Which part of the solar cooker

Question: Which part of the solar cooker is responsible for green house effect ? (a)Coating with black colour inside the box (b)Mirror (c)Glass sheet (d)Outer cover of the solar cooker Solution: (c). Explanation :Green house effect in a region occurs when heat radiation (infra-red radiation) are trapped in that region. When sunlight enters the solar cooker through a glass sheet, then the objects inside the solar cooker emit heat radiation (or infra-red radiation) due to their increased temperatu...

Question: Mark (✓) against the correct answer: If the simple interest on a sum of money at 10% per annum for 3 years is Rs 1500, then the compound interest on the same sum at the same rate for the same period is (a) Rs 1655 (b) Rs 1155 (c) Rs 1555 (d) Rs 1855 Solution: (a) Rs 1655 Here, SI $=\frac{P \times R \times T}{100}$ $\Rightarrow$ Rs. $1500=\frac{P \times 10 \times 3}{100}$ $\Rightarrow P=\frac{1500 \times 100}{10 \times 3}=$ Rs. 5000 Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ ...

The major problem in harnessing nuclear

Question: The major problem in harnessing nuclear energy is how to (a)split nuclei ? (b)sustain the reaction ? (c)dispose off spent fuel safely ? (d)convert nuclear energy into electrical energy ? Solution: (c). Explanation :This is because even spent fuel (nuclear waste) continues to emit harmful radiation....

Mark (✓) against the correct answer:

Question: Mark (✓) against the correct answer: At what rate per cent per annum will Rs 5000 amount to Rs 5832 in 2 years, compounded annually? (a) 11% (b) 10% (c) 9% (d) 8% Solution: (d) 8% Here, $A=$ Rs. $\mathrm{P} \times\left(1+\frac{R}{100}\right)^{n}$ $\Rightarrow$ Rs. $5832=$ Rs. $5000 \times\left(1+\frac{R}{100}\right)^{2}$ $\Rightarrow \frac{\text { Rs. } 5832}{\text { Rs. } 5000}=\left(1+\frac{R}{100}\right)^{2}$ $\Rightarrow\left(\frac{27}{25}\right)^{2}=\left(1+\frac{R}{100}\right)^{2...

Ocean thermal energy is due to

Question: Ocean thermal energy is due to (a)energy stored by waves in the ocean (b)temperature difference levels in the occean (c)pressure difference at different levels in the ocean (d)tides arising out in the ocean Solution: (b)temperature difference levels in the occean...

Which one of the following of energy leads

Question: Which one of the following of energy leads to least environmental pollution in the process of its harnessing and ultisation ? (a)Nuclear energy (b)Thermal energy (c)Solar energy (d)Geothermal energy Solution: (c)Solar energy...

Mark (✓) against the correct answer:

Question: Mark (✓) against the correct answer: The annual rate of growth in population of a town is 5%. If its present population is 4000, what will be its population after 2 years? (a) 4441 (b) 4400 (c) 4410 (d) 4800 Solution: (c) 4410 Present population =4000 Rate of growth = 5% To find the population of the town after 2 years, we have: $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=4000 \times\left(1+\frac{5}{100}\right)^{2}$ $=4000 \times\left(\frac{105}{100}\right)^{2}$ $=4000 \times\left(\...

Potential energy of water stored in a dam Kinetic

Question: Potential energy of water stored in a dam Kinetic energy of falling water - K.E. of rotation of turbine - electrical energy. Which is the ultimate souce of energy ? (a)Water (b)Sun (c)Uranium (d)Fossil fuels Solution: (b).Explanation :All forms of energy are derived from the sun....

Mark (✓) against the correct answer:

Question: Mark (✓) against the correct answer: The compound interest on Rs 5000 at 10% per annum for 2 years is (a) Rs 550 (b) Rs 1050 (c) Rs 950 (d) Rs 825 Solution: (b) Rs 1050 $P=$ Rs. 5000 $R=10 \%$ $n=2$ years Now, $A=$ Rs. $P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $5000 \times\left(1+\frac{10}{100}\right)^{2}$ $=$ Rs. $5000 \times\left(\frac{110}{100}\right)^{2}$ $=$ Rs. $5000 \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right)$ $=$ Rs. $(50 \times 11 \times 11)$ $=$...

