MCQs for JSSC

2091

Physics • Fluid Mechanics

A अनुप्रस्थ काट क्षेत्रफल वाले एक ऊर्ध्वाधर पात्र में आदर्श तरल भरा है। तल से A/4 क्षेत्रफल का छिद्र किया जाता है। छिद्र से निकलते समय तरल का त्वरण कितना होगा? A vertical vessel of cross-sectional area A is filled with an ideal liquid. A hole of area A/4 is made at the bottom. What is acceleration of liquid while flowing out?

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A. g/15 g/15 B. g/5 g/5 C. lg/4 lg/4 D. lg/3 lg/3

सही उत्तर: A Correct Answer: A

निरंतरता समीकरण और बर्नौली सिद्धांत लागू करने पर तरल का त्वरण g/15 प्राप्त होता है।

Applying continuity equation and Bernoulli's principle gives acceleration g/15.

2092

Physics • Electromagnetic Induction

50 cm लंबाई, 2 cm व्यास और 200 फेरों वाली एक परिनालिका का स्वप्रेरकत्व ज्ञात कीजिए। (μ₀ = 4π × 10⁻⁷ H/m) Calculate self-inductance of a solenoid of length 50 cm, diameter 2 cm and 200 turns. (μ₀ = 4π × 10⁻⁷ H/m)

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A. 31.55 H 31.55 H B. 31.55 μH 31.55 μH C. 3.55 H 3.55 H D. 31.55 mH 31.55 mH

सही उत्तर: B Correct Answer: B

परिनालिका के लिए L = μ₀N²A/l का उपयोग करने पर L = 31.55 μH मिलता है।

For a solenoid, L = μ₀N²A/l, giving L = 31.55 μH.

2093

Physics • Nuclear Physics

किसी रेडियोधर्मी पदार्थ की आरंभिक सक्रियता m₀ है और समय t बाद इसकी सक्रियता m हो जाती है। यदि (m₀/m) = e हो, तो क्षय नियतांक क्या होगा? Initial activity of a radioactive substance is m₀ and after time t it becomes m. If (m₀/m) = e, what is the decay constant?

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A. e² e² B. E E C. 3 3 D. 2 2

सही उत्तर: A Correct Answer: A

रेडियोधर्मी क्षय संबंध m = m₀e⁻ˡᵗ से प्रश्न-पत्रानुसार सही विकल्प e² है।

From radioactive decay relation m = m₀e⁻ˡᵗ, the correct option indicated in the paper is e².

2094

Physics • Nuclear Physics

किसी रेडियोधर्मी पदार्थ का आधा जीवन 1000 वर्ष है। कितने वर्षों बाद 75% नमूना क्षय हो जाएगा? A radioactive substance has half-life 1000 years. After how many years will 75% of the sample decay?

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A. 2000 वर्ष 2000 years B. 750 वर्ष 750 years C. 3000 वर्ष 3000 years D. 500 वर्ष 500 years

सही उत्तर: A Correct Answer: A

75% क्षय का अर्थ है 25% शेष रहना, अर्थात दो अर्ध-जीवन। अतः समय 2000 वर्ष है।

For 75% decay, 25% remains, which corresponds to two half-lives. Thus time is 2000 years.

2095

Physics • Electronic Devices

एक अर्ध-तरंग रेक्टिफायर में लोड प्रतिरोध 1 kΩ और इनपुट आपूर्ति 200 V है। डायोड के अग्र प्रतिरोध की उपेक्षा करते हुए Vdc ज्ञात कीजिए। In a half-wave rectifier, load resistance is 1 kΩ and input supply is 200 V. Neglecting forward resistance of diode, find Vdc.

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A. 200√2 V 200√2 V B. 200 V 200 V C. 200√2/π V 200√2/π V D. 200/π V 200/π V

सही उत्तर: C Correct Answer: C

हाफ-वेव रेक्टिफायर के लिए Vdc = Vm/π और Vm = √2Vrms है। अतः Vdc = 200√2/π V।

For a half-wave rectifier, Vdc = Vm/π and Vm = √2Vrms. Hence Vdc = 200√2/π V.

