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CBSE Class 10 Lakhmir Singh
Lakhmir Singh

The freezing point depression constant $\left(K_{f}\right)$ of benzene is $5.12 K kg mol ^{-1}$. The freezing point depression for the solution of molality $0.078$ m containing a non-electrolyte solute in benzene is (rounded off upto two decimal places):
(1) $0.80 K$ (2) $0.40 K$ (3) $0.60 K$ (4) $0.20 K$

Correct option: (2) As we know that, we evaluate the value using the formula directly, $\begin{aligned} \Delta T _{ f }= i k _{ f } m \\ \Rightarrow \quad \Delta T _{ f } &=1 \times 5.12 \times...

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Identify the incorrect statement.
(1) The transition metals and their compounds are known for their catalytic activity due to their ability to adopt multiple oxidation states and to form complexes.
(2) Interstitial compounds are those that are formed when small atoms like $H , C$ or $N$ are trapped inside the crystal lattices of metals.
(3) The oxidation states of chromium in $CrO _{4}^{2-}$ and $Cr _{2} O _{7}^{2-}$ are not the same.
(4) $Cr ^{2+}\left( d ^{4}\right)$ is a stronger reducing agent than $Fe ^{2+}\left( d ^{6}\right)$ in water.

Correct option (3) Explanation: Interstitial compounds are those formed when small atoms such as H, B, C, or N are trapped inside metal crystal lattices. Fact: On the basis of standard reduction...

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When a ray of light is incident normally on one refracting surface of an equilateral prism of refractive index 1.5, the emerging ray $\left[\sin ^{-1}\left(\frac{1}{1.5}\right)=41.8^{\circ}\right]$
A) just grazes the second refracting surface.
B) is deviated by $20^{\circ}$.
C) is deviated by $30^{\circ}$.
D) undergoes total internal reflection at second refracting surface.

Correct answer is D. Critical angle for the material of prism $C=\sin ^{-1}\left(\frac{1}{\mu}\right)$ $=\sin ^{-1}=42^{\circ}$ since angle of incidence at surface $A B\left(60^{\circ}\right)$ is...

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Calculate the work done during combustion of $0.138 \mathrm{~kg}$ of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(I)}$ at at $300 \mathrm{~K}$. Given : $R=8.314 J k^{-1} \mathrm{~mol}^{-1}$, molar mass of ethanol $=46 \mathrm{gmol}^{-1}$ (A) $-7482 J$ (B) $7482 J$ (C) $-2494 J$ (D) $2494 J$

The correct option is B Explanation: The combustion of ethanol, involves the following reaction. $ C_{2} H_{5} O H(l)+3 O_{2}(g) \rightarrow 2 C O_{2}+3 H_{2} O $ Given, Mass of ethanol $=0.138...

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The correct relation between elevation of boiling point and molar mass of solute is (A) $M_{2}=\frac{K_{b} \cdot W_{2}}{\Delta T_{b} \cdot W_{1}}$ (B) $M_{2}=\frac{K_{b} \cdot W_{1}}{\Delta T_{b} \cdot W_{2}}$ (C) $M_{2}=\frac{\Delta T_{b} \cdot K_{b}}{W_{1} \cdot W_{2}}$ (D) $M_{2}=\frac{\Delta T_{b} \cdot W_{1}}{K_{b} \cdot W_{2}}$

Correct option is  (A) $M_{2}=\frac{K_{b} \cdot W_{2}}{\Delta T_{b} \cdot W_{1}}$ EXPLANATION: The correct relation between elevation of boiling point (ΔTb​) and molar mass of solute (M2​) is...

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Molarity is (A) The number of moles of solute present in $1 \mathrm{dm}^{3}$ volueme of solution (B) The number of moles of solute dissolved in $1 \mathrm{~kg}$ of solvent (C) The number of moles of solute dissolved in $1 \mathrm{~kg}$ of solution (D) The number of moles of solute dissolved in $100 \mathrm{dm}^{3}$ volume of solution

Correct option is A. (the number of moles of solute present in $1 \mathrm{dm}^{3}$ volume of solution) Explanation: Since the molarity is moles per litre and $1 \mathrm{dm}^{3}$ is equal to $1...

