In a simple pendulum experiment for determination of acceleration due to gravity (g),
Question: In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be $30 \mathrm{~s}$. The length of pendulum is measured by using a meter scale of least count $1 \mathrm{~mm}$ and the value obtained is $55.0 \mathrm{~cm}$. The percentage error in the determination of $g$ is close to :(1) $0.7 \%$(2) $0.2 \%$(3) $3.5 \%$(4) $6.8 \%$Correct...
Read More →On treating a compound with warm dil.
Question: On treating a compound with warm dil. $\mathrm{H}_{2} \mathrm{SO}_{4}$, gas $\mathrm{X}$ is evolved which turns $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ paper acidified with dil. $\mathrm{H}_{2} \mathrm{SO}_{4}$ to a green compound $\mathrm{Y} . \mathrm{X}$ and $\mathrm{Y}$ respectively are :$X=S O_{2}, Y=C r_{2}\left(S O_{4}\right)_{3}$$\mathrm{X}=\mathrm{SO}_{2}, \mathrm{Y}=\mathrm{Cr}_{2} \mathrm{O}_{3}$$\mathrm{K}=\mathrm{SO}_{3}, \mathrm{Y}=\mathrm{Cr}_{2} \mathrm{O}_{3}$$\...
Read More →For what values of k are the roots of the quadratic equation
Question: For what values of $k$ are the roots of the quadratic equation $3 x^{2}+2 k x+27=0$ real and equal? Solution: Given: $3 x^{2}+2 k x+27=0$ Here, $a=3, b=2 k$ and $c=27$ It is given that the roots of the equation are real and equal; therefore, we have: $D=0$ $\Rightarrow(2 k)^{2}-4 \times 3 \times 27=0$ $\Rightarrow 4 k^{2}-324=0$ $\Rightarrow 4 k^{2}=324$ $\Rightarrow k^{2}=81$ $\Rightarrow k=\pm 9$ $\therefore k=9$ or $k=-9$...
Read More →Two particles move at right angle to each other.
Question: Two particles move at right angle to each other. Their de Broglie wavelengths are $\lambda_{1}$ and $\lambda_{2}$ respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength $\lambda$, of the final particle, is given by:(1) $\frac{1}{\lambda^{2}}=\frac{1}{\lambda_{1}^{2}}+\frac{1}{\lambda_{2}^{2}}$(2) $\lambda=\sqrt{\lambda_{1} \lambda_{2}}$(3) $\lambda=\frac{\lambda_{2}+\lambda_{2}}{2}$(4) $\frac{2}{\lambda}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}$C...
Read More →Show that the roots of the equation
Question: Show that the roots of the equation $x^{2}+p x-q^{2}=0$ are real for all real value of $p$ and $q$. Solution: Given: $x^{2}+p x-q^{2}=0$ Here, $a=1, b=p$ and $c=-q^{2}$ Discriminant $D$ is given by : $D=\left(b^{2}-4 a c\right)$ $=p^{2}-4 \times 1 \times\left(-q^{2}\right)$ $=\left(p^{2}+4 q^{2}\right)0$ $D0$ for all real values of $p$ and $q$. Thus, the roots of the equation are real....
Read More →If the screw on a screw-gauge is given six rotations,
Question: If the screw on a screw-gauge is given six rotations, it moves by $3 \mathrm{~mm}$ on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is:(1) $0.001 \mathrm{~cm}$(2) $0.02 \mathrm{~mm}$(3) $0.01 \mathrm{~cm}$(4) $0.001 \mathrm{~mm}$Correct Option: 4 Solution: (4) When screw on a screw-gauge is given six rotations, it moves by $3 \mathrm{~mm}$ on the main scale $\therefore \quad$ Pitch $=\frac{3}{6}=0.5 \mathrm{~mm}$ $\therefore \quad$ L...
