Question 1: Palette 1/106

Allen JEE (Main) 2023 MCQ

A cylindrical wire of mass $(0.4\pm0.01)g$ has length $(8\pm0.04)cm$ and radius $(6\pm0.03)mm$ . The maximum error in its density will be

A

1%

B

3.5%

C

4%

D

5%

Question 2: Palette 2/106

Allen JEE (Main) 2023 MCQ

In an experiment with Vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and $6^{th}$ division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm and 3.3 cm marks, and $4^{th}$ division of vernier scale coincides with the main scale division. The diameter of bob is measured as :

A

3.18 cm

B

3.25 cm

C

3.26 cm

D

3.22 cm

Question 3: Palette 3/106

Allen JEE (Main) 2023 MCQ

For the logic circuit shown, the output waveform at Y is:

A

B

C

D

Question 4: Palette 4/106

Allen JEE (Main) 2023 MCQ

A zener diode of power rating 1.6W is to be used as voltage regulator. If the zener diode has a breakdown of 8V and it has to regulate voltage fluctuating between 3V and 10V. The value of resistance $R_{s}$ for safe operation of diode will be :

A

$13.3\Omega$

B

12 $\Omega$

C

10$\Omega$

D

$13\Omega$

Question 5: Palette 5/106

Allen JEE (Advanced) 2022 Match the Columns

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is 0.5 mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Column-I	Column-II	Column-III
Measurement condition	Main scale reading	Circular scale reading
Two arms of gauge touching each other without wire	0 division	4 division
Attempt-1: With wire	4 divisions	20 divisions
Attempt-2: With wire	4 divisions	16 divisions

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

A

$2.22 \pm 0.02 \, mm$ , $\pi(1.23 \pm 0.02) \, mm^{2}$

B

$2.22 \pm 0.01 \, mm$ , $\pi(1.23 \pm 0.01) \, mm^{2}$

C

$2.14 \pm 0.02 \, mm$ , $\pi(1.14 \pm 0.02) \, mm^{2}$

D

$2.14 \pm 0.01 \, mm$ , $\pi(1.14 \pm 0.01) \, mm^{2}$

Question 6: Palette 6/106

Allen JEE (Main) 2021 MCQ

If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:

A

86.4 s

B

4.32 s

C

43.2 s

D

8.64 s

Question 7: Palette 7/106

Allen JEE (Main) 2021 MCQ

In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is :-

A

3.9

B

8.4

C

7.5

D

3.0

Question 8: Palette 8/106

Allen JEE (Main) 2021 Match the Columns

A student determined Young's Modulus of elasticity using the formula $Y = \frac{MgL^{3}}{4bd^{3}\delta}$ . The value of g is taken to be $9.8\ m/s^{2}$ , without any significant error, his observation are as following.

Column-I	Column-II	Column-III
Physical Quantity	Least Count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression (δ)	0.01 mm	5 mm

Then the fractional error in the measurement of Y is:

A

0.0083

B

0.0155

C

0.155

D

0.083

Question 9: Palette 9/106

Allen JEE (Main) 2021 MCQ

Choose the correct waveform that can represent the voltage across R of the following circuit, assuming the diode is ideal one:

A

B

C

D

Question 10: Palette 10/106

Allen JEE (Main) 2021 MCQ

Statement-I: To get a steady dc output from the pulsating voltage received from a full wave rectifier can connect a capacitor across the output parallel to the load $R_{L}$ . Statement-II : To get a steady dc output from the pulsating voltage received from a full wave rectifier can connect an inductor in series with $R_{L}$ . In the light of the above statements, choose the most appropriate answer from the options given below:

A

Statement I is true, but Statement II is false.

B

Statement I is false, but Statement II is true.

C

Both Statement I and Statement II are false.

D

Both Statement I and Statement II are true.

Question 11: Palette 11/106

Allen JEE (Main) 2021 MCQ

The logic circuit shown above is equivalent to:

A

B

C

D

Question 12: Palette 12/106

Allen JEE (Main) 2021 MCQ

If $V_{A}$ and $V_{B}$ are the input voltages (either 5V or $V_{0}$ ) and $V_{0}$ is the output voltage then the two gates represented in the following circuit (A) and (B) are:-

A

AND and OR Gate

B

OR and NOT Gate

C

NAND and NOR Gate

D

AND and NOT Gate

Question 13: Palette 13/106

Allen JEE (Advanced) 2021 MCQ

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is

A

3.07 cm

B

3.11 cm

C

3.15 cm

D

3.17 cm

Question 14: Palette 14/106

Allen JEE (Main) 2020 MCQ

A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:

A

3.40%

B

5.40%

C

4.40%

D

2.40%

Question 15: Palette 15/106

Allen JEE (Main) 2020 MCQ

The least count of the main scale of a vernier calipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the $7^{th}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and $4^{th}$ VSD coincides with a main scale division. The length of the cylinder is: (VSD is vernier scale division)