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Which of the following carboxylic acids is most reactive towards esterification? (A) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCOOH}$ (B) $\left(\mathrm{CH}_{3}\right){ }_{2} \mathrm{CHCOOH}$ (C) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}$ (D) $\left(\mathrm{C}_{2} \mathrm{H}_{5}\right){ }_{2} \mathrm{CHCOOH}$

Correct option is C Explanation: Because the C atom of the carboxylic group is the least sterically hindered, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}$ is the most reactive towards...

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The molarity of urea (molar mass $60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) solution by dissolving $15 \mathrm{~g}$ of urea in $500 \mathrm{~cm}^{3}$ of water is (A) 2 mol $\mathrm{dm}^{-3}$ (B) $0.5$ mol $\mathrm{dm}^{-3}$ (C) $0.125 \mathrm{~mol} \mathrm{dm}^{-3}$ (D) $0.0005 \mathrm{~mol} \mathrm{dm}^{-3}$

Correct option is B ($0.5 \mathrm{~mol} \mathrm{dm}^{-3}$) Explanation: The number of moles of urea $=\frac{\text { Mass of urea }}{\text { Molar mass of urea }}=\frac{15 \mathrm{~g}}{60 \mathrm{~g}...

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Which of the following compounds reacts immediately with Lucas reagent? (A) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ (B) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$(C) \(C{{H}_{3}}-\underset{\underset{OH}{\mathop |}\,}{\mathop{CH}}\,-C{{H}_{3}}\)(D)\(C{{H}_{3}}-\underset{\underset{OH}{\mathop{\text{ }|}}\,}{\mathop{\overset{\overset{C{{H}_{3}}}{\mathop{|}}\,}{\mathop{CH}}\,}}\,-C{{H}_{3}}\)

Correct option is D Explanation: A solution of anhydrous zinc chloride in strong hydrochloric acid is known as Lucas reagent. This solution is used to classify low-molecular-weight alcohols. The...

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Which among the following oxoacids of phosphorus shows a tendency of disproportionation? (A) Phosphinic acid $\left(\mathrm{H}_{3} \mathrm{PO}_{2}\right)$ (B) Orthophosphoric acid $\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right)$ (C) Phosphinic acid $\left(\mathrm{H}_{3} \mathrm{PO}_{3}\right)$ (D) Pyrophosphoric acid $\left(\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}\right)$

Correct option is C Phosphonic acid $\left(\mathrm{H}_{3} \mathrm{P} \mathrm{O}_{3}\right)$ Explanation: Phosphonic acid $\left(\mathrm{H}_{3} \mathrm{P} \mathrm{O}_{3}\right)$ shows a tendency of...

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Identify the product ${ }^{\prime} C^{\prime}$ in the following reaction. Aniline $\frac{\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}}{\text { Pyridine }} \mathrm{A} \frac{\mathrm{Br}_{2}}{\mathrm{CH}_{3} \mathrm{COOH}}{\longrightarrow} B \stackrel{\mathrm{H}^{+} \text {or } \mathrm{OH}^{-}}{\longrightarrow} C$ (A) Acetanilide (B) $p$-Bromoacetanilide (C) $p$-Bromoaniline (D) $o$-Bromoaniline

The correct answer is C. (p-Bromoaniline) Explanation: 1) The aniline's amino group is acetylated with acetic anhydride/pyridine. 2) It is then brominated with acetic acid and bromine. Because the...

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A certain reaction occurs in two steps as (i) $2 S O_{2(g)}+2 N O_{2(g)} \rightarrow 2 S O_{3(g)}+2 N O_{(g)}$ (ii) $2 N O_{(g)}+O_{2(g)} \rightarrow 2 N O_{2(g)}$ In the reaction, (A) $N O_{2(g)}$ is intermediate (B) $N O_{(g)}$ is intermediate (C) $N O_{(g)}$ is catalyst (D) $O_{2(g)}$ is intermediate

Correct option is B (NO (g) is intermediate) Explanation: Because NO (g) is created in the first stage and consumed in the second, it is considered intermediate. In the first process, a catalyst may...

