MHT-CET previous year questions (PYQ)

If molar conductance at infinite dilution for $\text{CH}_3\text{COO}^-$ and $\text{H}^+$ ions are $50\ \text{S cm}^2\ \text{mol}^{-1}$ and $350\ \text{S cm}^2\ \text{mol}^{-1}$ respectively, molar conductivity of $5 \times 10^{-2}$ M $\text{CH}_3\text{COOH}$ is $20\ \text{S cm}^2\text{mol}^{-1}$. What is the hydrogen ion concentration in $\text{mol/dm}^3$ of $\text{CH}_3\text{COOH}$?

In $\triangle ABC$, with usual notations, $(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2$, then $\angle A =$

A force acting on a body of mass 5 Kg is $(4 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$. If the body is initially at rest then the magnitude of its velocity at the end of 10 second in $\mathrm{m} / \mathrm{s}$ will be

Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $\left(\frac{\mathrm{r}}{3}\right)$ and lighter one in a radius r . The tangential speed of lighter stone is ' $n$ ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of $n$ is

Calculate the radius of the first orbit of $He^{+}$. (in $pm$)

What is the energy associated with the fourth orbit of a hydrogen atom?
$R_H = 2.18 \times 10^{-18} \ J$

The diagonal of a square is changing at the rate of $0.5 \text{ cm/sec}$. Then the rate of change of area when the area is $400 \text{ cm}^2$ is equal to

In $\triangle \mathrm{ABC}$ with usual notation, $\frac{\cos \mathrm{A}}{\mathrm{a}}=\frac{\cos \mathrm{B}}{\mathrm{b}}=\frac{\cos \mathrm{C}}{\mathrm{c}}$ and $\mathrm{a}=\frac{1}{\sqrt{6}}$, then the area of triangle is

Which one of the following is the activator for enzyme Pyruvate Kinase?

Which carbon atoms of fructose are bonded together through oxygen forming fructofuranose?

Which among the following oxides is acidic in nature?

The surface energy of a liquid drop is $U$. It splits up into $512$ equal droplets. The surface energy becomes (in $U$)

What will be the volume of oxygen gas produced, If the reaction $2 \mathrm{KClO}_{3(\mathrm{~s})} \longrightarrow 2 \mathrm{KCl}_{(\mathrm{s})}+3 \mathrm{O}_{2(\mathrm{~g})} \Delta \mathrm{H}^{\circ}=-78 \mathrm{k} \mathrm{J}$ is carried out at S.T.P.?

Mole fraction of solute in its $2$ molal aqueous solution is

$A$ coil has an inductance of $2 \ H$. The ratio of its reactance,when it is connected first to an $AC$ source and then to a $DC$ source,is

18 gram glucose (Molar mass = 180) is dissolved in 100 mol of water at 300 K. If R = 3 $0.0821L-\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}{K}^{-1}$ what is the osmotic pressure of solution?

In Mirabilis jalapa,when red and white varieties are crossed,the hybrid obtained will be . . . . . . pink. (in $\%$)

In case of $R, S$ configuration,the group having the highest priority is-

Glycolysis ends in formation of ________ .

$\int_0^1 x \tan^{-1} x \, dx =$

Which one of the following is the $CORRECT$ order of conversion of waste materials during biogas formation?

The spermatozoa $NOT$ ejaculated are reabsorbed in the

Which of the following factors is associated with optical activity of a molecule?

How many electrons and ATP are required for the biological fixation of a molecule of nitrogen to form ammonia?

The chromosome with centromere near the end is called . . . . . . .

In $DNA$ fingerprinting technique, . . . . . . probe is used for hybridization of $DNA$ fragments.

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be given by $\frac{dy}{dx} = \frac{y}{x} + \sec \left(\frac{y}{x}\right)$,where $x \gt 0$. Then the equation of the curve is:

The materials suitable for making electromagnets should have

Divide $10$ into two parts such that the sum of double of the first and the square of the second is minimum.

Find the vector perpendicular to the vectors $4 i-j+3 k$ and $-2 i+j-2 k$ whose magnitude is $9$.

$A$ diet of a sick person must contain at least $4000$ units of vitamins,$50$ units of proteins,and $1400$ calories. Two foods $A$ and $B$ are available at a cost of ₹ $4$ and ₹ $3$ per unit respectively. If one unit of $A$ contains $200$ units of vitamins,$1$ unit of protein,and $40$ calories,while one unit of food $B$ contains $100$ units of vitamins,$2$ units of protein,and $40$ calories,formulate the problem so that the diet is the cheapest.

Which of the following is the evidence to show that there must be a force acting on earth and directed towards the sun?

KE per unit volume is $E$. The pressure exerted by the gas is given by

If $u_{0}=8, u_{1}=3, u_{2}=12, u_{3}=51$,then the value of $\Delta^{3} u_{0}$ is

In the Electron Transport System $(ETS)$, the water molecule is formed at which stage?

Iso-propyl amine is a

If an electron and a proton have the same de-Broglie wavelength,then the kinetic energy of the electron is

The charge carriers in a $p$-type semiconductor are

Which of the following phenomena exhibits the particle nature of light?

If a coil is open,then its self-inductance $L$ and resistance $R$ become:

Five capacitors,each of capacitance $C$,are connected as shown in the figure. The ratio of the equivalent capacitance between $P$ and $R$ to the equivalent capacitance between $P$ and $Q$ is:

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?

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

Which of the following compounds is not chiral?

Which of the following is an odd pollutant?

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$,and $kx + 5y - 3 = 0$ are concurrent,then $k=$

In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

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?

The equation of the directrix of the parabola $y^2+4y+4x+2=0$ is

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

A person underwent surgery that leads to tremendous blood loss. He was detected with anemia due to ------.

Match List I with List II

$A$ 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:

The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3 \sin^2 x - 7 \sin x + 2 = 0$ is

$A$ glucose molecule reacts with $X$ number of molecules of phenylhydrazine to yield osazone. The value of $X$ is

If $g(x) = \int_0^x \cos^4 t \,dt$, then $g(x+\pi)$ equals

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:

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