33,157 previous year MHT-CET questions, grouped by year, with answers and solutions.
$\dfrac{(\cos 2\theta + i\sin 2\theta)^7}{(\cos 4\theta + i\sin 4\theta)^3} =$
$A$ slab of material of dielectric constant $K$ has the same area as the plates of a parallel plate capacitor but has a thickness $(4/5)d$, where $d$ is the separation of the plates. The capacitance in the presence and absence of dielectric are $C$ and $C_0$ respectively. The ratio $(C/C_0)$ is
A coil of self-inductance $L$ is connected in series with a bulb and an a.c. source. Brightness of the bulb decreases when
Calculate velocity of an electron having de Broglie's wavelength 58 nm and mass $9.1 \times 10^{-31} \mathrm{~kg} ?\left[\mathrm{~h}=6.63 \times 10^{-34} \mathrm{Js}\right]$
The abscissa of the point on the curve $y=a\left(e^{\frac{x}{a}}+e^{-\frac{x}{a}}\right)$ where the tangent is parallel to the $X$-axis is
Which of the following molecules is an example of sp hybridization?
Identify the nonbenzenoid aromatic compound from the following.
If $\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$, then the value of $\cos ^{-1} x+\sin ^{-1} y$ is
$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_2(\mathrm{~g}), \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=0.052 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$. Calculate $-\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}}$
$A$ clock with an iron pendulum keeps correct time at $15^{\circ} C$. If the room temperature is $20^{\circ} C$,the error in seconds per day will be nearly (coefficient of linear expansion of iron is $\alpha = 1.2 \times 10^{-5} /{ }^{\circ} C$) (in $s$)
The moment of inertia of a body about a given axis,rotating with an angular velocity of $1 \ rad/s$,is numerically equal to '$P$' times its rotational kinetic energy. The value of '$P$' is:
$A$ capacitor of capacity $C_1$ is charged to potential $V_1$ and then disconnected. An uncharged capacitor of capacity $C_2$ is connected in parallel with $C_1$. The resultant potential $V_2$ is
If the sum of slopes of the pair of lines given by $4x^{2} + 2hxy - 7y^{2} = 0$ is equal to the product of the slopes,then $h$ is
The susceptibility of tungsten is $6 \cdot 8 \times 10^{-5}$ at temperature $300 \mathrm{~K}$. The susceptibility at temperature $400 \mathrm{~K}$ is
$\int \frac{\cos x-\sin x}{8-\sin 2x} dx = \frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c$,then $p = \ldots$
When $CuSO_4$ solution in water is treated with concentrated $HCl$,it turns:
What is the oxidation number of gold in the complex $[AuCl_{4}]^{-}$?
Two moles of an ideal gas are allowed to expand from a volume of to at against a pressure of Calculate the work done.
The magnetic flux near the axis and inside the air-core solenoid of length carrying current is Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length, SI units)
$(+)$ $2-$Methylbutan$-1-$ol and $(-)$ $2-$Methylbutan$-1-$ol have different values for which property?
In a face-centred cubic $(FCC)$ unit cell,what is the total volume occupied by the atoms?
During a dihybrid cross, in the $F_2$ generation, the ratio of individuals showing one dominant and the other recessive character will be . . . . . . of the total population. (in $/16$)
The area (in sq. units) of the region described by $\{(x, y) : y^2 \leq 2x \text{ and } y \geq 4x - 1\}$ is
With reference to working of heart, complete the analogy.
Pace setter : $\underline{x}$ :: Pacemaker : $\underline{y}$
Identify the $CORRECT$ match from the Columns $I$,$II$ and $III$.
| $I$ | $II$ | $III$ |
| $1$. Interstitial cells | $a$. Cortex of ovary | $i$. Follicular fluid |
| $2$. Sertoli cells | $b$. Ovarian follicle | $ii$. Progesterone |
| $3$. Granulosa cells | $c$. Testis | $iii$. Attachment of sperm bundle |
| $4$. Cells of corpus luteum | $d$. Seminiferous tubules | $iv$. Testosterone |
The chromosome with centromere near the end is called . . . . . . .