A

3.21 cm

B

2.99 cm

C

3.2 cm

D

3.07 cm

Question 16: Palette 16/106

Allen JEE (Main) 2020 MCQ

Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as :

A

2.123 cm

B

2.125 cm

C

2.121 cm

D

2.124 cm

Question 17: Palette 17/106

Allen JEE (Main) 2020 MCQ

A physical quantity z depends on four observables a, b, c and d, as $z = \frac{a^{2}b^{\frac{2}{3}}}{\sqrt{c}d^{3}}$ . The percentage of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

A

12.25%

B

14.5%

C

16.5%

D

13.5%

Question 18: Palette 18/106

Allen JEE (Main) 2020 MCQ

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

A

(5.5375 ± 0.0739) mm

B

(5.538 ± 0.074) mm

C

(5.54 ± 0.07) mm

D

(5.5375 ± 0.0740) mm

Question 19: Palette 19/106

Allen JEE (Main) 2019 MCQ

For the circuit shown below, the current through the Zener diode is:

A

$5mA$

B

Zero

C

$14mA$

D

$9mA$

Question 20: Palette 20/106

Allen JEE (Main) 2018 MCQ

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

A

3.5 %

B

4.5 %

C

6 %

D

2.5 %

Question 21: Palette 21/106

Allen JEE (Advanced) 2018 MCQ

PARAGRAPH FOR QUESTION NO. 8 and 9 If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are $\Delta x$ , $\Delta y$ and $\Delta z$ , respectively, then $z \pm \Delta z = \frac {x \pm \Delta x}{y \pm \Delta y} = \frac {x}{y} \left(1 \pm \frac {\Delta x}{x}\right) \left(1 \pm \frac {\Delta y}{y}\right) ^ {- 1} $ The series expansion for $\left(1\pm\frac{\Delta y}{y}\right)^{-1}$ , to first power in $\Delta y/y$ , is $1\mp(\Delta y/y)$ . The relative errors in independent variables are always added. So the error in z will be $ \varDelta z = z \left(\frac {\varDelta x}{x} + \frac {\varDelta y}{y}\right) $ The above derivation makes the assumption that $\frac{\Delta x}{x} \ll 1$ , $\frac{\Delta y}{y} \ll 1$ . Therefore, the higher powers of these quantities are neglected. Consider the ratio $r = \frac{(1-a)}{(1+a)}$ to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is $\Delta a(\Delta a/a \ll 1)$ , then what is the error $\Delta r$ in determining r?

A

$\frac{\Delta a}{(1+a)^{2}}$

B

$\frac{2\Delta a}{(1+a)^{2}}$

C

$\frac{2\Delta a}{(1-a^{2})}$

D

$\frac{2a\Delta a}{(1-a^{2})}$

Question 22: Palette 22/106

Allen JEE (Advanced) 2018 MCQ

PARAGRAPH FOR QUESTION NO. 8 and 9 If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are $\Delta x$ , $\Delta y$ and $\Delta z$ , respectively, then $z \pm \Delta z = \frac {x \pm \Delta x}{y \pm \Delta y} = \frac {x}{y} \left(1 \pm \frac {\Delta x}{x}\right) \left(1 \pm \frac {\Delta y}{y}\right) ^ {- 1} $ The series expansion for $\left(1\pm\frac{\Delta y}{y}\right)^{-1}$ , to first power in $\Delta y/y$ , is $1\mp(\Delta y/y)$ . The relative errors in independent variables are always added. So the error in z will be $ \varDelta z = z \left(\frac {\varDelta x}{x} + \frac {\varDelta y}{y}\right) $ The above derivation makes the assumption that $\frac{\Delta x}{x} \ll 1$ , $\frac{\Delta y}{y} \ll 1$ . Therefore, the higher powers of these quantities are neglected. In an experiment the initial number of radioactive nuclei is 3000. It is found that $1000 \pm 40$ nuclei decayed in the first 1.0 s. For $|x| << 1$ , $\ln (1 + x) = x$ up to first power in $x$ . The error $\Delta \lambda$ , in the determination of the decay constant $\lambda$ , in $s^{-1}$ , is :-

A

0.04

B

0.03

C

0.02

D

0.01

Question 23: Palette 23/106

Allen JEE (Main) 2017 MCQ

The following observations were taken for determining surface tension T of water by capillary method: Diameter of capillary, $D = 1.25 \times 10^{-2} m$ Rise of water, $h = 1.45 \times 10^{-2} m$ Using $g = 9.80 \, m/s^{2}$ and the simplified relation $T = \frac{rhg}{2} \times 10^{3} \, N/m$ , the possible error in surface tension is closest to:

A

2.4%

B

10%

C

0.15%

D

1.5%

Question 24: Palette 24/106

Allen JEE (Advanced) 2017 MCQ

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T = 0.01$ second and he measures the depth of the well to be $L = 20$ meters. Take the acceleration due to gravity $g = 10\mathrm{ms}^{-2}$ and the velocity of sound is $300\mathrm{ms}^{-1}$ . Then the fractional error in the measurement, $\delta L / L$ , is closest to

A

$0.2\%$

B

$5\%$

C

$3\%$

D

$1\%$

Question 25: Palette 25/106

Allen JEE (Main) 2016 MCQ

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{th}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the $25^{th}$ division coincides with the main scale line?

