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A heat engine is involved with exchange of heat of 1915 J, –40J, + 125J and –QJ, during one cycle achieving an efficiency of 50.0%. The value of Q is:

1) 980 J 2) 640 J 3) 40 J 4) 400 J Answer: (1) \(\begin{array}{l}\eta =\frac{W}{\sum Q_{+}}=\frac{Q_{1}+Q_{2}+Q_{3}+Q_{4}}{Q_{1}+Q_{3}}\end{array} \) \(\begin{array}{l}0.5 =\frac{1915-40+125-Q}{1915+125}\end{array}... View Article

In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be:

1) 28 2) 24 3) 30 4) 18 Answer: (1) \(\begin{array}{l}y =\frac{D\lambda }{d}\end{array} \) \(\begin{array}{l}n_{1}\frac{D\lambda_{1} }{d}=n_{2}\frac{D\lambda_{2} }{d}\end{array} \) \(\begin{array}{l}\frac{n_{1}}{n_{2}}=\frac{\lambda _{2}}{\lambda... View Article

This displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion? (A) The force is zero at t = 3T/4 (B)... View Article

An inductance coil has a reactance of 100 Ω. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is:

1) 6.7 × 10–7 H 2) 5.5 × 10–5 H 3) 1.1 × 10–1 H 4) 1.1 × 10–2 H... View Article

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by [latex]hat{k}[/latex] and [latex]2hat{i}-2hat{j}[/latex], respectively. What is the unit vector along direction of propagation of the wave.

1) \(\begin{array}{l}\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\end{array} \) 2) \(\begin{array}{l}\frac{1}{\sqrt{5}}(2\hat{i}+\hat{j})\end{array} \) 3) \(\begin{array}{l}\frac{1}{\sqrt{5}}(\hat{i}+2\hat{j})\end{array} \) 4) \(\begin{array}{l}\frac{1}{\sqrt{2}}(\hat{j}+\hat{k})\end{array} \) Answer: (1) \(\begin{array}{l}\vec{E}\times\vec{B} =\hat{k}\times (2\hat{i}-2\hat{j})=2\hat{k}\times \hat{i}-2\hat{k}\times \hat{j} =... View Article

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

Answer: (3) Since it is released from rest. And anet is constant. If will have straight line path along net... View Article

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is:

1) \(\begin{array}{l}\sqrt{2}abI,along \left [ \frac{\hat{j}}{\sqrt{5}}+\frac{2\hat{k}}{\sqrt{5}} \right]\end{array} \) 2) \(\begin{array}{l}abI,along \left [ \frac{\hat{j}}{\sqrt{5}}+\frac{2\hat{k}}{\sqrt{5}} \right ]\end{array} \) 3) \(\begin{array}{l}\sqrt{2}abI,along \left [ \frac{\hat{j}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}... View Article

In the following digital circuit, what will be the output at ‘Z’, when the input (A,B) are (1,0), (0,0), (1,1), (0,1):

1) 0,1,0,0 2) 1,1,0,1 3) 0,0,1,0 4) 1,0,1,1 Answer: (3)

A potentiometer wire PQ of 1 m length is connected to a standard cell E₁. Another cell E₂ of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in figure). With switch S open, the null positon is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is:

1) 0.03V/cm 2) 0.02 V/cm 3) 0.04 V/cm 4) 0.01 V/cm Answer: (2) PQ= 1 m QJ = 49 cm... View Article

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 × 10^–4. The mass of the particle is close to:

1) 4.8 × 10–27 kg 2) 9.1 × 10–31 kg 3) 9.7 × 10–28 kg 4) 1.2 × 10–28 kg... View Article

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg –m² and 10 rad s^–1 respectively while those for the second one are 0.2 kg–m² and 5 rad s^–1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is:

1) 2/3 J 2) 10/3 J 3) 5/3 J 4) 20/3 J Answer: (4) \(\begin{array}{l}I_{1}\omega _{1}+I_{2}\omega _{2}=(I_{1}+I_{2})\omega\end{array} \) \(\begin{array}{l}\omega =\frac{I_{1}\omega... View Article

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is:

1) [P1/2 AT–1] 2) [PA1/2 T–1] 3) [PA ½ T–1] 4) [P2 AT–2] Answer: (2) \(\begin{array}{l}\left [ P \right ]=MLT^{-1}\leftarrow... View Article

The number of CH2 = 0 groups present in a tripeptide Asp–Glu–Lys is ____.

Answer: 5

6.023 × 10²² molecules are present in 10 g of a substance ‘x’. The molarity of a solution containing 5 g of substance ‘x’ in 2 L solution is _____ × 10^–3.

Answer: 25 Mol. wt of ‘x’ = {10 / [6.023 × 1022]} × 6.023 × 1023 M = [5 /... View Article

If 250 cm³ of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of another aqueous solution containing 1.65 g of a protein B, at 298 K, the ratio of the molecular masses of A and B is ______ × 10^–2 (to the nearest integer).

Answer: 177 [0.73 / MA] × [1000 / 250] = 1.65 / MB [MA / MB] = [73 × 4]... View Article

An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation

Cr₂O₇^2- + 14H⁺ + 6e^– → 2Cr³⁺+ + 7H₂O

The amount of Cr³⁺ obtained was 0.104 g. The efficiency of the process (in %) is (Take: F = 96000 C, At. mass of chromium = 52) _______.

Answer: 60 % [moles of Cr3+] × 3 = [8 × 60 × 2] / 96000 Moles of Cr3+ =... View Article

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