MHT CET Mock Test

A parallel plate capacitor has a capacitance $C$. If the distance between the plates is doubled and the area of each plate is halved, what is the new capacitance?

A wire of resistance $R$ is stretched to double its length. How does the new resistance compare to the original resistance, assuming the density and resistivity of the material remain constant?

The magnetic field inside a long straight solenoid carrying current $I$ is $B$. If the current is doubled and the number of turns per unit length is halved, what is the new magnetic field?

Which of the following statements is true regarding the electromagnetic waves?

In a Young's double-slit experiment, the fringe width is $\beta$. If the wavelength of light is doubled and the distance between the slits is halved, what happens to the fringe width?

The de Broglie wavelength of an electron with kinetic energy $K$ is $\lambda$. If the kinetic energy is increased four times, what will be the new de Broglie wavelength?

What is the effect on the photoelectric current if the intensity of incident light is doubled, while the frequency remains constant and is above the threshold frequency?

In a nuclear reaction, if the binding energy per nucleon of the reactants is less than that of the products, what can be inferred about the reaction?

In a common-emitter transistor amplifier, what is the phase difference between the input signal voltage and the output signal voltage?

Which of the following is the primary advantage of using optical fibers in communication systems?

A body is in simple harmonic motion (SHM) with a period $T$. What fraction of the total energy is kinetic energy when the displacement is half of the amplitude?

A gas undergoes isothermal expansion from volume $V_1$ to $V_2$. If the initial pressure is $P$, what is the work done by the gas?

The efficiency of a Carnot engine is 40% when the source temperature is 500 K. If the engine's efficiency is to be increased to 60%, what should the new source temperature be, keeping the sink temperature constant?

Two waves of the same frequency have amplitudes $A$ and $2A$. They interfere at a point where the phase difference is $\pi/2$. What is the resultant amplitude at that point?

A convex lens of focal length 20 cm and a concave lens of focal length 25 cm are placed in contact. What is the power of the combination?

In a hydrogen atom, the electron transitions from energy level $n=3$ to $n=1$. What is the wavelength of the emitted photon? (Rydberg constant = $R$)

What is the velocity of an electron placed in the orbit with quantum number $n$ in a Hydrogen atom?

A Zener diode is primarily used for what purpose in electronic circuits?

What type of electromagnetic wave is used in remote controls for televisions and other electronic devices?

A carnot engine operates between two reservoirs of temperature $T_1$ and $T_2$ where $T_1 > T_2$. If the entropy change in the hot reservoir is $S$, whats the entropy change in the cold reservoir?

An object is placed at a distance of $2f$ from a convex lens of focal length $f$. Where is the image formed?

What is the effect of increasing the reverse bias voltage on the width of the depletion region in a PN junction diode?

What is the SI unit of magnetic flux?

A particle executes simple harmonic motion with an amplitude $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?

Two point charges, $+q$ and $-q$, are placed a distance $d$ apart. What is the electric potential at a point midway between the charges?

What is the effect on the angular width of the central maximum in a single-slit diffraction pattern if the width of the slit is doubled?

The half-life of a radioactive substance is 20 minutes. What fraction of the original sample will remain after 80 minutes?

Which of the following gates is considered a universal gate?

What is the effect of increasing the temperature of a metallic conductor on its drift velocity?

A transformer is used to step down the voltage from 220 V to 11 V. If the number of turns in the primary coil is 1000, what is the number of turns in the secondary coil?

What is the magnitude of the torque on a square coil with area $A$, carrying current $I$, placed in a uniform magnetic field $B$, when the plane of the coil is parallel to the magnetic field?

If an electron and a proton have the same de Broglie wavelength, which particle has greater kinetic energy?

Which of the following is NOT a property of laser light?

A capacitor of capacitance $C$ is charged to a potential $V$ and then discharged through a resistor $R$. What is the time constant of the circuit?

What is the primary function of a moderator in a nuclear reactor?

The energy levels of an electron in a hydrogen atom are given by $E_n = -13.6/n^2$ eV. What is the energy required to ionize a hydrogen atom from the ground state?

If the earth suddenly contracts such that its radius becomes half of its original value, but its mass remains the same, what happens to the duration of the day?

What is the resolving power of a microscope if the numerical aperture is 0.2 and the wavelength of light used is 6000 Angstroms?

A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with the horizontal. At what angle will its kinetic energy be half of its initial kinetic energy?

A particle of mass $m$ is moving in a circle of radius $r$ with uniform speed $v$. What is the work done by the centripetal force in moving it through half the circle?

Two identical sinusoidal waves, each of amplitude $A$, are traveling in opposite directions and form a standing wave. The distance between two consecutive nodes is $\lambda/2$. What is the amplitude of the standing wave at an antinode?

A black body at temperature $T$ radiates energy at a rate proportional to $T^4$. If the temperature of the black body is doubled, by what factor will the radiated energy increase?

What is the ratio of the radii of the first Bohr orbit for hydrogen to the first Bohr orbit for deuterium? (Deuterium has approximately twice the mass of hydrogen)

A radioactive sample has a decay constant of $\lambda$. What is the average lifetime of a nucleus in the sample?