2096

Physics • Gravitation

सूर्य के चारों ओर किसी ग्रह की कक्षा में अधिकतम और न्यूनतम वेग क्रमशः 30 km/s तथा 29.2 km/s हैं। कक्षा की उत्केंद्रता ज्ञात कीजिए। The greatest and least velocities of a planet in its orbit around the Sun are 30 km/s and 29.2 km/s respectively. Find eccentricity of the orbit.

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A. 0.0135 0.0135 B. 0.027 0.027 C. 0.12 0.12 D. 0.13 0.13

सही उत्तर: A Correct Answer: A

उत्केंद्रता e = (vmax−vmin)/(vmax+vmin) = 0.8/59.2 ≈ 0.0135 है।

Eccentricity e = (vmax−vmin)/(vmax+vmin) = 0.8/59.2 ≈ 0.0135.

2097

Advanced Mathematics • Probability

Consider 10 tosses of a fair die. Let X_i denote the number of times digit i appears. Find P(X_2 = 2 | X_1 = 2). Consider 10 tosses of a fair die. Let X_i denote the number of times digit i appears. Find P(X_2 = 2 | X_1 = 2).

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A. C(10,2)(1/6)^2(5/6)^8 C(10,2)(1/6)^2(5/6)^8 B. C(8,2)(1/5)^2(4/5)^6 C(8,2)(1/5)^2(4/5)^6 C. C(8,2)(1/6)^2(5/6)^6 C(8,2)(1/6)^2(5/6)^6 D. (1/6)^2 (1/6)^2

सही उत्तर: B Correct Answer: B

Given X_1 = 2, the remaining 8 outcomes are non-one. For each such outcome, the conditional probability of getting 2 is 1/5. Hence X_2 is binomial with n = 8 and p = 1/5.

2098

Advanced Mathematics • Probability

We have P(X = x, Y = y) = 1/9 for all x, y in {1, 2, 3}. Find P(X > Y). We have P(X = x, Y = y) = 1/9 for all x, y in {1, 2, 3}. Find P(X > Y).

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A. 0 0 B. 1/3 1/3 C. 1 1 D. 1/2 1/2

सही उत्तर: B Correct Answer: B

The ordered pairs satisfying X > Y are (2,1), (3,1), and (3,2). Their total probability is 3 x (1/9) = 1/3.

2099

Advanced Mathematics • Convex Functions

Let f and g be two real-valued functions defined on [a,b], and h(x) = max(f(x), g(x)) for x in [a,b]. Which of the following is true? Let f and g be two real-valued functions defined on [a,b], and h(x) = max(f(x), g(x)) for x in [a,b]. Which of the following is true?

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A. If f and g are differentiable, then so is h; and if f and g are convex, then h is also convex. If f and g are differentiable, then so is h; and if f and g are convex, then h is also convex. B. If f and g are convex, then h is also convex. If f and g are convex, then h is also convex. C. If f and g are differentiable, then so is h. If f and g are differentiable, then so is h. D. If f and g are linear, then h is also linear. If f and g are linear, then h is also linear.

सही उत्तर: B Correct Answer: B

The pointwise maximum of convex functions is convex. Differentiability or linearity need not be preserved at points where the two functions cross.

2100

Advanced Mathematics • Fluid Mechanics

A block of concrete weighs 100 kg in air and weighs 60 kg when immersed in water. The average specific weight of the block is: A block of concrete weighs 100 kg in air and weighs 60 kg when immersed in water. The average specific weight of the block is:

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A. 3.2 ton/m^3 3.2 ton/m^3 B. 2.5 ton/m^3 2.5 ton/m^3 C. 2.2 ton/m^3 2.2 ton/m^3 D. 2.1 ton/m^3 2.1 ton/m^3

सही उत्तर: B Correct Answer: B

Loss of weight in water = 100 - 60 = 40 kg, which equals the weight of displaced water. Therefore, relative density = 100/40 = 2.5 and the specific weight is 2.5 ton/m^3.

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