List of top Questions asked in MHT CET

When one end of a capillary tube is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the weight of water column. The inner circumference of the capillary tube is ______.

A circular coil carrying current 'I' has a radius 'r' and 'n' turns. The magnetic field along the axis of a coil at a distance '2√2 r' from its centre is ______.

With a resistance 'X' connected in series with a galvanometer of resistance 100$\Omega$, it acts as a voltmeter of range 0 – 15 V. To double the range, a resistance of 1500$\Omega$ is to be connected in series with 'X'. The value of 'X' in ohm is \dots

A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is ______.

A black body emits radiation of maximum intensity at wavelength '$\lambda$' at temperature $T$ K. Its corresponding wavelength at temperature $1.5 T$ K will be ______.

Two equally charged small balls placed at a fixed distance experience a force 'F'. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. The force experienced by this ball is ______.

In a single slit diffraction experiment, slit width 'a' is illuminated by wavelength '$\lambda$' and the width of central maxima is 'y'. When half the slit is covered and illuminated by $(1.5)\lambda$, the width of the central maximum becomes ______.

An a.c. source of frequency 'f' is connected to a circuit containing an inductance 'L' and resistance 'R' in series. The impedance of this circuit is ______.

In an $LR$ circuit, the value of $L$ is $(0.3/\pi)$ henry and the value of $R$ is $40 \Omega$. If an alternating e.m.f of 230 V at 50 cycles per second is connected, the impedance of the circuit and current will be respectively ______.

To protect the instrument from magnetic field, it is completely surrounded by ______.

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the coordinates of the point of contact are \dots

A doctor assumes patient has $d_1, d_2,$ or $d_3$ with equal probability. A test is positive with probability 0.7 for $d_1$, 0.5 for $d_2$, and 0.8 for $d_3$. If the test is positive, what is the probability the patient has $d_2$?

A coil of 'n' turns and resistance $R \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time 't' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is ______.

$\lim_{x \to 0} \frac{63^x - 9^x - 7^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}} = \dots$

A particle P starts from $Z_0 = 1 + 2i$. It moves horizontally away from origin by 5 units, then vertically up by 3 units to $Z_1$. From $Z_1$ it moves $\sqrt{2}$ units in direction $\hat{i} + \hat{j}$, then moves through $\pi/2$ anticlockwise on a circle with centre at origin to reach $Z_2$. Then $Z_2 = \dots$

Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?

If $\theta$ is an obtuse angle between vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}| = 5, |\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 5\sqrt{5}$ then $\vec{a} \cdot \vec{b} = \dots$

The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \text{adj } A = A A^T$, then $5a + b = \dots$

The slopes of the lines represented by $6x^2 + 2hxy + y^2 = 0$ are in the ratio 2 : 3, then $h = \dots$

If the plane $x/2 - y/3 - z/5 = 1$ cuts the co-ordinate axes in points A, B, C respectively, then the area of the triangle ABC is ______.

The equation of the curve passing through origin and satisfying $(1 + x^2) \frac{dy}{dx} + 2xy = 4x^2$ is ______.

The rate of increase of population of a city is proportional to population present. In 40 years it increased from 30,000 to 40,000. At time $t$ population is $a(b)^{t/40}$. Then $a$ and $b$ are \dots}

Consider the probability distribution:

Then the value of $P(X > 2)$ is ______.

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students selected at random 4 are swimmers is ______.