In a series LCR circuit connected to an AC source, the voltage across the inductor is 40 V, the voltage across the capacitor is 80 V, and the voltage across the resistor is 30 V. What is the total voltage across the circuit?

Two point charges, $+q$ and $+4q$, are separated by a distance $r$. At what distance from the $+q$ charge, on the line joining the two charges, is the electric field zero?

The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

A current $I$ flows through a long straight wire. What is the magnetic field at a distance $r$ from the wire?

What is the effect of increasing the doping concentration in the base region of a Bipolar Junction Transistor (BJT) on its base width and current gain?

A photon of energy 3.4 eV is incident on a metal surface having a work function of 1.9 eV. What is the maximum kinetic energy of the emitted photoelectrons?

Which of the following solutions will have the highest boiling point?

What is the cell potential for a zinc-copper voltaic cell? Given: $E^0_{Cu^{2+}/Cu} = +0.34V$ and $E^0_{Zn^{2+}/Zn} = -0.76V$

For a first-order reaction, if the concentration of the reactant is doubled, how is the half-life affected?

Which of the following compounds will exhibit optical isomerism?

What is the IUPAC name of the compound with the formula $(CH_3)_2CHCH=CHCH_3$?

Which of the following reagents can be used to distinguish between ethanol and propanol?

What is the major product formed when phenol is treated with concentrated nitric acid?

Which of the following monomers is used to prepare Buna-S rubber?

Which of the following is an example of a fat-soluble vitamin?

What type of glycosidic linkage is present in sucrose?

What is the coordination number of cobalt in $[Co(en)_2Cl_2]^+$?

Which of the following has the highest magnetic moment?

Which of the following is not a colligative property?

The rate constant of a reaction is found to be $2.5 \times 10^{-3} L mol^{-1} s^{-1}$. What is the order of the reaction?

Which of the following shows greater value of adsorption?

Which of the following ores is concentrated by froth floatation process?

What is the hybridisation of the central atom in $XeF_4$?

Which of the following species is amphoteric in nature?

Which of the following complexes is expected to exhibit geometrical isomerism?

What is the product formed when acetone reacts with Grignard reagent followed by hydrolysis?

Which of the following is the strongest acid?

Which reagent is used for the Hoffmann bromamide degradation reaction?

What is the major product when ethyl chloride is treated with aqueous KOH?

What is the primary use of silicones?

What is the formula of Wilkinson's catalyst?

Which of the following can act as both a Bronsted acid and a Bronsted base?

What is the coordination number of the central metal ion in $[Cu(NH_3)_4]^{2+}$?

What is the major product of the reaction between benzene and acetyl chloride in the presence of anhydrous $AlCl_3$?

Which of the following compounds gives silver mirror test with Tollen’s reagent?

The van't Hoff factor (i) for a dilute solution of $K_2SO_4$ is?

Which of the following elements is used as a semiconductor in transistors?

What is the role of cryolite in the extraction of aluminum?

What is the product of the reaction between ammonia and excess chlorine?

Which of the following vitamins contains a metal ion?

Which of the following is an example of a non-narcotic analgesic?

Which of the following statements is true about the electromotive force (EMF) of a cell?

Which of the following is the correct order of decreasing acidic strength?

Which of the following polymers is biodegradable?

What is the role of zinc chloride in Lucas reagent?

What is the major organic product formed when ethanol is heated with concentrated sulfuric acid at 170°C?

What is the effect of a catalyst on the equilibrium constant of a reversible reaction?

Which of the following is an example of a cationic detergent?

A solution is prepared by dissolving 10g of a non-volatile solute in 180g of water. If the relative lowering of vapor pressure is 0.005, what is the molar mass of the solute?

For a reaction, $2A + B \rightarrow C$, the rate law is given by Rate = $k[A][B]^2$. If the initial concentrations of both A and B are doubled, by what factor will the initial rate increase?

Which of the following coordination compounds is expected to exhibit linkage isomerism?

The standard electrode potential ($E^\circ$) for the cell $Zn\vert Zn^{2+}(1M)\vert\vert Cu^{2+}(1M)\vert Cu$ is 1.10 V. If the value of $\Delta G^\circ$ is -212.3 kJ/mol, how many electrons are involved in the overall reaction?

What is the product formed when propan-2-ol is oxidized with acidified potassium dichromate?

Which of the following is the most effective in causing coagulation of a positively charged sol?

The activation energy of a reaction is zero. What is the relationship between the rate constant (k) and temperature (T)?

Given the following cell reaction: $X(s) + 2Y^+(aq) \rightleftharpoons X^{2+}(aq) + 2Y(s)$. The standard reduction potentials are: $E^\circ_{X^{2+}/X} = -0.25 V$ and $E^\circ_{Y^{+}/Y} = +0.15 V$. Calculate the EMF of the cell.

If $A$ is a square matrix of order 3 and $|A| = 5$, then what is the value of $|adj(A)|$?