A

0.50 mm

B

0.75 mm

C

0.80 mm

D

0.70 mm

Question 26: Palette 26/106

Allen JEE (Main) 2016 MCQ

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:

A

$92 \pm 3$ s

B

$92 \pm 2$ s

C

$92 \pm 5.0$ s

D

$92 \pm 1.8$ s

Question 27: Palette 27/106

Allen JEE (Main) 2016 MCQ

If $a, b, c, d$ are inputs to a gate and $x$ is its output, then as per the following time graph, the gate is

A

NAND

B

NOT

C

AND

D

OR

Question 28: Palette 28/106

Allen JEE (Main) 2016 MCQ

Identify the semiconductor devices whose characteristics are given below, in the order $(a)$ , $(b)$ , $(c)$ , $(d)$ :
(a)

(b)

(c)

(d)

A

Zener diode, Solar cell, Simple diode, Light dependent resistance

B

Simple diode, Zener diode, Solar cell, Light dependent resistance

C

Zener diode, Simple diode, Light dependent resistance, Solar cell

D

Solar cell, Light dependent resistance, Zener diode, Simple diode

Question 29: Palette 29/106

Allen JEE (Advanced) 2016 MCQ

There are two vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers ( $C_{1}$ ) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper ( $C_{2}$ ) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers $C_{1}$ and $C_{2}$ respectively, are

A

2.87 and 2.86

B

2.87 and 2.87

C

2.87 and 2.83

D

2.85 and 2.82

Question 30: Palette 30/106

Allen JEE (Advanced) 2016 MSQ

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is $T = 2\pi \sqrt{\frac{7(R-r)}{5g}}$ . The values of R and r are measured to be $(60 \pm 1)$ mm and $(10 \pm 1)$ mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

A

The error in the measurement of $r$ is 10%.

B

The error in the measurement of $T$ is 3.57%.

C

The error in the measurement of $T$ is 2%.

D

The error in the determined value of g is 11%.

Question 31: Palette 31/106

Allen JEE (Advanced) 2015 MSQ

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then :

A

If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

B

If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm.

C

If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

D

If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm.

Question 32: Palette 32/106

Allen JEE (Main) 2014 MCQ

The current voltage relation of diode is given by $I = (e^{1000V/T} - 1) \, mA$ , where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring $\pm 0.01V$ while measuring the current of 5 mA at 300 K, what will be error in the value of current in mA?

A

0.5 mA

B

0.05 mA

C

0.2 mA

D

0.02 mA

Question 33: Palette 33/106

Allen JEE (Main) 2014 MCQ

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

A

A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

B

A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.

C

A meter scale.

D

A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in 1 cm.

Question 34: Palette 34/106

Allen JEE (Main) 2014 MCQ

The forward biased diode connection is:

A

B

C

D

Question 35: Palette 35/106

Allen JEE (Advanced) 2013 MCQ

Using the expression $2d \sin \theta = \lambda$ , one calculates the values of d by measuring the corresponding angles $\theta$ in the range 0 to $90^{\circ}$ . The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$ . As $\theta$ increases from $0^{\circ}$ :-

A

the absolute error in d remains constant

B

the absolute error in $d$ increases

C

the fractional error in d remains constant

D

the fractional error in d decreases

Question 36: Palette 36/106

Allen MCQ

Round off the following number within three significant figures $-4.735 \times 10^{-6} kg$

A

$4.74 \times 10^{-6} kg$

B

$5.00 \times 10^{-6} kg$

C

$4.70 \times 10^{-6} kg$

D

$4.73 \times 10^{-6} kg$

Question 37: Palette 37/106

Allen MCQ

$4.338 + 4.835 \times 3.88 \div 3.0$ is equal to:

A

10.6

B

10.59

C

10.5912

D

10.591267

Question 38: Palette 38/106

Allen MCQ

The length, breadth and thickness of a block are given by $l = 12 \text{ cm}$ , $b = 6 \text{ cm}$ and $t = 2.45 \text{ cm}$ . The volume of the block according to the idea of significant figures should be

A

$1 \times 10^{2} \text{cm}^{3}$

B

$2 \times 10^{2} \text{cm}^{3}$

C

$1.763 \times 10^{2} \text{cm}^{3}$

D

None of these

Question 39: Palette 39/106

Allen MCQ

The vernier of a circular scale is divided in to 30 divisions, which coincides with 29 main scale divisions. If each main scale division is $(1/2)^{\circ}$ , the least count of the instrument is

