and radius \(R_p = 3R_e\), we have \(v_{p} = \sqrt{\frac{3M_e}{3R_e}} = \sqrt{\frac{M_e}{R_e}} = v_e\). Thus, the escape velocity from the planet is \(v_e\).
Since escape velocity is proportional to \(\sqrt{\frac{M}{R}}\), for a planet with mass \(M_p = 3M_e\) and radius \(R_p = 3R_e\), we have \(v_{p} = \sqrt{\frac{3M_e}{3R_e}} = \sqrt{\frac{M_e}{R_e}} = v_e\). Thus, the escape velocity from the planet is \(v_e\).
Q5. In meter bridge, the balancing length from left is found to be 20 cm when standard resistance of 1Ω is in right gap. The value of unknown resistance is?
Answer: A
Let the unknown resistance be X. Then condition of Wheatstone bridge gives, \( \frac{X}{R} = \frac{20}{80} \) where, \( R = 1Ω \). Hence, unknown resistance is \( X = R \times \frac{20}{80} = 1 \times \frac{1}{4} = 0.25Ω \).
Let the unknown resistance be X. Then condition of Wheatstone bridge gives, \( \frac{X}{R} = \frac{20}{80} \) where, \( R = 1Ω \). Hence, unknown resistance is \( X = R \times \frac{20}{80} = 1 \times \frac{1}{4} = 0.25Ω \).
Chemistry
Q6. Camphor is often used in molecular mass determination because
Answer: C
Camphor is utilized in molecular mass determination due to its volatile nature, which allows it to be easily removed after use. This technique is known as Rast’s camphor method, where camphor acts as a solid solvent.
Camphor is utilized in molecular mass determination due to its volatile nature, which allows it to be easily removed after use. This technique is known as Rast’s camphor method, where camphor acts as a solid solvent.
Q7. Which one is a nucleophilic substitution reaction among the following?
Answer: B
The reaction CH3CH2CH2CHBr + NH2CH3 → CH3CH2CH2CH(NH2)CH3 represents nucleophilic substitution where the nucleophile (NH2CH3) substitutes the bromine atom in the alkyl bromide.
The reaction CH3CH2CH2CHBr + NH2CH3 → CH3CH2CH2CH(NH2)CH3 represents nucleophilic substitution where the nucleophile (NH2CH3) substitutes the bromine atom in the alkyl bromide.
Q8. Which of these is least likely to act as a Lewis base?
Answer: C
Lewis bases are electron pair donors. CO has a lone pair of electrons that can be donated, and F^- can also act as a Lewis base due to its negative charge. PF_3 has a lone pair on the phosphorus atom as well. However, BF_3 is an electron-deficient species and does not have a lone pair to donate, making it least likely to act as a Lewis base.
Lewis bases are electron pair donors. CO has a lone pair of electrons that can be donated, and F^- can also act as a Lewis base due to its negative charge. PF_3 has a lone pair on the phosphorus atom as well. However, BF_3 is an electron-deficient species and does not have a lone pair to donate, making it least likely to act as a Lewis base.
Q9. In the preparation of alkene from alcohol using Al₂O₃, which is the effective factor?
Answer: B
Temperature is the effective factor for the dehydration of alcohol by Al₂O₃ (alumina), which acts as a dehydrating reagent. Higher temperatures (350-380°C) favor the formation of alkenes, while lower temperatures (220-250°C) may lead to ether formation.
Temperature is the effective factor for the dehydration of alcohol by Al₂O₃ (alumina), which acts as a dehydrating reagent. Higher temperatures (350-380°C) favor the formation of alkenes, while lower temperatures (220-250°C) may lead to ether formation.
Q10. Which one of the following is an amine hormone?
Answer: A
Thyroxin is an amine hormone which is secreted by the thyroid gland.
Thyroxin is an amine hormone which is secreted by the thyroid gland.
Maths
Q11. Given that \( y = x \sin(x) \) is negative in the neighbourhood of \( -\frac{\pi}{6} \), what is the derivative \( \frac{dy}{dx} \)?
Answer: A
To differentiate \( y = x \sin(x) \), we apply the product rule: \( \frac{dy}{dx} = \sin(x) + x \cos(x) \). Given that \( y < 0 \) in the neighbourhood of \( -\frac{\pi}{6} \), we find the derivative at that point considering the signs of sine and cosine.
To differentiate \( y = x \sin(x) \), we apply the product rule: \( \frac{dy}{dx} = \sin(x) + x \cos(x) \). Given that \( y < 0 \) in the neighbourhood of \( -\frac{\pi}{6} \), we find the derivative at that point considering the signs of sine and cosine.
Q12. What type of differential equation is said to be partial?
Answer: C
A differential equation is classified as partial if there are two or more independent variables involved in the equation. For example, the equation \( \frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} = kz \) contains two independent variables, \( x \) and \( y \).
A differential equation is classified as partial if there are two or more independent variables involved in the equation. For example, the equation \( \frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} = kz \) contains two independent variables, \( x \) and \( y \).
Q13. The probability that the noted number is either 7 or 8 is
Answer: B
This problem involves multiple outcomes based on the result of a coin toss. The total outcomes for heads (rolling dice) and tails (picking cards) need to be calculated, factoring in the specific outcomes for 7 and 8. By calculating the probabilities for each outcome and combining them, we find that the probability of getting either 7 or 8 is \frac{193}{401}, so the correct answer is B: \frac{193}{401}.
This problem involves multiple outcomes based on the result of a coin toss. The total outcomes for heads (rolling dice) and tails (picking cards) need to be calculated, factoring in the specific outcomes for 7 and 8. By calculating the probabilities for each outcome and combining them, we find that the probability of getting either 7 or 8 is \frac{193}{401}, so the correct answer is B: \frac{193}{401}.
Q14. What is the limit of \( \lim_{x \to 0} \frac{\sin(x)}{x} \)?
Answer: B
The limit \( \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \) is a standard limit in calculus that can be proven using L'Hôpital's rule or the squeeze theorem.
The limit \( \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \) is a standard limit in calculus that can be proven using L'Hôpital's rule or the squeeze theorem.
Q15. If a, b, c are positive real numbers and a + b + c = 1, what can we conclude from the equations derived from the matrix properties?
Answer: B
From the derived equations, we find that for positive real numbers a, b, and c, the condition a + b + c = 1 holds true. This is important in establishing the relationship between the elements of the matrix.
From the derived equations, we find that for positive real numbers a, b, and c, the condition a + b + c = 1 holds true. This is important in establishing the relationship between the elements of the matrix.
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