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Sample Mock Test CET
15 questions · Physics, Chemistry, Maths · tap an option to check your answer
Physics
Q1. The position x of a particle varies with time t as \( x = at - bt^2 \). The acceleration of the particle will be zero at time t equals to
Answer: B
Acceleration, \( a = \frac{d^2x}{dt^2} \). From the given equation \( x = at - bt^2 \), differentiating gives \( v = a - 2bt \). Differentiating again gives \( a = -2b \). Setting this equation to zero gives \( 0 = -2b \) or \( t = \frac{a}{b} \).
Acceleration, \( a = \frac{d^2x}{dt^2} \). From the given equation \( x = at - bt^2 \), differentiating gives \( v = a - 2bt \). Differentiating again gives \( a = -2b \). Setting this equation to zero gives \( 0 = -2b \) or \( t = \frac{a}{b} \).
Q2. Sound waves travel at 350 m/s through warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air
Answer: B
Using the relation \(v = f \lambda\), we have for air \(350 = 700 \lambda_1\) leading to \(\lambda_1 = 0.5 m\) and for brass \(3500 = 700 \lambda_2\), leading to \(\lambda_2 = 5 m\). The ratio \(\frac{\lambda_2}{\lambda_1} = \frac{5}{0.5} = 10\) indicates that the wavelength increases by a factor of 10. Thus, the answer is (b).
Using the relation \(v = f \lambda\), we have for air \(350 = 700 \lambda_1\) leading to \(\lambda_1 = 0.5 m\) and for brass \(3500 = 700 \lambda_2\), leading to \(\lambda_2 = 5 m\). The ratio \(\frac{\lambda_2}{\lambda_1} = \frac{5}{0.5} = 10\) indicates that the wavelength increases by a factor of 10. Thus, the answer is (b).
Q3. Work done for rotating the coil by 180° against the torque is?
Answer: A
The work done for rotating the coil is given by \(W = -M B (cos \theta_1 - cos \theta_2)\). Given that the magnetic moment \(M = NIA\) and substituting for \(\theta_1 = 0°\) and \(\theta_2 = 180°\), we find that the work done is approximately \(9.5 \times 10^{-6} J = 9.5 \mu J\), the closest option is (a).
The work done for rotating the coil is given by \(W = -M B (cos \theta_1 - cos \theta_2)\). Given that the magnetic moment \(M = NIA\) and substituting for \(\theta_1 = 0°\) and \(\theta_2 = 180°\), we find that the work done is approximately \(9.5 \times 10^{-6} J = 9.5 \mu J\), the closest option is (a).
Q4. In any fission process the ratio \( \frac{mass \ of \ fission \ products}{mass \ of \ parent \ nucleus} \) is
Answer: A
In fission process, when a parent nucleus breaks into daughter products, then some mass is lost in the form of energy. Thus, \( \frac{mass \ of \ fission \ products}{mass \ of \ parent \ nucleus} < 1 \).
In fission process, when a parent nucleus breaks into daughter products, then some mass is lost in the form of energy. Thus, \( \frac{mass \ of \ fission \ products}{mass \ of \ parent \ nucleus} < 1 \).
Q5. In a n-type semiconductor, which of the following statement is true?
Answer: C
The n-type semiconductor can be produced by doping an impurity atom of valency 5, i.e. pentavalent atoms (phosphorus). Holes are minority carriers in them.
The n-type semiconductor can be produced by doping an impurity atom of valency 5, i.e. pentavalent atoms (phosphorus). Holes are minority carriers in them.
Chemistry
Q6. Match the coordination number and type of hybridisation with distribution of hybrid orbitals in space based on valence bond theory.
Answer: B
The correct matches are: A) 4, sp3 - III (tetrahedral), B) 4, dsp2 - IV (square planar), C) 5, sp3d - I (trigonal bipyramidal), D) 6, d2sp3 - II (octahedral). This is based on the coordination number and hybridization types.
The correct matches are: A) 4, sp3 - III (tetrahedral), B) 4, dsp2 - IV (square planar), C) 5, sp3d - I (trigonal bipyramidal), D) 6, d2sp3 - II (octahedral). This is based on the coordination number and hybridization types.
Q7. The reaction is described as
Answer: C
When the attack of the nucleophile takes place on the opposite side of the leaving group in the substrate molecule, a transition state is obtained. It is partially bonded to both the attacking nucleophile and the leaving group and results in the formation of product. Such reactions are called S₂N (bimolecular nucleophilic substitution reaction) because in such reactions, the rate depends on the concentration of both, the substrate and the nucleophile.
When the attack of the nucleophile takes place on the opposite side of the leaving group in the substrate molecule, a transition state is obtained. It is partially bonded to both the attacking nucleophile and the leaving group and results in the formation of product. Such reactions are called S₂N (bimolecular nucleophilic substitution reaction) because in such reactions, the rate depends on the concentration of both, the substrate and the nucleophile.
