UPSC NDA-1

31. The time period of a 1 m long pendulum approximates to

The time period of a 1 m long pendulum approximates to

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6 s
4 s
2 s
1 s
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The time period of a 1 m long pendulum approximates to 2 s.
The time period ($T$) of a simple pendulum for small oscillations is given by the formula $T = 2\pi \sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity.
Given length $L = 1$ m. Taking the standard value of $g \approx 9.8$ m/s² and $\pi \approx 3.14$: $T = 2 \times 3.14 \times \sqrt{\frac{1}{9.8}} \approx 6.28 \times \sqrt{0.102} \approx 6.28 \times 0.319 \approx 2.005$ s. A common approximation for calculation purposes is sometimes $\pi^2 \approx g$, which gives $T = 2\pi \sqrt{\frac{1}{\pi^2}} = 2\pi \times \frac{1}{\pi} = 2$ s. Both calculations yield a value very close to 2 seconds.

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32. A ball is thrown vertically upward with a speed of 40 m/s. The time ta

A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately

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2 s
3 s
4 s
5 s
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The time taken by the ball to reach the maximum height would be approximately 4 s.
When an object is thrown vertically upward, its velocity decreases due to the acceleration due to gravity ($g$) acting downwards. At the maximum height, the velocity of the object momentarily becomes zero. We can use kinematic equations to find the time taken.
Given initial velocity $u = 40$ m/s. At maximum height, final velocity $v = 0$ m/s. The acceleration due to gravity is $a = -g$. Taking $g \approx 10$ m/s² (a common approximation for simplicity), $a = -10$ m/s². Using the kinematic equation $v = u + at$: $0 = 40 + (-10)t$. Solving for $t$: $10t = 40$, so $t = \frac{40}{10} = 4$ s. Using $g \approx 9.8$ m/s² would give a time slightly less than 4s, but 4s is the closest approximation among the options.

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33. What is the dimension of gravitational constant?

What is the dimension of gravitational constant?

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ML³T⁻²
M⁻¹L³T⁻²
M²L⁻²T⁻²
M²L⁻¹T⁻²
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The dimension of the gravitational constant ($G$) is M⁻¹L³T⁻².
The gravitational constant $G$ appears in Newton’s Law of Universal Gravitation, which states that the force ($F$) between two masses ($m_1$, $m_2$) separated by a distance ($r$) is given by $F = G \frac{m_1 m_2}{r^2}$.
We can determine the dimensions of $G$ by rearranging the formula: $G = \frac{F r^2}{m_1 m_2}$. The dimensions of Force ($F$) are [MLT⁻²], distance ($r$) are [L], and mass ($m$) are [M]. Substituting these dimensions: $[G] = \frac{[MLT⁻²] [L]^2}{[M][M]} = \frac{[ML³T⁻²]}{[M²]} = [M^{1-2} L³ T⁻²] = [M⁻¹L³T⁻²]$.

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34. The magnetic field produced by a current-carrying straight wire at a p

The magnetic field produced by a current-carrying straight wire at a point outside the wire depends

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inversely on the distance from it
directly on the distance from it
inversely at short distances and directly at large distances from it
directly on the distance (at short distances) and inversely on the distance (at long distances) from it
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The magnetic field produced by a current-carrying straight wire at a point outside the wire depends inversely on the distance from it.
The magnitude of the magnetic field ($B$) at a distance ($r$) from a long, straight conductor carrying current ($I$) is given by the formula $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0$ is the permeability of free space.
From the formula $B = \frac{\mu_0 I}{2\pi r}$, it is clear that for a constant current $I$, the magnetic field strength $B$ is inversely proportional to the distance $r$ from the wire ($B \propto \frac{1}{r}$). This relationship holds true for points outside the wire.

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35. What is the current required to light a 60 W incandescent bulb in a do

What is the current required to light a 60 W incandescent bulb in a domestic supply of 240 V ?

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0·5 A
0·25 A
1·0 A
5·0 A
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The current required is 0.25 A.
The power ($P$) consumed by an electrical device is related to the voltage ($V$) across it and the current ($I$) flowing through it by the formula $P = V \times I$.
Given Power $P = 60$ W and Voltage $V = 240$ V. Using the formula $P = V \times I$, we can find the current $I$: $I = \frac{P}{V} = \frac{60 \text{ W}}{240 \text{ V}} = \frac{60}{240} \text{ A} = \frac{1}{4} \text{ A} = 0.25 \text{ A}$.

