A photoemissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_o$. Expression for de-Broglie wavelength is given by:
(m: mass of the electron, h: Planck's constant and c: speed of light)
A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is :
(use acceleration due to gravity g = 10 m/s2 and neglect air resistance)
Answer
(C)
2$\sqrt{2}$ km
4
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Refractive index of glass is higher than that of air.
Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer
(B)
(A) is correct but (R) is not correct
5
Which one of the following forces cannot be expressed in terms of potential energy?
Answer
(A)
Frictional force
6
Match List - I with List - II.
List - I
List - II
(A) Mass density
(I) [ML2T−3]
(B) Impulse
(II) [MLT−1]
(C) Power
(III) [ML2T0]
(D) Moment of inertia
(IV) [ML−3T0]
Choose the correct answer from the options given below :
Answer
(D)
(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
7
The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:
(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)
Answer
(D)
1 : 1
8
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R): For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer
(C)
Both (A) and (R) are correct and (R) is the correct explanation of (A)
9
The unit of $\sqrt{\frac{2I}{\varepsilon_0 c}}$ is :
(I = intensity of an electromagnetic wave, c = speed of light)
Answer
(B)
NC-1
10
A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:
Answer
(D)
5×10−9 Nm
11
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes.
Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.
In the light of the above statements, choose the most appropriate answer from the options given below :
Answer
(C)
Both (A) and (R) are correct and (R) is the correct explanation of (A)
12
A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.
Answer
(C)
10.7 cm
13
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper $(^ {64}_{29} \text{Cu})$ nucleus is greater than that of the carbon $(^ {12}_{6} \text{C})$ nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $ A^{1/3} $.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer
(C)
(A) is not correct but (R) is correct
14
A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g = 9.8 \text{ m/s}^2$)
Answer
(A)
$\frac{82}{5}$
15
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Magnetic monopoles do not exist.
Reason (R): Magnetic field lines are continuous and form closed loops.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer
(A)
Both (A) and (R) are correct and (R) is the correct explanation of (A)
16
Consider the following logic circuit.
The output is Y = 0 when :
Answer
(C)
A = 1 and B = 1
17
The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :
Answer
(D)
5.0 cm
18
A transparent block A having refractive index $\mu = 1.25$ is surrounded by another medium of refractive index $\mu = 1.0$ as shown in the figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in the figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block?
Answer
(B)
$\sin^{-1}(3/4)$
19
Match List - I with List - II.
List - I
List - II
(A) Isothermal
(I) ΔW (work done) = 0
(B) Adiabatic
(II) ΔQ (supplied heat) = 0
(C) Isobaric
(III) ΔU (change in internal energy) ≠ 0
(D) Isochoric
(IV) ΔU = 0
Choose the correct answer from the options given below :
Answer
(C)
(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
20
M and R be the mass and radius of a disc. A small disc of radius $\mathrm{R} / 3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis $A B$ passing through the centre $O$ and perpendicular to the plane of disc is $\frac{4}{x} \mathrm{MR}^2$. The value of $x$ is ____________.
Answer
9
21
Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivites of these rods are: $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2$ and $\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}$. The free ends of rods A and B are maintained at 400 K , 200 K , respectively. The temperature of rods interface is ______________ $K$, when equilibrium is established.
Answer
360
22
The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \,\mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of the surface is _____________ $\mathrm{cm}^2$.
Answer
15
23
An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of $10 \mathrm{~V}, 50 \mathrm{~Hz}$. Average power dissipated by the circuit is ___________ W.
Answer
1
24
A parallel plate capacitor has charge $5 \times 10^{-6} \mathrm{C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6} \mathrm{C}$ then the dielectric constant of the slab is _______________.
Answer
5
25
An object with mass 500 g moves along x-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is :
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