The probability that a randomly chosen leap year contains 53 Sundays is:

The range of the function $f(x) = \sin^{-1}x + \cos x$ is:

If $y = x^x$, then what is $\frac{dy}{dx}$?

What is the area of the region bounded by the curve $y = x^2$, the x-axis, and the lines $x = 1$ and $x = 3$?

The general solution of the differential equation $\frac{dy}{dx} = \frac{y}{x}$ is:

If $\vec{a} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} - 2\hat{k}$, then what is the angle between $\vec{a}$ and $\vec{b}$?

The equation of the plane passing through the point (1, 2, 3) and perpendicular to the vector $2\hat{i} - \hat{j} + \hat{k}$ is:

If $\int_{0}^{a} x^2 dx = \frac{a^3}{3}$, then what is the value of $\int_{0}^{a} x^3 dx$?

If lines represented by equation $px^2 - qy^2 = 0$ are perpendicular to each other then

If $A$ is a skew-symmetric matrix of order $n$, then what is the determinant of $A$ when $n$ is odd?

If $f(x) = x^2 \sin(1/x)$ for $x eq 0$ and $f(0) = 0$, then what is the value of $f'(0)$?

What is the integrating factor of the differential equation $\frac{dy}{dx} + y = e^{-x}$?

Evaluate $\int_{0}^{\pi/2} \sin^2x , dx$.

If two lines have direction cosines $l_1, m_1, n_1$ and $l_2, m_2, n_2$, what condition must be satisfied such that the lines are perpendicular?

What is the probability of getting exactly two heads in three tosses of a fair coin?

If $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$, find $A^{-1}$.

Given the function $f(x) = |x-1|$, which of the following statements is true?

What is the degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{dy}{dx} \right)^4 + y = 0$?

What is the area of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$?

If $\vec{a}$ and $\vec{b}$ are unit vectors and the angle between them is $\theta$, what is the value of $|\vec{a} - \vec{b}|$?

Find the maximum value of $f(x) = \sin x + \cos x$.

What is the equation of the plane which cuts intercepts 2, 3, and 4 on the x, y, and z axes, respectively?

If $y = \log(\cos x)$, then what is $\frac{dy}{dx}$?

Find the general solution of the differential equation $\frac{dy}{dx} + 2y = 0$.

If $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$, and $P(A \cap B) = \frac{1}{4}$, what is $P(A \cup B)$?

What is the shortest distance from the point (1, 2, 3) to the z-axis?

If $A$ is a square matrix such that $A^2 = A$, then what is the value of $(I + A)^3 - 7A$, where $I$ is the identity matrix?

What is the derivative of $\tan^{-1}(\frac{\sqrt{1-x^2}}{x})$ with respect to $x$?

A bag contains 3 red and 5 black balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

The radius of a circle is increasing at a rate of 0.7 cm/s. What is the rate of increase of its circumference?

For what value of $k$ is the function $f(x) = \begin{cases} kx^2, & \text{if } x \le 2 \ 3, & \text{if } x > 2 \end{cases}$ continuous at $x = 2$?

Given vectors $\vec{a} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} + 2\hat{k}$, find a unit vector in the direction of $\vec{a} + \vec{b}$.

What is the value of $\int_{-\pi/2}^{\pi/2} \cos^5(x) dx$?

Find the particular solution of the differential equation $\frac{dy}{dx} = x + 1$, given that $y(0) = 1$.

If $A = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$, then $adj(A)$ is:

The angle between the lines $2x - y + 3 = 0$ and $x + 2y - 7 = 0$ is:

Determine the area of the region bounded by $y = x^3$, $y = 0$, $x = 1$, and $x = 2$.

A fair die is thrown twice. What is the probability of getting a sum of 9?

Given three points A(1, 1, 1), B(1, 2, 3), and C(2, 3, 1), find the area of the triangle ABC.

If $f(x) = x^3 - 6x^2 + 9x + 1$, find the points where $f(x)$ has local extrema.

Find the general solution to the differential equation $\frac{d^2y}{dx^2} - 4\frac{dy}{dx} + 4y = 0$.

If the line $y = mx + c$ touches the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, then which of the following conditions must be satisfied?

Given that $x = \cos t$ and $y = \sin^3 t$, find $\frac{d^2y}{dx^2}$ at $t = \frac{\pi}{2}$.

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that both cards are queens?

What is the minimum value of the function $f(x) = x + \frac{1}{x}$ for $x > 0$?

A line passes through the point (2, 2) and is perpendicular to the line $3x + y = 3$. Its y-intercept is:

If $f(x) = \begin{vmatrix} a & b & c \ l & m & n \ p & q & r \end{vmatrix}$, then what is the value of $\begin{vmatrix} ka & kb & kc \ kl & km & kn \ kp & kq & kr \end{vmatrix}$?

Let $f(x) = \frac{x}{1+x^2}$. Determine the range of $f(x)$.

Evaluate: $\lim_{x \to 0} (\frac{\sin x}{x})^{\frac{1}{x^2}}$