The value of $\cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right)$ is
If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then the value of $\alpha$ is:
If $\bar{a}$ and $\bar{b}$ are vectors such that $|\bar{a}+\bar{b}|=\sqrt{29}$ and $\bar{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \bar{b}$,then a possible value of $(\bar{a}+\bar{b}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$ is
The false statement regarding alkane is
If $a, b, c$ and $d$ are positive,then $\lim_{x \to \infty} \left(1 + \frac{1}{a+bx}\right)^{c+dx}$ is equal to:
The atomic number of $\mathrm{Sn}$ is $50 .$ The shape of gaseous $\mathrm{SnCl}_{2}$ molecule is
When a rod of length $l$ is rotated with angular velocity of $\omega$ in a perpendicular field of induction $B$, about one end, the emf across its ends is
The common names of the lower fatty acids are obtained from
The compound from which formic acid cannot be prepared is
Moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between centre and end is
The point on the curve $y^2=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is
If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is
For an ideal gas,the heat of reaction at constant pressure and constant volume are related as:
Which of the following is an amphoteric oxide?
Syngamy results in
The process of expulsion of urine from the urinary bladder is called:
If $I_0$ is the intensity of the principal maximum in the single slit diffraction pattern,then what will be the intensity when the slit width is doubled?
. . . . . . liters of glomerular filtrate is produced by kidneys per day.
From the cranial nerves,find the odd man out.
The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2 \, s$. The magnet is cut along its length into three equal parts and these three parts are then placed on each other with their like poles together. The time period of this combination will be
The value of $k$ such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies in the plane $2x-4y+z=7$ is:
$A$ photoelectric cell is illuminated by a point source of light $1 \ m$ away. When the source is shifted to $2 \ m$,then:
The number of integral values of $k$,for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution,is
Which of the following is a redox reaction?
According to Hooke's law of elasticity,if stress is increased,then the ratio of stress to strain
The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is
What is IUPAC name of $(\text{CH}_3)_3\text{CBr}$?
Which of the following statements is NOT true regarding dihydrogen?
$A$ parallel plate capacitor with oil between the plates (dielectric constant of oil $K = 2$) has a capacitance $C$. If the oil is removed,then the capacitance of the capacitor becomes:
Aspirin is an acetylation product of
$A$ glucose molecule reacts with $X$ number of molecules of phenylhydrazine to yield osazone. The value of $X$ is
As per the Bohr model,the minimum energy (in $eV$) required to remove an electron from the ground state of a doubly ionized $Li$ atom $(Z = 3)$ is:
If $g(x) = \int_0^x \cos^4 t \,dt$, then $g(x+\pi)$ equals
The angle between a pair of tangents drawn from a point $P$ to the circle ${x^2} + {y^2} + 4x - 6y + 9{\sin ^2}\alpha + 13{\cos ^2}\alpha = 0$ is $2\alpha$. The equation of the locus of the point $P$ is
At a certain instant,a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is:
If $y=4x-5$ is tangent to the curve $y^2=px^3+q$ at $(2,3)$,then
If $y=(\sin x)^{\tan x}$,then $\frac{dy}{dx}$ is equal to
Let $a, b, c$ be distinct non-negative numbers. If the vectors $a\hat{i} + a\hat{j} + c\hat{k}$,$\hat{i} + \hat{k}$,and $c\hat{i} + c\hat{j} + b\hat{k}$ lie in a plane,then $c$ is
The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on
For a gas,$\frac{R}{C_{v}} = 0.67$. This gas is made up of molecules which are
The moment of inertia of a body about a given axis is $1.2 \; kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 \; J$,an angular acceleration of $25 \; rad/s^2$ must be applied about that axis for a duration of: (in $; s$)
$A$ ray of light of intensity $I$ is incident on a parallel glass slab at a point $A$ as shown in the figure. It undergoes partial reflection and refraction. At each reflection,$25\%$ of the incident energy is reflected. The rays $AB$ and $A^1B^1$ undergo interference. The ratio $I_{\text{max}} / I_{\text{min}}$ is (in $: 1$)
One hundred identical coins,each with probability $p$ of showing up heads,are tossed once. If $0 \lt p \lt 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is
Sign up free to unlock every previous year question paper with detailed solutions, practice in timed exam mode, and evaluate your rank.
Sign up free to unlock every previous year question and generate papers from them.