Tick (✓) the correct answer
Question: Tick (✓) the correct answer: If the simple interest on a sum of money at 5% per annum for 3 years is Rs 1200 then the compound interest on the same sum for the same period at the same rate will be (a) Rs 1225 (b) Rs 1236 (c) Rs 1248 (d) Rs 1261 Solution: (d) Rs 1261 Here, SI $=\frac{P \times 5 \times 3}{100}$ $\Rightarrow 1200=\frac{P \times 5 \times 3}{100}$ $\Rightarrow P=\frac{1200 \times 100}{5 \times 3}=$ Rs 8000 Amount at the end of 3 years $=$ Rs $8000 \times\left(1+\frac{5}{100...
Read More →What is the difference between direct current
Question: What is the difference between direct current and an alternating current ? How many times does AC used in India change direction in one second ? Solution: Difference between Direct current and an Alternating current: Since frequency is 50 Hz, so a.c. completes 50 cycles in 1 second. Therefore, it reverses its direction 100 times in one second....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The annual rate of growth in population of a town is 10%. If its present population is 33275, what was it 3 years ago? (a) 25000 (b) 27500 (c) 30000 (d) 26000 Solution: (a) 25000 Let $P$ be the popultion 3 years ago. Now, present population $=33275$ $\Rightarrow 33275=P \times\left(1+\frac{10}{100}\right)^{3}$ $\Rightarrow 33275=P \times\left(\frac{110}{100}\right)^{3}$ $\Rightarrow 33275=P \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right) \...
Read More →What is the role of two conducting
Question: What is the role of two conducting stationary brushes in a simple electric motor ? Solution: These brushes act as the contacts between the commutator and the terminals of the battery....
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Question: Tick (✓) the correct answer: The value of a machine depreciates at the rate of 20% per annum. It was purchased 2 years ago. If its present value is Rs 40000, for how much was it purchased? (a) Rs 56000 (b) Rs 62500 (c) Rs 65200 (d) Rs 56500 Solution: (b) Rs. 62500 Here, $A=P \times\left(1-\frac{R}{100}\right)^{n}$ $=P \times\left(1-\frac{20}{100}\right)^{2}$ $=P \times\left(\frac{80}{100}\right)^{2}$ $=P \times\left(\frac{4}{5}\right) \times\left(\frac{4}{5}\right)$ $\Rightarrow 40000=...
Read More →Name four appliances wherein an electric motor,
Question: Name four appliances wherein an electric motor, a rotating device that converts electrical energy to mechanical energy is used as an important component. In what respect motors are different from generators ? Solution: Appliances wherein an electric motor is used are electric fan, electric mixer, washing machine and a toy car. Motor converts electrical energy into mechanical energy. How-ever, generator converts mechanical energy into electrical energy....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago for Rs 60000. What is the present value of the machine? (a) Rs 53640 (b) Rs 51680 (c) Rs 43740 (d) Rs 43470 Solution: (c) Rs. 43740 Here, $A=$ Rs. $P \times\left(1-\frac{R}{100}\right)^{n}$ $=$ Rs. $60000 \times\left(1-\frac{10}{100}\right)^{3}$ $=$ Rs. $60000 \times\left(\frac{90}{100}\right)^{3}$ $=$ Rs. $60000 \times\left(\frac{9}{10}\right) \times\left(\frac{9}...
Read More →What does the divergence of magnetic
Question: What does the divergence of magnetic field lines near the ends of a current carrying straight solenoid indicate ? Solution: Divergence of magnetic field lines means the magnetic field lines are far apart. Such field lines indicate weak magnetic field. Therefore, divergence of magnetic field lines near the ends of the current carrying solenoid indicates that the magnetic field near the ends of the current carrying solenoid is weak and non-uniform....
Read More →Solve this
Question: Find $\frac{d y}{d x}$, when $y=(\tan x)^{\cot x}+(\cot x)^{\tan x}$ Solution: let $y=(\tan x)^{\cot x}+(\cot x)^{\tan x}$ $\Rightarrow y=a+b$ where $a=(\tan x)^{\cot x} ; b=(\cot x)^{\tan x}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\mathrm{dx}}$ where a and $\mathrm{u}$ are any variables $...