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What is the volume of water consumed during acid hydrolysis of $1.368 \mathrm{Kg}$ of sucrose? (Given $-$ molar masses of sucrose $=342$, water $=18$, density of water $=1 \mathrm{~g} / \mathrm{cm}^{3}$ ) A) $0.072 \mathrm{dm}^{3}$ B) $0.720 \mathrm{dm}^{3}$ C) $0.18 \mathrm{dm}^{3}$ D) $0.018 \mathrm{dm}^{3}$

Correct option is A ($0.072 \mathrm{dm}^{3}$) $ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{H}^{+}}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12}...

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The correct order of reactivity of aldehydes and ketones towards hydrogen cyanide is A) $\left.\left.\mathrm{CH}_{3} \mathrm{COCH}_{3}\right\rangle \mathrm{CH}_{3} \mathrm{CHO}\right\rangle \mathrm{HCHO}$ B) $\left.\left.\mathrm{CH}_{3} \mathrm{COCH}_{3}\right\rangle \mathrm{HCHO}\right\rangle \mathrm{CH}_{3} \mathrm{CHO}$ C) $\left.\left.\mathrm{CH}_{3} \mathrm{CHO}\right\rangle \mathrm{CH}_{3} \mathrm{COCH}_{3}\right\rangle \mathrm{HCHO}$ D) $\left.\mathrm{HCHO}\rangle \mathrm{CH}_{3} \mathrm{CHO}\right\rangle \mathrm{CH}_{3} \mathrm{COCH}_{3}$

Correct option is D) $\left.\mathrm{HCHO}\rangle \mathrm{CH}_{3} \mathrm{CHO}\right\rangle \mathrm{CH}_{3} \mathrm{COCH}_{3}$ The following is the right order of reactivity of aldehydes and ketones...

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$\mathrm{R}-\mathrm{C} \equiv \mathrm{N}+2(\mathrm{H}) \frac{\text { (i) } \mathrm{SnCl}_{2} / \mathrm{dil} \mathrm{HCl}}{\text { (ii) } \mathrm{H}_{3} \mathrm{O}^{+}} \mathrm{RCHO}+\mathrm{NH}_{4} \mathrm{Cl}$ this reaction is known as A) Etard reaction B) Stephen reaction C) Hell-Vohlard-Zelinsky reaction D) Balz-Schiemann reaction

B is the correct answer. Explanation: Using tin chloride and dilution, aldehydes (R-CHO) are synthesised from nitriles (R-CN). Stephen's reaction is the reaction of HCl in an acidic media. As an...

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For the reaction $\mathrm{O}_{3(\mathrm{~g})}+\mathrm{O}_{(\mathrm{g})} \rightarrow 2 \mathrm{O}_{2}(\mathrm{~g})$ if the rate law expression is, rate $=\mathrm{K}\left[\mathrm{O}_{3}\right][\mathrm{O}]$ the molecularity and order of the reaction are respectively A) 2 and 2 B) 2 and $1.33$ C) 2 and 1 D) 1 and 2

Correct option is A (2 and 2) Rate $=\mathrm{K}\left[\mathrm{O}_{3}\right][\mathrm{O}]$ Order $=1+1=2$ Hence, the overall order of the reaction is 2 . Now, $ \mathrm{O}_{3(9)}+\mathrm{O}_{(9)}...

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$ \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]\left[\mathrm{Cr}(\mathrm{SCN})_{6}\right] \text { and }\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{SCN})_{4}\right]\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{SCN})_{2}\right] $ are the examples of what type of isomerism ? A) Ionisation isomerism B) Linkage isomerism C) Coordination isomerism D) Solvate isomerism

Correct option is C (Coordination isomerism) Explanation: The above examples are of coordination isomerism. It is because there are two coordination spheres in a compound.