A

$0.1'$

B

$1'$

C

$10'$

D

$30'$

Question 40: Palette 40/106

Allen MCQ

The pitch of a screw gauge is 0.5 mm and there are 100 divisions on it circular scale. The instrument reads +2 circular scale divisions when nothing is put in-between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and $83^{rd}$ circular scale division coincides with the reference line. Then the diameter of the wire is

A

4.05 mm

B

4.405 mm

C

3.05 mm

D

1.25 mm

Question 41: Palette 41/106

Allen MCQ

The circular divisions of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is

A

2.25 mm

B

$2.20 \mathrm{~mm}$

C

$1.20 \, mm$

D

1.25 mm

Question 42: Palette 42/106

Allen MCQ

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

A

0.9%

B

2.4%

C

3.1%

D

4.2%

Question 43: Palette 43/106

Allen MCQ

An experiment measures quantities x, y, z and then t is calculated from the data as $t = \frac{xy^{2}}{z^{3}}$ . If percentage errors in x, y and z are respectively 1%, 3%, 2%, then percentage error in t is:

A

10%

B

4%

C

7%

D

13%

Question 44: Palette 44/106

Allen MCQ

Two resistance are measured in ohm and is given as: $R_{1} = 3\Omega \pm 1\% ; R_{2} = 6\Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is

A

$3\%$

B

$4.5\%$

C

$0.67\%$

D

$1.33\%$

Question 45: Palette 45/106

Allen MCQ

In a resonance-column experiment, the tuning fork is held above the open end of the glass tube. This can be done in two ways position (1) one prong below the other, and position (2) the two prongs at the same horizontal level. The correct position is –

A

(1) in all cases

B

(2) in all cases

C

(1) for first resonance and (2) for second resonance

D

(2) for first resonance and (1) for second resonance

Question 46: Palette 46/106

Allen MCQ

A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The distance frequency of the tuning fork is 512 Hz. The air temperature is $38^{\circ}$ C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance column. When first resonance occurs, the reading of the water level in the column is

A

14.0

B

15.2

C

16.4

D

17.6

Question 47: Palette 47/106

Allen MCQ

Following observation are taken from a travelling microscope to determine the refractive index of a liquid. Reading for the bottom of an empty beaker = 12.324 cm. Reading for the bottom of the beaker when partially filled with the liquid = 12.802 cm. Reading for the liquid surface = 13.895 cm. What is the refractive index of the liquid?

A

1.232

B

1.389

C

1.437

D

1.208

Question 48: Palette 48/106

Allen MCQ

An experiment with convex lens gives certain result which is represented by a student in the shown graph. What would be the power of the lens used.

A

0.2D

B

1D

C

0.1D

D

20D

Question 49: Palette 49/106

Allen MCQ

In an optics experiment, with the position of the object fixed, a student varies the position of the convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45^{\circ}$ with the x-axis meets the experimental curve at P. The coordinates of P will be:

A

$\left(\frac{f}{2}, \frac{f}{2}\right)$

B

$(f, f)$

C

$(4f, 4f)$

D

$(2f, 2f)$

Question 50: Palette 50/106

Allen MCQ

In Searle's apparatus, when experimental wire is loaded and unloaded, the air bubble in spirit level gets shifted.

A

towards reference wire while loading and towards experimental wire while unloading

B

towards experimental wire while loading and towards reference wire while unloading

C

towards experimental wire, both the times, during loading and unloading

D

towards reference wire, both the times during loading and unloading

Question 51: Palette 51/106

Allen MCQ

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.80 mm with an uncertainty of $\pm0.05$ mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $\pm0.01$ mm. Take $g=9.8\ m/s^{2}$ (exact). The Young's modulus obtained from the reading is

A

$(2.0 \pm 0.3) \times 10^{11}\ N/m^{2}$

B

$(2.0 \pm 0.2) \times 10^{11}\ N/m^{2}$

C

$(2.0 \pm 0.1) \times 10^{11}\ N/m^{2}$

D

$(2.0 \pm 0.05) \times 10^{11}\ N/m^{2}$

Question 52: Palette 52/106

Allen MCQ

In a meter bridge circuit, the known resistance used in resistance box is $100 \Omega$ (without any error, and the unknown resistor is put in right arm). The null point is found to be 40 cm from left end. If mm scale is used in the meter bridge then resistance of the unknown resistor is:

A

$150\Omega \pm \frac{3}{8}\Omega$

B

$150\Omega \pm \frac{1}{8}\Omega$

C

$150\Omega \pm \frac{5}{8}\Omega$

D

$150\Omega \pm \frac{7}{16}\Omega$

Question 53: Palette 53/106

Allen MCQ

The manifestation of band structure in solids is due to -

A

Bohr's correspondence principle.

B

Pauli's exclusion principle.

C

Heisenberg's uncertainty principle.

D

Boltzmann's law.