Read More →Meena draws magnetic field lines of field
Question: Meena draws magnetic field lines of field close to the axis of a current carrying circular loop. As she moves away from the centre of the circular loop, she observes that the lines keep on diverging. How will you explain her observation ? (CBSE 2010) Solution: Magnetic field due to current carrying circular loop decreases as we move away from the centre of the loop. Diverging field lines represent weak magnetic field....
Read More →Using the principle of mathematical induction, prove each of the following
Question: Using the principle of mathematical induction, prove each of the following for all n ϵ N: $\left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \ldots\left\{1+\frac{(2 n+1)}{n^{2}}\right\}=(n+1)^{2}$ Solution: To Prove: $\left(1+\frac{3}{1}\right) \times\left(1+\frac{5}{4}\right) \times\left(1+\frac{7}{9}\right) \times \ldots \ldots \times\left\{1+\frac{2 n+1}{n^{2}}\right\}=(n+1)^{2}$ Let us prove this question by principle of mathematical induction (PMI) Let...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The present population of a town is 24000. If it increases at the rate of 5% per annum, what will be its population after 2 years? (a) 26400 (b) 26460 (c) 24460 (d) 26640 Solution: (b) 26460 Here, $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $24000 \times\left(1+\frac{5}{100}\right)^{2}$ $=$ Rs. $24000 \times\left(\frac{105}{100}\right)^{2}$ $=$ Rs. $24000 \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20}\right)$ $=$ Rs. $(60 \times 21 \tim...
Read More →What does the direction of thumb indicate
Question: What does the direction of thumb indicate in the right-hand thumb rule. In what way this rule is different from Flemings left-hand rule ? (CBSE 2010,2012) Solution: In the right hand rule, the direction of thumb indicates the direction of flow of current in the straight conductor. Right-hand thumb rule is used to determine the direction of the magnetic field produced by a current carrying straight conductor. However, Flemings left hand rule is used to determine the direction of the for...
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Question: Tick (✓) the correct answer: The compound interest on Rs 40000 at 6% per annum for 6 months, compounded quarterly, is (a) Rs 1209 (b) Rs 1902 (c) Rs 1200 (d) Rs 1306 Solution: (a) Rs 1209 Time $=6$ months $=2$ quater years Rate compounded quarter yearly $=\frac{6}{4} \%=\frac{3}{2} \%$ Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $40000 \times\left(1+\frac{3}{100 \times 2}\right)^{2}$ $=$ Rs. $40000 \times\left(\frac{203}{200}\right)^{2}$ $=$ Rs. $40000 \times\left(\frac{2...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The compound interest on Rs 6250 at 8% per annum for 1 year, compounded half yearly, is (a) Rs 500 (b) Rs 510 (c) Rs 550 (d) Rs 512.50 Solution: (b) Rs 510 Rate of interest compounded half yearly $=\frac{8}{2} \%=4 \%$ Time $=1$ year $=2$ half years Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $6250 \times\left(1+\frac{4}{100}\right)^{2}$ $=$ Rs. $6250 \times\left(\frac{104}{100}\right)^{2}$ $=$ Rs. $6250 \times\left(\frac{26}{25}\right) \times...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A sum of Rs 25000 was given as loan on compound interest for 3 years compounded annually at 5% per annum during the first year, 6% per annum during the second year and 8% per annum during the third year. The compound interest is (a) Rs 5035 (b) Rs 5051 (c) Rs 5072 (d) Rs 5150 Solution: (b) Rs. 5051 Here, $A=$ Rs. $P \times\left(1+\frac{p}{100}\right) \times\left(1+\frac{q}{100}\right) \times\left(1+\frac{r}{100}\right)$ $=$ Rs. $25000 \times\left(1+\frac{5}...
Read More →It is established that an electric current through
Question: It is established that an electric current through a metallic conductor produces a magnetic field around it. Is there a similar magnetic field produced around a thin beam of moving alpha particles, neutrons ? Justify your answer.(CBSE 2012) Solution: A thin beam of moving alpha particles constitute an electric current. Thus, beam of moving alpha particles behaves as a current carrying conductor. Hence, magnetic field is produced around the thin beam of moving alpha particles. Neutrons ...