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36. Which one of the following correctly represents the SI unit of

Which one of the following correctly represents the SI unit of resistivity?

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$Omega$
$Omega$/m
$Omega$ cm
$Omega$ m
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The correct SI unit of resistivity is Ohm meter ($\Omega$ m).
Resistivity ($\rho$) is an intrinsic property of a material that quantifies how strongly it resists electric current. It is related to resistance ($R$), length ($L$), and cross-sectional area ($A$) of a conductor by the formula $R = \rho \frac{L}{A}$.
Rearranging the formula, $\rho = \frac{R \times A}{L}$. Substituting the SI units: $R$ is in Ohms ($\Omega$), $A$ is in square meters (m²), and $L$ is in meters (m). Therefore, the unit of resistivity is $\frac{\Omega \times \text{m}^2}{\text{m}} = \Omega \text{ m}$.

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37. The frequency of an alternating current is 3 Hz. It implies that

The frequency of an alternating current is 3 Hz. It implies that

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there are 6 cycles/s
there are 3 cycles/s
there are 2 cycles/s
there is only 1 cycle/s
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A frequency of 3 Hz implies that there are 3 cycles per second.
Frequency is defined as the number of cycles or oscillations per unit time. The SI unit of frequency is Hertz (Hz), where 1 Hz equals 1 cycle per second.
In the context of alternating current (AC), one cycle represents a complete sequence of changes in voltage or current from zero to maximum positive, back to zero, to maximum negative, and back to zero again. A frequency of 3 Hz means this complete cycle repeats 3 times every second.

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38. Which one of the following is the correct order of the valencies of el

Which one of the following is the correct order of the valencies of elements Ne, Si, N and Mg ?

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[amp_mcq option1=”Ne < Mg < N < Si" option2="Si < N < Mg < Ne" option3="Ne < N < Si < Mg" option4="Mg < Ne < N < Si" correct="option1"]

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The correct order of the valencies of elements Ne, Si, N and Mg is Ne < Mg < N < Si.
Valency is the combining capacity of an element, typically the number of electrons an atom needs to gain, lose, or share to form a chemical bond and achieve a stable electron configuration.
Neon (Ne) is a noble gas with a full outer electron shell, so its valency is generally 0. Magnesium (Mg) is in Group 2 and typically loses 2 electrons, so its valency is 2. Nitrogen (N) is in Group 15 and typically gains 3 electrons or forms 3 covalent bonds, so its valency is 3. Silicon (Si) is in Group 14 and typically forms 4 covalent bonds, so its valency is 4. Ordering these valencies (0, 2, 3, 4) gives Ne < Mg < N < Si.

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39. The mass number of argon is 40. Which one of the following statements

The mass number of argon is 40. Which one of the following statements is correct?

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The number of protons in argon is 22.
The number of neutrons in argon is 18.
The number of electrons in argon is 18.
The sum of numbers of protons and electrons in argon is 40.
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The number of electrons in a neutral atom of argon is 18.
The mass number of an element is the sum of the number of protons and neutrons in the nucleus. The atomic number, which defines the element, is equal to the number of protons. In a neutral atom, the number of protons is equal to the number of electrons. Argon (Ar) has an atomic number of 18.
Given mass number = 40. Atomic number of Argon = 18. Number of protons = 18. For a neutral atom, number of electrons = number of protons = 18. Number of neutrons = Mass number – Number of protons = 40 – 18 = 22.

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40. Which one of the following is a covalent compound?

Which one of the following is a covalent compound?

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Calcium oxide
Sodium nitride
Silicon carbide
Zinc sulphide
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Among the given options, Silicon carbide (SiC) is predominantly a covalent compound.
Covalent compounds are formed by the sharing of electrons between atoms, typically non-metals or metalloids. Ionic compounds are formed by the transfer of electrons between a metal and a non-metal, resulting in the formation of ions held together by electrostatic attraction.
Calcium oxide (CaO), Sodium nitride (Na₃N), and Zinc sulphide (ZnS) are compounds formed between a metal and a non-metal. While ZnS has some covalent character, CaO and Na₃N are strongly ionic. SiC is a ceramic material where silicon and carbon atoms are bonded covalently in a crystal lattice structure, forming a giant covalent network.

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