Question 54: Palette 54/106

Allen MCQ

In a P-N junction diode not connected to any circuit -

A

the potential in the same everywhere.

B

the P-type side is at a higher potential then the N-type side.

C

there is an electric field at the junction directed from the N-type side to the P-type side.

D

there is an electric field at the junction directed from the P-type to the N-type side.

Question 55: Palette 55/106

Allen MCQ

If the ratio of the concentration of electrons to that of holes in a semiconductor is $\frac{7}{5}$ and the ratio of currents is $\frac{7}{4}$ then what is the ratio of their drift velocities -

A

$\frac{5}{4}$

B

$\frac{4}{7}$

C

$\frac{5}{6}$

D

$\frac{4}{5}$

Question 56: Palette 56/106

Allen MCQ

For extrinsic semiconductors; when doping level is increased;

A

Fermi-level of p-type semiconductor will go upward, and Fermi-level of n-type semiconductors will go downward.

B

Fermi-level of p-type semiconductors will go downward, and Fermi-level of n-type semiconductor will go upward.

C

Fermi-level of both p-type and n-type semiconductors will go upward for $T > T_{F} K$ and downward for $T < T_{F} K$ , where $T_{F}$ is Fermi temperature.

D

Fermi-level of p and n-type semiconductors will not be affected.

Question 57: Palette 57/106

Allen MCQ

A semiconductor pn junction at thermal equilibrium has the space charge density $\rho(x)$ profile as shown in the figure. The figure that best depicts the variation of the electric field E with x is :-(W denotes the width of the depletion layer)

A

B

C

D

Question 58: Palette 58/106

Allen MCQ

In the following circuits $PN$ -junction diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal for the following potential of $A$ and $B$ , the correct increasing order of resistance between $A$ and $B$ will be - (i) $-10V, -5V,$ (ii) $-5V, -10V$ (iii) $-4V, -12V$

A

(i) < (ii) < (iii)

B

(iii) < (ii) < (i)

C

(ii) = (iii) < (i)

D

(i) = (iii) < (ii)

Question 59: Palette 59/106

Allen MCQ

The circuit has two oppositely connected ideal diodes in parallel. What is the current flowing in the circuit?

A

2.31 A

B

$1.33A$

C

$1.71A$

D

2.00 A

Question 60: Palette 60/106

Allen MCQ

In given figure when input voltage increases,

A

the current through $R_{S}$ , $R_{L}$ and Zener increases.

B

the current through $R_{S}$ increases, Zener increases but through $R_{L}$ remains constant.

C

the current through $R_{S}$ increases, through Zener decreases, $R_{L}$ increases.

D

the current through $R_{S}$ increases, through Zener remains constant but $R_{L}$ increases.

Question 61: Palette 61/106

Allen MCQ

If in a p-n junction diode, a square input signal of 10V is applied as shown. Then the output signal across $R_{L}$ will be :-

A

B

C

D

Question 62: Palette 62/106

Allen MCQ

Ge and Si diodes start conducting at 0.3V and 0.7V respectively. In the following figure if Ge diode connection are reversed, the value of $V_{o}$ changes by: (Assume that the Ge diode has large breakdown voltage)

A

$0.6V$

B

0.8 V

C

0.4 V

D

$0.2V$

Question 63: Palette 63/106

Allen MCQ

Figure shown a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the unregulated input voltage varies between 10 V to 16 V, then what is the maximum Zener current?

A

2.5 mA

B

3.5 mA

C

7.5 mA

D

1.5 mA

Question 64: Palette 64/106

Allen MCQ

Take the breakdown voltage of the Zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of the output voltage is : (Graphs drawn are schematic and not to scale)

A

B

C

D

Question 65: Palette 65/106

Allen MCQ

Zener breakdown occurs in a p-n junction having p and n both:

A

lightly doped and have wide depletion layer.

B

heavily doped and have narrow depletion layer.

C

lightly doped and have narrow depletion layer.

D

heavily doped and have wide depletion layer.

Question 66: Palette 66/106

Allen MCQ

Which of the following circuits correctly represents the following truth table? $\begin{array}{c c c} \text {A} & \text {B} & \text {C} \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}$

A

B

C

D

Question 67: Palette 67/106

Allen MCQ

For the given combination of gates, if the logic states of inputs A, B, C are as follows A = B = C = 0 and A = B = 1, C = 0 then the logic states of output D are -

A

0, 0

B

0, 1

C

1, 0

D

1,1

Question 68: Palette 68/106

Allen MCQ

In the circuit below, A and B represent two inputs and C represents the output. The circuit represents.