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If $\mathrm{M}, \mathrm{W}$ and $\mathrm{V}$ represent molar mass of solute, mass of solute and volume of solution in litres respectively, which among following equations is true? A) $\pi=\frac{\text { MWR }}{\text { TV }}$ B) $\pi=\frac{T M R}{W V}$ C) $\pi=\frac{\text { TWR }}{\text { VM }}$ D) $\pi=\frac{\text { TRV }}{\mathrm{WM}}$

Correct option is C $\pi=\frac{\mathrm{TWR}}{\mathrm{VM}}$ $\pi=$ CRT where $\mathrm{C}$ is the concentration $\mathrm{C}=\frac{\text { Moles of solute }}{\text { volume }}$...

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The correct IUPAC name of $\left[\mathrm{CO}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{2}\right)_{3}\right]$ A) Triammine trinitrito – N cobalt (III) B) Triammine trinitrito $-\mathrm{N}$ cobalt (II) C) Triammine cobalt (III) nitrite D) Triammine trinitrito – N cobaltate (III)

Correct option is A) Triammine trinitrito - N cobalt Triammine trinitro-N-cobalt is the correct IUPAC name (III). In this scenario, the groups are ordered alphabetically, with the ammine group...

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Which of the following is the most stable diazonium salt ? A) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{~N}_{2}^{+} \mathrm{X}^{-}$ B) $\mathrm{CH}_{3} \mathrm{~N}_{2}^{+} \mathrm{X}^{-}$ C) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{~N}_{2}^{+} \mathrm{X}^{-}$ D) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{~N}_{2}^{+} \mathrm{X}^{-}$

Correct option is B Due to resonance stabilisation between the benzene nucleus and the nitrogen atom, dizonium salts with an aryl group immediately connected to the nitrogen atom are the most...

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The relationship between rate constant and half life period of zero order reaction is given by A) $\mathrm{t}_{\frac{1}{2}}=[\mathrm{A}]_{0} 2 \mathrm{k}$ B) $t_{\frac{1}{2}}=\frac{0.693}{\mathrm{k}}$ C) $t_{\frac{1}{2}}=\frac{[\mathrm{A}]_{0}}{2 \mathrm{k}}$ D) $\mathrm{t}_{\frac{1}{2}}=\frac{2[\mathrm{~A}]_{0}}{\mathrm{k}}$

Correct option is C $\mathrm{t}_{1 / 2}=\frac{\left[\mathrm{A}_{0}\right]}{2 \mathrm{k}}$ The relationship between rate constant and half-life period of zero-order reaction is given by: $...

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Molarity is defined as A) the number of moles of solute dissolved in one dm3 of the solution B) the number of moles of solute dissolved in 1 kg of solvent C) the number of moles of solute dissolved in 1 dm3 of the solvent D) the number of moles of solute dissolved in 100 ml of the solvent

Correct option is (A) The number of moles of solute dissolved in 1dm3 of the solution is called molarity. Molarity = (moles of solute dissoved) / (volume of solvent in dm3) So, answer is...

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When a resistance ‘ $R_{1}{ }^{\prime}$ is connected across the terminal of a cell of e.m.f. ‘ $\mathrm{E}_{1}$ ‘ the current is ‘ $\mathrm{I}_{1}$ ‘. When the resistance is changed to $\mathrm{R}_{2}$ ‘ the current is ‘ $I_{2}$ ‘. The internal resistance of the cell is
A. $\frac{I_{1} R_{2}+I_{2} R_{1}}{I_{1}+I_{2}}$
B. $\frac{I_{2} R_{2}+I_{1} R_{1}}{I_{1}+I_{2}}$
C. $\frac{I_{2} R_{2}-I_{1} R_{1}}{I_{1}-I_{2}}$
D. $\frac{I_{1} R_{2}-I_{2} R_{1}}{I_{1}-I_{2}}$

Correct answer is C. $\begin{array}{l} I_{1}=\frac{E}{r+R_{1}} \\ I_{2}=\frac{E}{r+R_{2}} \\ \frac{I_{1}}{I_{2}}=\frac{r+R_{2}}{r+R_{1}} \\ I_{1} r+I_{1} R_{1}=I_{2} r+I_{2} R_{2} \\...