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Question: Tick (✓) the correct answer: The compound interest on Rs 4000 at 10% per annum for 2 years 3 months, compounded annually, is (a) Rs 916 (b) Rs 900 (c) Rs 961 (d) Rs 896 Solution: (c) Rs 961 Here, $A=P \times\left(1+\frac{R}{100}\right)^{2} \times\left(1+\frac{\frac{1}{4} R}{100}\right)$ $=$ Rs. $4000 \times\left(1+\frac{10}{100}\right)^{2} \times\left(1+\frac{\frac{1}{4} \times 10}{100}\right)$ $=$ Rs. $4000 \times\left(\frac{100+10}{100}\right)^{2} \times\left(\frac{40+1}{40}\right)$ ...
Read More →A magnetic compass shows a deflection
Question: A magnetic compass shows a deflection when placed near a current carrying wire. How will the deflection of the compass get affected if the current in the wire is increased ? Support your answer with a reason. (CBSE 2012) Solution: A magnetic compass is a tiny magnet. It gets deflected when placed in a magnetic field. When the current in the wire increases, then the magnetic field produced by the wire also increases (B I). Hence, deflection of the compass increases....
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Question: Tick (✓) the correct answer The compound interest on Rs 10000 at $12 \%$ per annum for $1 \frac{1}{2}$ years, compounded annually, is (a) Rs 1872 (b) Rs 1720 (c) Rs 1910.16 (d) Rs 1782 Solution: (a) Rs 1872 Here, $A=P \times\left(1+\frac{R}{100}\right)^{1} \times\left(1+\frac{\frac{1}{2} R}{100}\right)$ $=\operatorname{Rs} 10000 \times\left(1+\frac{12}{100}\right) \times\left(1+\frac{\frac{1}{2} \times 12}{100}\right)$ $=\operatorname{Rs} 10000 \times\left(\frac{100+12}{100}\right) \ti...
Read More →Using the principle of mathematical induction, prove each of the following
Question: Using the principle of mathematical induction, prove each of the following for all n ϵ N: $\frac{1}{2 \times 5}+\frac{1}{(5 \times 8)}+\ldots \ldots+\frac{1}{(3 n-1) \times(3 n+2)}=\frac{n}{(6 n+4)}$ Solution: To Prove: $\frac{1}{2 \times 5}+\frac{1}{(5 \times 8)}+\ldots \ldots+\frac{1}{(3 n-1) \times(3 n+2)}=\frac{n}{(6 n+4)}$ For n = 1 $\mathrm{LHS}=\frac{1}{2 \times 5}=\frac{1}{10}$ $\mathrm{RHS}=\frac{1 \times 1}{(6+4)}=\frac{1}{10}$ Hence, LHS = RHS $P(n)$ is true for $n=1$ Assume...
Read More →AB is a current carrying conductor
Question: AB is a current carrying conductor in the plane of the paper as shown in figure. What are the directions of magnetic fields produced by it at points P and Q ? Given, r1 r2, where will the strength of the magnetic field be larger ? (CBSE 2010, 2012) Solution: According to Right hand thumb rule, the direction of the magnetic field is into the plane of the paper at P and the direction of the magnetic field is out of the plane of the paper at Q. The strength of the magnetic field due to a ...
Read More →Solve this
Question: Find $\frac{d y}{d x}$, when $y=(\sin x)^{\cos x}+(\cos x)^{\sin x}$ Solution: let $y=(\sin x)^{\cos x}+(\cos x)^{\sin x}$ $\Rightarrow y=a+b$ where $a=(\sin x)^{\cos x} ; b=(\cos x)^{\sin x}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\mathrm{dx}}$ where a and $\mathrm{u}$ are any variables $...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: The compound interest on Rs 10000 at 10% per annum for 3 years, compounded annually, is (a) Rs 1331 (b) Rs 3310 (c) Rs 3130 (d) Rs 13310 Solution: (b) Rs. 3310 $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $10000 \times\left(1+\frac{10}{100}\right)^{3}$ $=$ Rs. $10000 \times\left(\frac{110}{100}\right)^{3}$ $=$ Rs. $10000 \times\left(\frac{11}{10}\right)^{3}$ $=$ Rs. $10000 \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right) \times\left...
Read More →Under what conditions permanent electromagnet
Question: Under what conditions permanent electromagnet is obtained if a current carrying solenoid is used ? Support your answer with the help of a labelled circuit diagram. Solution: Permanent electromagnet is obtained if direct current flows through the solenoid and steel rod (a magnetic substance) is placed inside the solenoid. In other words, a steel rod can be made a permanent electro-magnet if it is placed inside a solenoid carrying direct current as shown in figure....
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