Q8. The correction factor ‘a’ to the ideal gas equation corresponds to
Answer: D
According to van der Waals’ equation, 'a' is a measure of force of attraction between gas molecules. Therefore, the correction factor ‘a’ corresponds to the forces of attraction between the gas molecules.
According to van der Waals’ equation, 'a' is a measure of force of attraction between gas molecules. Therefore, the correction factor ‘a’ corresponds to the forces of attraction between the gas molecules.
Q9. The name of complex ion, [Fe(CN) 6] 3− is
Answer: D
When complex ion is an anion, the name of the metal ends with suffix -ate along with its oxidation number in the complex ion. [Fe(CN) 6] 3− = Hexacyanoferrate (III) ion.
When complex ion is an anion, the name of the metal ends with suffix -ate along with its oxidation number in the complex ion. [Fe(CN) 6] 3− = Hexacyanoferrate (III) ion.
Q10. The hydrogen ion concentration of a 10⁻⁸ M HCl aqueous solution at 298 K is?
Answer: B
In a 10⁻⁸ M HCl solution, the concentration of H⁺ ions is influenced by both the H⁺ from HCl and the H⁺ from water. The concentration from water is 1 × 10⁻⁷ M. Therefore, the total concentration of hydrogen ions is:
\[ [H^+] = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7} M \approx 1.0525 \times 10^{-7} M. \]
Thus, the answer is (b).
In a 10⁻⁸ M HCl solution, the concentration of H⁺ ions is influenced by both the H⁺ from HCl and the H⁺ from water. The concentration from water is 1 × 10⁻⁷ M. Therefore, the total concentration of hydrogen ions is:
\[ [H^+] = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7} M \approx 1.0525 \times 10^{-7} M. \]
Thus, the answer is (b).
Maths
Q11. Find the angle between the X-axis and the line joining the points (3, –1) and (4, –2).
Answer: B
To find the angle \( q \) between the X-axis and the line joining the points (3, –1) and (4, –2), we first calculate the slope \( m \) of the line. Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), we have: \( m = \frac{-2 - (-1)}{4 - 3} = \frac{-1}{1} = -1 \). The angle \( q \) can be found using the tangent function: \( \tan(q) = m = -1 \). Therefore, \( q = \tan^{-1}(-1) \), which gives us \( q = -45° \). To find the angle in the standard position, we add 180° to get \( q = 135° \). Thus, the angle between the X-axis and the line is 135°.
To find the angle \( q \) between the X-axis and the line joining the points (3, –1) and (4, –2), we first calculate the slope \( m \) of the line. Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), we have: \( m = \frac{-2 - (-1)}{4 - 3} = \frac{-1}{1} = -1 \). The angle \( q \) can be found using the tangent function: \( \tan(q) = m = -1 \). Therefore, \( q = \tan^{-1}(-1) \), which gives us \( q = -45° \). To find the angle in the standard position, we add 180° to get \( q = 135° \). Thus, the angle between the X-axis and the line is 135°.
Q12. What is the probability that a chosen number is divisible by 3 or 4 given the numbers from 1 to 25?
Answer: A
The numbers divisible by 3 are {3, 6, 9, 12, 15, 18, 21, 24} (8 total). The numbers divisible by 4 are {4, 8, 12, 16, 20, 24} (6 total). The overlap (divisible by both) is {12, 24} (2 total). Using the formula for probability of union, P(3 or 4) = P(3) + P(4) - P(3 and 4). Thus, the required probability is (8 + 6 - 2) / 25 = 12/25.
The numbers divisible by 3 are {3, 6, 9, 12, 15, 18, 21, 24} (8 total). The numbers divisible by 4 are {4, 8, 12, 16, 20, 24} (6 total). The overlap (divisible by both) is {12, 24} (2 total). Using the formula for probability of union, P(3 or 4) = P(3) + P(4) - P(3 and 4). Thus, the required probability is (8 + 6 - 2) / 25 = 12/25.
Q13. Evaluate the limit: \( \lim_{x \to 0} \frac{\sin(x)}{x} \)
Answer: A
The limit \( \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \) is a standard result in calculus, derived using L'Hôpital's rule or the squeeze theorem.
The limit \( \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \) is a standard result in calculus, derived using L'Hôpital's rule or the squeeze theorem.
Q14. What is the mean of a discrete random variable defined as?
Answer: B
The mean of a discrete random variable is defined as the weighted average of all possible values, where each value is weighted by its probability, thus giving the expected value of the random variable.
The mean of a discrete random variable is defined as the weighted average of all possible values, where each value is weighted by its probability, thus giving the expected value of the random variable.
Q15. What is the sum of the angles in a triangle?
Answer: B
In Euclidean geometry, the sum of the angles in a triangle is always 180 degrees. This can be demonstrated through various methods, such as drawing a parallel line through one vertex of the triangle and using alternate interior angles.
In Euclidean geometry, the sum of the angles in a triangle is always 180 degrees. This can be demonstrated through various methods, such as drawing a parallel line through one vertex of the triangle and using alternate interior angles.
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