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Three vessels A, B, C of different shapes have same base area and are filled with water up to same height ‘ $\mathrm{h}$ ‘. The respective forces exerted by water on the bases are ‘ $F_{A}^{\prime}, ‘ F_{B}^{\prime}, ‘ F_{c}^{\prime}$ and respective weights are ${ }^{\prime} \mathrm{W}_{\mathrm{A}}^{\prime},^{\prime} \mathrm{W}_{\mathrm{e}}^{\prime}, \mathrm{‘} \mathrm{W}_{\mathrm{c}}^{\prime}$. Then
A. $\quad \mathrm{F}_{\mathrm{A}}<\mathrm{F}_{\mathrm{B}}<\mathrm{F}_{\mathrm{C}} ; \mathrm{W}_{\mathrm{A}}<\mathrm{W}_{\mathrm{B}}>\mathrm{W}_{\mathrm{C}}$
B. $\quad F_{A}=F_{B}=F_{C} ; W_{A}>W_{B}>W_{C}$
C. $\quad F_{A}=F_{B}=F_{C} ; W_{A}D. $\quad \mathrm{F}_{\mathrm{A}}>\mathrm{F}_{\mathrm{B}}>\mathrm{F}_{\mathrm{C}} ; \mathrm{W}_{\mathrm{A}}>\mathrm{W}_{\mathrm{B}}<\mathrm{W}_{\mathrm{C}}$

Correct answer is B.

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The sequence of harmonics of a pipe open at one end and closed at the other end is $250 \mathrm{~Hz}$ and $350 \mathrm{~Hz}$. The resonating length of the air column in its fundamental mode will be (velocity of sound in air $=340 \mathrm{~m} / \mathrm{s})$
A. $1.8 \mathrm{~m}$
B. $1.6 \mathrm{~m}$
C. $1.7 \mathrm{~m}$
D. $1.4 \mathrm{~m}$

Correct answer is C. $\begin{array}{l} 2 n=n_{2}-n_{1} \\ =350-250=100 \\ n=\frac{100}{2}=50 H z \\ n=\frac{v}{4 l_{0}}=\frac{340}{4 \times l_{0}} \\ \therefore l=\frac{340}{4 \times...

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Two long, straight wires are set parallel to each other. Both the wires carry a current ‘I’ in opposite directions and separation between them is ‘ $2 \mathrm{R}$ ‘. The magnetic induction at the midway between them is $\left(\mu_{0}=\right.$ permeability of free space)
A. Zero
B. $\frac{\mu_{0} I}{4 \pi r}$
C. $\frac{\mu_{0} I}{\pi r}$
D. $\frac{\mu_{0} I}{2 \pi r}$

Correct answer is A. $\begin{array}{l} \mathrm{x}=\frac{\mathrm{r}}{2} \\ \mathrm{~B}_{1}=-\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{x}} \\ \mathrm{B}_{2}=\frac{\mu_{0} \mathrm{i}}{2...

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A charged capacitor has charge ‘ $\mathrm{Q}_{1}$ ‘ at potential ${ }^{\prime} \mathrm{V}_{1}$ ‘. The charge on capacitor is increased to ‘ $\mathrm{Q}_{2}$ ‘ so that its potential increases to $\mathrm{V}_{2}$, then the difference between final and initial energy stored in capacitor is
A. $\frac{1}{2}\left(Q_{2}-Q_{1}\right)\left(V_{2}-V_{1}\right)$
B. $\frac{1}{2}\left(Q_{2} V_{2}-Q_{1} V_{1}\right)$
C. $\frac{1}{2}\left(\frac{Q_{2}^{2}}{V_{2}}-\frac{Q_{1}^{2}}{V_{1}}\right)$
D. $\frac{1}{2}\left(Q_{2} V_{2}^{2}-Q_{1} V_{1}^{2}\right)$

Correct answer is B.