Read More →If the screw on a screw-gauge is given six rotations,
Question: If the screw on a screw-gauge is given six rotations, it moves by $3 \mathrm{~mm}$ on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is:(1) $0.001 \mathrm{~cm}$(2) $0.02 \mathrm{~mm}$(3) $0.01 \mathrm{~cm}$(4) $0.001 \mathrm{~mm}$Correct Option: 4 Solution: (4) When screw on a screw-gauge is given six rotations, it moves by $3 \mathrm{~mm}$ on the main scale $\therefore \quad$ Pitch $=\frac{3}{6}=0.5 \mathrm{~mm}$ $\therefore \quad$ L...
Read More →If P and Q are two statements,
Question: If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?(1) $((\mathrm{P} \Rightarrow \mathrm{Q}) \wedge \sim \mathrm{Q}) \Rightarrow \mathrm{Q}$(2) $((\mathrm{P} \Rightarrow \mathrm{Q}) \wedge \sim \mathrm{Q}) \Rightarrow \sim \mathrm{P}$(3) $((\mathrm{P} \Rightarrow \mathrm{Q}) \wedge \sim \mathrm{Q}) \Rightarrow \mathrm{P}$(4) $((\mathrm{P} \Rightarrow \mathrm{Q}) \wedge \sim \mathrm{Q}) \Rightarrow(\mathrm{P} \wedge \mathrm{Q})$Correct Optio...
Read More →If a and b are distinct real numbers, show that the quadratic equation
Question: If $a$ and $b$ are distinct real numbers, show that the quadratic equation $2\left(a^{2}+b^{2}\right) x^{2}+2(a+b) x+1=0$ has no real roots. Solution: The given equation is $2\left(a^{2}+b^{2}\right) x^{2}+2(a+b) x+1=0$. $\therefore D=[2(a+b)]^{2}-4 \times 2\left(a^{2}+b^{2}\right) \times 1$ $=4\left(a^{2}+2 a b+b^{2}\right)-8\left(a^{2}+b^{2}\right)$ $=4 a^{2}+8 a b+4 b^{2}-8 a^{2}-8 b^{2}$ $=-4 a^{2}+8 a b-4 b^{2}$ $=-4\left(a^{2}-2 a b+b^{2}\right)$ $=-4(a-b)^{2}0$ Hence, the given ...
Read More →In which of the following pairs,
Question: In which of the following pairs, the outer most electronic configuration will be the same?$\mathrm{Fe}^{2+}$ and $\mathrm{Co}^{+}$$\mathrm{Cr}^{+}$and $\mathrm{Mn}^{2+}$$\mathrm{Ni}^{2+}$ and $\mathrm{Cu}^{+}$$\mathrm{V}^{2+}$ and $\mathrm{Cr}^{+}$Correct Option: , 2 Solution: $\mathrm{Cr}^{+} \rightarrow[\mathrm{Ar}] 3 \mathrm{~d}^{5}$ $\mathrm{Mn}^{2+} \Rightarrow[\mathrm{Ar}] 3 \mathrm{~d}^{5}$...
Read More →A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place.
Question: A simple pendulum is being used to determine the value of gravitational acceleration $g$ at a certain place. The length of the pendulum is $25.0 \mathrm{~cm}$ and a stop watch with $1 \mathrm{~s}$ resolution measures the time taken for 40 oscillations to be $50 \mathrm{~s}$. The accuracy in $g$ is:(1) $5.40 \%$(2) $3.40 \%$(3) $4.40 \%$(4) $2.40 \%$Correct Option: 3 Solution: (3) Given, Length of simple pendulum, $l=25.0 \mathrm{~cm}$ Time of 40 oscillation, $T=50 \mathrm{~s}$ Time per...