A

AND gate

B

NAND gate

C

OR gate

D

NOR gate

Question 69: Palette 69/106

Allen MCQ

To get output '1' at R, for the given logic gate circuit the input values must be:

A

$X = 0, Y = 1$

B

$X = 1, Y = 1$

C

$X = 0, Y = 0$

D

$X = 1, Y = 0$

Question 70: Palette 70/106

Allen MCQ

Boolean relation at the output stage-Y for the following circuit is:

A

$A + B$

B

$\vec{A}+\vec{B}$

C

$\vec{A}\cdot\vec{B}$

D

$A\cdot B$

Question 71: Palette 71/106

Allen MSQ

A cuboid has sides of 10.4 cm, 3.8 cm and 1.02 cm. Choose the correct statement(s) about the area of the faces and its volume with due regard to significant digits.

A

The largest face area is $39.52 \, cm^{2}$ .

B

The smallest face area is $3.9 \, cm^{2}$ .

C

The volume of the cuboid is $4.0 \times 10^{1} \, cm^{3}$ .

D

The perimeter of the smallest face is 9.64 cm.

Question 72: Palette 72/106

Allen MSQ

In ordinary Vernier callipers, 10 $^{th}$ division of the Vernier scale coincides with 9 $^{th}$ division of the main scale. In a specially designed Vernier callipers the Vernier scale is so constructed that 10 $^{th}$ division on it coincides with 11 $^{th}$ division on the main scale. Each division on the main scale equals to 1 mm. The callipers have a zero error as shown in the figure-I. When the Vernier calliper is used to measure a length, the concerned portion of its scale is shown in figure-II.

A

Zero error in the callipers has magnitude 0.7 mm.

B

The length being measured is 1.08 cm.

C

The length being measured is 1.22 cm.

D

Zero error in the callipers has magnitude 0.3 mm

Question 73: Palette 73/106

Allen MSQ

want to design a carbon resistor in shape of a cylinder. Its resistivity is known precisely. The diameter is measured by a screw gauge whose main scale has a least count of 1 mm and circular scale has 100 divisions. The length is measured by a vernier callipers whose main scale is 1 mm and 9 main scale divisions coincide with 10 vernier scale divisions. wish that the fourth band in the colour code be painted gold. In which of the following screw gauge readings and vernier callipers readings will our goal be achieved?

A

Screw gauge: msr 2 divisions, $50^{\text{th}}$ csd coinciding, Vernier scale: msr: $1.2 \, \text{cm}$ , $5^{\text{th}}$ vernier division coinciding.

B

Screw gauge: msr 1 divisions, $0^{\text{th}}$ csd coinciding, Vernier scale: msr: $0.3 \, \text{cm}$ , $3^{\text{rd}}$ vernier division coinciding.

C

Screw gauge: msr 0 divisions, $40^{\text{th}}$ csd coinciding, Vernier scale: msr: 5 cm, $0^{\text{th}}$ vernier division coinciding.

D

Screw gauge: msr 1 divisions, $10^{\text{th}}$ csd coinciding, Vernier scale: msr: 8 cm, $8^{\text{th}}$ vernier division coinciding.

Question 74: Palette 74/106

Allen MSQ

In resonance air-column method, two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

A

the intensity of the sound heard at the first resonance was more than that at the second resonance.

B

the prongs of the tuning fork were kept in a horizontal plane above the resonance tube.

C

the amplitude of vibration of the ends of the prongs is typically around 1 cm.

D

the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.

Question 75: Palette 75/106

Allen MSQ

In an experiment to measure surface tension of completely wetting liquid, the capillary was dipped in liquid. The level of water in beaker was measured using travelling microscope to be 1.43cm. The level of water in capillary was measured to be 6.23cm. The readings for inner diameter were 0.00cm and 0.32cm respectively. Neglect the expansion of capillary and water on heating.

A

% error in measurement of h is 0.4%

B

% error in measurement of surface tension is 6.46%

C

if temperature increases, level of water in capillary will be less than 6.23cm.

D

$s = 0.38 \pm 0.04N / m$

Question 76: Palette 76/106

Allen MSQ

In the meter bridge circuit, the point D is the balance point.

A

If the jockey is shifted to the left of D, current will flow from the meter bridge wire to the point B.

B

If jockey is shifted to the right of $D$ , current will flow from point $B$ to the meter bridge wire.

C

If the jockey is at point D, but now the resistance P is heated, then the current will flow from point B to the meter bridge wire.

D

If the jockey is at point D, but now the resistance P is heated, then the current will flow from the meter bridge wire to the point B.

Question 77: Palette 77/106

Allen MSQ

In the Searle's experiment, after every step of loading, why should wait for two minutes before taking the readings?

A

So that the wire can have its desired change in length.

B

So that the wire can attain room temperature.

C

So that vertical oscillations can get subsided.

D

So that the wire has no change in its radius.