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In Biprism experiment the distance between the two virtual images of the slits in the magnified and diminished position are $2.4 \mathrm{~mm}$ and $0.6 \mathrm{~mm}$ respectively. The distance between two coherent sources is
A. $1 \mathrm{~mm}$
B. $3.0 \mathrm{~mm}$
C. $1.2 \mathrm{~mm}$
D. $2.4 \mathrm{~mm}$

Correct answer is C. When, 1) magnified, distance between images, $\mathrm{d}_{1}=2.4$ 2) dimnished, distance between images, $\mathrm{d}_{2}=0.6$ $\therefore$ Distance between virtual sources...

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A sonometer wire of length ‘ $\mathrm{L}_{1}$ ‘ is in unison with a tuning fork of frequency’n’. When the vibrating length of the wire is reduced to ‘ $\mathrm{L}_{2}$ ‘, it produces ‘ $\mathrm{x}$ ‘ beats per second with the fork. The frequency of the fork is
A. $\frac{L_{2} x}{L_{2}-L_{1}}$
B. $\frac{L_{1} x}{L_{1}-L_{2}}$
C. $\frac{L_{2} x}{L_{2}-L_{1}}$
D. $\frac{L_{2} x}{L_{1}-L_{2}}$

Correct answer is D. For the length $L_{1}, n_{1}=\frac{1}{2 L_{1}} \sqrt{\frac{T}{m}}=n \ldots(1)$ where $m=$ mass per unit length For the length $L_{2}, n_{2}=\frac{1}{2 L_{2}} \sqrt{\frac{T}{m}}...

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A particle performs simple harmonic motion from mean position, with period $8 \mathrm{~s}$. The distance travelled by it between 1 st and 2 nd second of its motion is (A = amplitude of S. H. M.)
A. $A \frac{1}{2}$
B. $A\left(\frac{1}{\sqrt{2}}-1\right)$
C. $A\left(1-\frac{1}{\sqrt{2}}\right)$
D. $A\left(\frac{1}{\sqrt{2}}\right)$

Correct answer is C. In $2 \mathrm{~s}$ (which is equal to $\frac{T}{4}$ ), one amplitude will be convered. In $1 \mathrm{st}$ second $x=a \sin \left(\frac{\pi}{4}\right)=\frac{a}{\sqrt{2}}$...

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The rate of cooling of a body is $2{ }^{0} \mathrm{C} / \mathrm{min}$ when the body is at $50{ }^{0} \mathrm{C}$ above the temperature of surroundings. When the body is at $30^{\circ} \mathrm{C}$ above the temperature of surroundings, its rate of cooling will be
A. $0.6^{0} \mathrm{C} / \mathrm{min}$
B. $0.9^{0} \mathrm{C} / \mathrm{min}$
C. $1.2^{0} \mathrm{C} / \mathrm{min}$
D. $1.5^{0} \mathrm{C} / \mathrm{min}$

Correct answer is C. Rate of cooling $\frac{\mathrm{dT}}{\mathrm{dt}}=-\frac{\mathrm{k}}{\mathrm{ms}}\left(\mathrm{T}-\mathrm{T}_{\mathrm{s}}\right)$ Or $2=\frac{-\mathrm{k}}{\mathrm{ms}}(50)$ Or...

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The mass and radius of earth is $\mathrm{M}_{\mathrm{c}}$, and $\mathrm{R}_{\mathrm{c}}$, respectively and that of moon is $\mathrm{M}_{\mathrm{m}}$ and $\mathrm{R}_{\mathrm{m}}$ respectively. The distance between the centre of earth and that of moon is ‘D’ . The minimum speed required for a body (mass ‘m’) to project from a point midway between their centres to escape to infinity is
A. $\left(\frac{G D}{M_{e}}\right)^{1 / 2}$
B. $\sqrt{\frac{\left(M_{e}+M_{m}\right)}{D}}$
C. $2 \sqrt{G\left(M_{e}+M_{m}\right) / D}$
D. $\frac{G\left(M_{e}+M_{m}\right)}{2 D}$

Correct answer is C. From conservation of energy, since the velocity will be o at infinity, $\frac{1}{2} \mathrm{mv}^{2}-\frac{\mathrm{GmM}_{e}}{\mathrm{~d} / 2}-\frac{\mathrm{GmM}_{d}}{\mathrm{~d}...