Read More →Find the nature of the roots of the following quadratic equations:
Question: Find the nature of the roots of the following quadratic equations: (i) $2 x^{2}-8 x+5=0$ (ii) $3 x^{2}-2 \sqrt{6} x+2=0$ (iii) $5 x^{2}-4 x+1=0$ (iv) $5 x(x-2)+6=0$ (v) $12 x^{2}-4 \sqrt{15} x+5=0$ (vi) $x^{2}-x+2=0$ Solution: (i) The given equation is $2 x^{2}-8 x+5=0$. This is of the form $a x^{2}+b x+c=0$, where $a=2, b=-8$ and $c=5$. $\therefore$ Discriminant, $D=b^{2}-4 a c=(-8)^{2}-4 \times 2 \times 5=64-40=240$ Hence, the given equation has real and unequal roots. (ii) The given...
Read More →What is the correct order of the following elements with respect to their density?
Question: What is the correct order of the following elements with respect to their density?$\mathrm{Cr}\mathrm{Fe}\mathrm{Co}\mathrm{Cu}\mathrm{Zn}$$\mathrm{Cr}\mathrm{Zn}\mathrm{Co}\mathrm{Cu}\mathrm{Fe}$$\mathrm{Zn}\mathrm{Cu}\mathrm{Co}\mathrm{Fe}\mathrm{Cr}$$\mathrm{Zn}\mathrm{Cr}\mathrm{Fe}\mathrm{Co}\mathrm{Cu}$Correct Option: , 4 Solution: Fact Based Density depend on many factor like atomic mass. atomic radius and packing efficiency....
Read More →If the Boolean expression
Question: If the Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \circledast(\mathrm{p} \otimes \mathrm{q})$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by(1) $\rightarrow, \rightarrow$(2) $\wedge, \vee$(3) $\vee, \rightarrow$(4) $\wedge, \rightarrow$Correct Option: 1 Solution: Option (1) $(\mathrm{p} \wedge \mathrm{q}) \longrightarrow(\mathrm{p} \rightarrow \mathrm{q})$ $=\sim(\mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \vee \mathrm{q})$ $=(\sim \mathrm{p} ...
Read More →The incorrect statement among the following is :
Question: The incorrect statement among the following is :$\mathrm{VOSO}_{4}$ is a reducing agentRed colour of ruby is due to the presence of $\mathrm{CO}^{3+}$$\mathrm{Cr}_{2} \mathrm{O}_{3}$ is an amphoteric oxide$\mathrm{RuO}_{4}$ is an oxidizing agentCorrect Option: , 2 Solution: Red colour of ruby is due to presence of $\mathrm{CrO}_{3}$ or $\mathrm{Cr}^{+6}$ not $\mathrm{CO}^{3+}$...
Read More →A circuit to verify Ohm's law uses ammeter and voltmeter
Question: A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:(1) ammeter is always used in parallel and voltmeter is series(2) Both ammeter and voltmeter must be connected in parallel(3) ammeter is always connected in series and voltmeter in parallel(4) Both, ammeter and voltmeter must be connected in seriesCorrect Option: 4 Solution: (4) Ammeter : In series connection, the same current flows through all the componen...
Read More →On complete reaction of $
Question: On complete reaction of $\mathrm{FeCl}_{3}$ with oxalic acid in aqueous solution containing $\mathrm{KOH}$, resulted in the formation of product A. The secondary valency of Fe in the product $A$ is ____________ . Solution: (6) $\mathrm{Fe}^{3+}+3 \mathrm{~K}^{+}+3 \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \rightarrow \mathrm{K}_{3}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]$ (A) Secondary valency of Fe in 'A' is 6 ....
Read More →A screw gauge has 50 divisions on its circular scale.
Question: A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $0.5 \mathrm{~mm}$ is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively:(1) Negative, $2 \mu \mathrm{m}$(2) Positive, $10 \mu \mathrm{m}$(3) Positive, $0.1 \mathrm{~mm}$(4) Positive, $0.1 \mu \mathrm{m}$Correct Option: 2...