Question 78: Palette 78/106

Allen MCQ

If $a = 8 \pm 0.08$ and $b = 6 \pm 0.06$ . Let $x = a + b$ , $y = a - b$ , $z = a \times b$ . The correct order of % error in x, y and z is :-

A

x = y < z

B

x = y > z

C

x < z < y

D

x > z < y

Question 79: Palette 79/106

Allen MCQ

The edge of a cube is $a = 1.2 \times 10^{-2} m$ . Then its volume will be recorded as:

A

$1.7 \times 10^{-6} m^{3}$

B

$1.70 \times 10^{-6} m^{3}$

C

$1.70 \times 10^{-7} m^{3}$

D

$1.78 \times 10^{-6} m^{3}$

Question 80: Palette 80/106

Allen MCQ

On the basis of detail given about two measuring instruments, select the correct statement. (i) Vernier callipers having main scale division = 0.05 cm and Vernier scale division = $\frac{2.45}{50}$ cm. (ii) Screw gauge having pitch 0.5 mm and its circular scale division measures 0.01 mm.

A

Both the instruments have same least count.

B

Least count of screw gauge is lesser than that of vernier callipers.

C

Both the instruments have same least count but screw gauge is more precise.

D

Both the instruments have different least count and screw gauge is more precise.

Question 81: Palette 81/106

Allen MCQ

In a Searle's experiment for determination of Young's Modulus, when a load of 50 kg is added to a 3 meter long wire micrometer screw having pitch 1 mm needs to be given a quarter turn in order to restore the horizontal position of spirit level. Young's modulus of the wire if its cross-sectional area is $10^{-5}$ m $^{2}$ is

A

$6 \times 10^{11} N/m^{2}$

B

$1.5 \times 10^{11} N/m^{2}$

C

$3 \times 10^{11} N/m^{2}$

D

None

Question 82: Palette 82/106

Allen MCQ

An electric field is applied to a semi-conductor. Let the number of charge carriers be n and the average drift speed be v. If the temperature is increased:

A

Both n and v will increase

B

n will increase but v will decrease

C

v will increase but n will decrease

D

Both n and v will decrease

Question 83: Palette 83/106

Allen MCQ

P-type semiconductor is formed when A. As impurity is mixed in Si B. Al impurity is mixed in Si C. B impurity is mixed in Ge D. P impurity is mixed in Ge

A

A and C

B

A and D

C

B and C

D

B and D

Question 84: Palette 84/106

Allen MCQ

A strip of copper and another of germanium are cooled from room temperature to 80K. The resistance of -

A

copper strip increases and that of germanium decreases

B

copper strip decreases and that of germanium increases

C

each of these increases

D

each of these decreases

Question 85: Palette 85/106

Allen MCQ

The V-I characteristic for a p-n junction diode is plotted as shown in the figure. From the plot can conclude that $[V_b \to$ breakdown voltage, $V_k \to$ knee voltage]

A

The forward bias resistance of diode is very high; almost infinity for small values of $V$ and after a certain value it becomes very low.

B

The reverse bias resistance of diode is very high in the beginning up to breakdown voltage is not achieved.

C

Both forward and reverse bias resistances are same for all voltages.

D

Both (1) and (2) are correct.

Question 86: Palette 86/106

Allen MCQ

A 2V battery is connected across AB as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to A and in other case when positive terminal of battery is connected to B will respectively be :-

A

$0.1A$ and $0.2A$

B

$0.4A$ and $0.2A$

C

$0.2A$ and $0.4A$

D

$0.2A$ and $0.1A$
PSC005

Question 87: Palette 87/106

Allen MCQ

In the half-wave rectifier circuit shown. Which one of the following wave forms is true for VCD, if the input is as shown?

A

B

C

D

Question 88: Palette 88/106

Allen MCQ

Name the logic gate equivalent to the diagram attached

A

OR

B

NOR

C

NAND

D

AND

Question 89: Palette 89/106

Allen MCQ

The logic performed by the circuit shown in figure is equivalent to :

A

AND

B

NAND

C

OR

D

NOR

Question 90: Palette 90/106

Allen MCQ

The output from a NAND gate having inputs A and B given below will be.

A

B

C

D

Question 91: Palette 91/106

Allen MCQ

Given below are four logic gate symbols (figure). Those for OR, NOR and NAND are respectively.

A

1, 4, 3

B

4, 1, 2

C

1, 3, 4

D

4, 2, 1

Question 92: Palette 92/106

Allen MCQ

The following truth table corresponds to the logic gate - A- 0 0 1 1 B- 0 1 0 1 X- 0 1 1 1

A

NAND

B

OR

C

AND

D

XOR

Question 93: Palette 93/106

Allen MCQ

The following figure shows a logic gate circuit with two input A and B output C. The voltage waveforms of A, B and C are as shown in second figure below. The logic gate is:

A

OR gate

B

NAND gate

C

AND gate

D

NOR gate

Question 94: Palette 94/106

Allen MCQ

The combination of 'NAND' gates shown here under (figure) are equivalent to -

A

An OR gate and an AND gate respectively

B

An AND gate and a NOT gate respectively

C

An AND gate and an OR gate respectively

D

An OR gate and a NOT gate respectively

Question 95: Palette 95/106

Allen MCQ

A wire has a mass $0.3 \pm 0.003$ g, radius $0.5 \pm 0.005$ mm and length $6 \pm 0.06$ cm. The maximum percentage error in the measurement of its density is :-