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A point source is placed in air. The spherical wavefront has radius ‘ $r_{\mathrm{a}}$ ‘ after time ‘t’. If the same point source is placed in the medium of refractive index ‘ $\mu$ ‘, the radius of spherical wavefront in the medium in same time $t$ is
A. $\frac{r_{a}}{\mu}$
B. $\frac{r_{a}}{\mu^{2}}$
C. $\mu . r_{a}$
D. $\mu^{2} \cdot r_{a}$

Correct answer is A. Here Velocity of wave front $=\frac{R_{9}}{t}$ $\begin{array}{l} u=-1 \\ \frac{e}{R a / t}=1 \\ e=R a / t \end{array}$ in the meduim $u$ $\text { velochy }=R \frac{a}{t}$ so,...

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A solid sphere is rolling down a frictionless surface with translational velocity $\mathrm{V}$. It climbs the inclined plane from ‘A’ to ‘ $\mathrm{B}^{\prime}$ and then moves away from ‘ $\mathrm{B}^{\prime}$ on the smooth horizontal surface. The value of $V$ should be
A. $\sqrt{g h}$
B. $\geq\left[\frac{10 g h}{7}\right]^{1 / 2}$
C. $\sqrt{2 g h}$
D. $10 g h$

Correct answer is B. Applying law of conservation of energy for rotating body, $\begin{array}{l} \frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}=\mathrm{mgh} \\ \frac{1}{2}...

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Glass has refractive index $\frac{3}{2}$ and water has refractive index $\frac{4}{3} .$ If the speed of light in glass is $2 \times 10^{8} \mathrm{~m} / \mathrm{s}$, then the speed of light in water will be
A. $1.6 \times 10^{8} \mathrm{~m} / \mathrm{s}$
B. $2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}$
C. $1.8 \times 10^{8} \mathrm{~m} / \mathrm{s}$
D. $2 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Correct answer is B. $\begin{array}{l} \quad \mathrm{v}_{\text {water }}=\frac{\mathrm{c}}{\mathrm{n}_{\text {water }}} \\ \therefore \quad \mathrm{v}_{\mathrm{water}}=\frac{3 \times 10^{8}}{(4 /...

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A transverse wave is travelling on a string with velocity ‘ $\mathrm{V}^{\prime} .$ The extension in the string is ‘ $\mathrm{x}^{\prime}$. If the string is extended by $50 \%$, then the speed of wave along the string will be nearly (Hooke’s law is obeyed)
A. $1.22 \mathrm{~V}$
B. $\frac{V}{1.5}$
C. $\frac{V}{1.22}$ D. $1.5 \mathrm{~V}$

Correct option is A. $\begin{array}{l} v=\sqrt{\frac{T}{m}} \\ \therefore \frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}=\sqrt{\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}} \\ =\sqrt{1.5} \approx 1.22...

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A galvanometer of resistance $100 \Omega$ is connected to a battery of $2 \mathrm{~V}$ with a resistance of $1900 \Omega$ in series. The deflection obtained is 30 divisions. To reduce this deflection by 10 divisions the additional resistance required to be connected in series is
A. $1500 \Omega$
B. $500 \Omega$
C. $1000 \Omega$
D. $2000 \Omega$

Correct option is C. Total resistance in the circuit is $R=1900+100=2000 \Omega$ $\therefore$ Current $I_{1}=\frac{2}{2000}=10^{-3} A$ The deflection is decreased from 30 to 20 divisions $\therefore...

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