Read More →The common positive oxidation states for an element with atomic number 24,
Question: The common positive oxidation states for an element with atomic number 24, are :$+2$ to $+6$$+1$ and $+3$ to $+6$$+1$ and $+3$$+1$ to $+6$Correct Option: 1 Solution: $\operatorname{Cr}(Z=24)$ [Ar] 4s $3 \mathrm{~d}^{5} \mathrm{Cr}$ shows common oxidation states starting from $+2$ to $+6$....
Read More →If the Boolean expression
Question: If the Boolean expression $(\mathrm{p} \Rightarrow \mathrm{q}) \Leftrightarrow(\mathrm{q} *(\sim \mathrm{p}))$ is a tautology, then the Boolean expression $\mathrm{p} *(\sim \mathrm{q})$ is equivalent to(1) $\mathrm{q} \Rightarrow \mathrm{p}$(2) $\sim \mathrm{q} \Rightarrow \mathrm{p}$(3) $\mathrm{p} \Rightarrow \sim \mathrm{q}$(4) $\mathrm{p} \Rightarrow \mathrm{q}$Correct Option: 1, Solution: $\because p \rightarrow q \equiv \sim p \vee q$ $\mathrm{So}, * \equiv \mathrm{v}$ Thus, $\m...
Read More →A galvanometer is used in laboratory for detecting the null point in electrical experiments. If,
Question: A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of $6 \mathrm{~mA}$ it produces a deflection of $2^{\circ}$, its figure of merit is close to :(1) $333^{\circ} \mathrm{A} /$ div.(2) $6 \times 10^{-3} \mathrm{~A} / \mathrm{div}$.(3) $666^{\circ} \mathrm{A} / \mathrm{div}$.(4) $3 \times 10^{-3} \mathrm{~A} / \mathrm{div}$Correct Option: 4 Solution: (4) Given, Current passing through galvanometer, $I=6 \mathrm{~mA}$ Defl...
Read More →Given below are two statements:
Question: Given below are two statements: Statement I : Potassium permanganate on heating at $573 \mathrm{~K}$ forms potassium manganate. Statement II : Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature. In the light of the above statements, choose the most appropriate answer from the options given below:Statement I is true but statement II is falseBoth statement I and statement II are trueStatement I is false but statement II is trueBoth statement I ...
Read More →Which of the following Boolean expression is a tautology ?
Question: Which of the following Boolean expression is a tautology ?(1) $(\mathrm{p} \wedge \mathrm{q}) \vee(\mathrm{p} \vee \mathrm{q})$(2) $(\mathrm{p} \wedge \mathrm{q}) \vee(\mathrm{p} \rightarrow \mathrm{q})$(3) $(p \wedge q) \wedge(p \rightarrow q)$(4) $(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$Correct Option: 4, Solution: $(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is tautolog $\mathrm{y}$...
Read More →A galvanometer of resistance G is converted into
Question: A galvanometer of resistance $G$ is converted into a voltmeter of ragne $0-1 \mathrm{~V}$ by connecting a resistance $\mathrm{R}_{1}$ in series with it. The additional resistance $R_{1}$ in series with it. The additional resistance that should be connected in series with $R_{1}$ to increase the range of the voltmeter to $0-2 \mathrm{~V}$ will be:(1) $\mathrm{G}$(2) $\mathrm{R}_{1}$(3) $\mathrm{R}_{1}-\mathrm{G}$(4) $\mathrm{R}_{1}+\mathrm{G}$Correct Option: 4 Solution: (4) Galvanometer...
Read More →Solve the following
Question: When $35 \mathrm{~mL}$ of $0.15 \mathrm{M}$ lead nitrate solution is mixed with $20 \mathrm{~mL}$ of $0.12 \mathrm{M}$ chromic sulphate solution, _______________ $\times 10^{-5}$ moles of lead sulphate precipitate out. (Round off to the Nearest Solution: (525) $3 \mathrm{~Pb}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3} \rightarrow 3 \mathrm{PbSO}_{4}+2 \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}$ $35 \mathrm{ml} \quad 20 \mathrm{ml}$ $0.15 \mathrm{M}...
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