A

1

B

2

C

3

D

4

Question 96: Palette 96/106

Allen MCQ

A vernier callipers having 1 main scale division = 0.1 cm is designed to have a least count of 0.02 cm. If n be the number of divisions on vernier scale and m be the length of vernier scale, then:

A

n = 10, m = 0.5 cm

B

n = 9, m = 0.4 cm

C

n = 10, m = 0.8 cm

D

n = 10, m = 0.2 cm

Question 97: Palette 97/106

Allen MCQ

When the gap is closed without placing any object in the screw gauge whose least count is 0.005 mm, the $5^{th}$ division on its circular scale coincides with the reference line on main scale, and when a small sphere is placed reading on main scale advances by 4 divisions, whereas circular scale reading advances to five times to the corresponding reading when no object was placed. There are 200 divisions on the circular scale. The radius of the sphere is

A

4.10 mm

B

4.05 mm

C

2.10 mm

D

2.05 mm

Question 98: Palette 98/106

Allen MCQ

In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decide to balance a resistance of 4X against Y -

A

50 cm

B

80 cm

C

40 cm

D

70 cm

Question 99: Palette 99/106

Allen MCQ

A student performs an experiment for determination of $g\left(=\frac{4\pi^{2}l}{T^{2}}\right)l\approx1m$ and he commits an error of $\Delta l$ . For the experiment takes the time of n oscillations with the stop watch of least count $\Delta T$ and he commits a human error of 0.1sec. For which of the following data, the measurement of g will be most accurate?

A

ΔI-5 mm, ΔT-0.2 sec, n-10, Amplitude of oscillation-5mm

B

ΔI-5 mm, ΔT-0.2 sec, n-20, Amplitude of oscillation-5mm

C

ΔI-5 mm, ΔT-0.1 sec, n-20, Amplitude of oscillation-1mm

D

ΔI-1 mm, ΔT-0.1 sec, n-50, Amplitude of oscillation-1mm

Question 100: Palette 100/106

Allen MCQ

In an experiment to determine the focal length $(f)$ of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

A

$x < f$

B

$f < x < 2f$

C

$x = 2f$

D

$x > 2f$

Question 101: Palette 101/106

Allen MCQ

In Wheatstone bridge experiment as shown in figure -

A

Key $K_{1}$ should be pressed first and then $K_{2}$ .

B

Key $K_{2}$ should be pressed first and then $K_{1}$ .

C

Any key can be pressed in any order.

D

Both keys should be pressed simultaneously.

Question 102: Palette 102/106

Allen MCQ

In a resonance column method, resonance occurs at two successive level of $l_{1} = 30.7 \, cm$ and $l_{2} = 63.2 \, cm$ using a tuning fork of f = 512 Hz. What is the maximum error in measuring speed of sound using relations $v = f\lambda$ and $\lambda = 2(l_{2} - l_{1})$

A

256 cm/sec

B

92 cm/sec

C

128 cm/sec

D

102.4 cm/sec

Question 103: Palette 103/106

Allen MSQ

In the Searle's experiment, after every step of loading, why should wait for two minutes before taking the readings?

A

So that the wire can have its desired change in length.

B

So that the wire can attain room temperature.

C

So that vertical oscillations can get subsided.

D

So that the wire has no change in its radius.

Question 104: Palette 104/106

Allen MSQ

Two resistance are $R_{1} = 5.0 \pm 0.2 \Omega$ and $R_{2} = 10.0 \pm 0.1 \Omega$ . Equivalent resistance with limit of possible error is $R_{s}$ and $R_{p}$ when both resistances are connected in series and parallel respectively.

A

$R_{s} = 15.0 \Omega \pm 2\%$

B

$R_{p} = 3.3 \Omega \pm 3\%$

C

$R_{s} = 15.0 \Omega \pm 1\%$

D

$R_{p} = 3.3 \Omega \pm 2\%$

Question 105: Palette 105/106

Allen MSQ

A physical quantity P is related to four observables A, B, C and D as $P = 4\pi^{2}A^{3}B^{2}/(\sqrt{C}D)$ . The percentage error of the measurement in A, B, C and D are 1%, 3% and 2%, 4% respectively. Value of P is calculated 3.763.

A

Percentage error is 12%

B

Percentage error is 14%

C

Absolute error is 0.53

D

Absolute error is 0.27

Question 106: Palette 106/106

Allen MSQ

The period of oscillation of a simple pendulum in an experiment is recorded as 2.63 sec, 2.56 sec, 2.42 sec, 2.71 sec and 2.80 sec respectively:-

A

Time period is 2.62 sec

B

Average absolute error is 0.01 sec

C

Percentage error is $2.4\%$

D

Percentage error is $4.2\%$