In a hydro power plant

Question: In a hydro power plant (a)Potential energy possessed by stored water is converted into electricity (b)Kinetic energy possessed by stored water is converted into potential energy (c)Electricity is extracted from water (d)Water is converted into steam to produce electricity Solution: (a).Explanation :Sequence of energy transformation in hydro power plant :...

A scooter is bought for Rs 32000.

Question: A scooter is bought for Rs 32000. Its value depreciates at 10% per annum. What will be its value after 2 years? Solution: Let the principal amount be $P=\mathrm{Rs} 32000$. Rate of interest $(R)=10 \%$ Time $(n)=2$ years Now, $\mathrm{A}=$ Rs. $\mathrm{P} \times\left(1-\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $=$ Rs. $32000 \times\left(1-\frac{10}{100}\right)^{2}$ $=$ Rs. $32000 \times\left(\frac{90}{100}\right)^{2}$ $=$ Rs. $32000 \times\left(\frac{9}{10}\right) \times\left(\frac{9...

The rain containing these acids

Question: The rain containing these acids is called acid rain. Fuel used in thermal power plants is (a)water (b)uranium (c)biomass (d)fossil fuels Solution: (c)biomass...

Acid rain happen because

Question: Acid rain happen because (a)Sun leades to heating of upper layer of atmospher (b)burning of fossil fuels release oxides of carbon, nitrogen and sulphur in the atmosphere (c)electrical charges are produced due to friction amongst clouds (d)earth atmosphere contains acids. Solution: (c). Explanation :When oxides of carbon, nitrogen and sulphur react with water vapours in the atmosphere, they form carbonic acid, nitric acid and sulphuric acid respectively. These acids come down to the ear...

A sum amounts to Rs 23762 in 2 years at 9% per annum, compounded annually.

Question: A sum amounts to Rs 23762 in 2 years at 9% per annum, compounded annually. Find the sum Solution: Amount $(A)=$ Rs 23762 Rate of interest $(\mathrm{R})=9 \%$ Time $(n)=2$ years Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $\Rightarrow$ Rs $23762=P \times\left(1+\frac{9}{100}\right)^{2}$ $\Rightarrow$ Rs $23762=P \times\left(\frac{109}{100}\right) \times\left(\frac{109}{100}\right)$ $\Rightarrow P=$ Rs $\frac{23762 \times 100 \times 100}{109 \times 109}$ $\Rightarrow P=$ Rs 20000 $...

Which of the following is a non-renewable

Question: Which of the following is a non-renewable source of energy ? (a)Wood (b)Sun (c)Fossile fuels (d)Wind Solution: (c)Fossile fuels...

Find the amount and the compound interest on Rs 6000

Question: Find the amount and the compound interest on Rs 6000 for 1 year at 10% per annum compounded half-yearly. Solution: Let the principal amount be $P=\mathrm{Rs} 6000$. Rate of interest $=10 \%$ p. a. $=5 \%$ for half yearly Time $(n)=1$ year $=2$ half years Now, $\mathrm{A}=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs $6000 \times\left(1+\frac{5}{100}\right)^{2}$ $=$ Rs $6000 \times\left(\frac{105}{100}\right)^{2}$ $=$ Rs $6000 \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20...

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: $\left(1+\frac{1}{1}\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right) \ldots\left\{1+\frac{1}{n}\right\}=(n+1)$ Solution: To Prove: $\left(1+\frac{1}{1}\right) \times\left(1+\frac{1}{2}\right) \times\left(1+\frac{1}{3}\right) \times \ldots \ldots \times\left\{1+\frac{1}{n^{1}}\right\}=(n+1)^{1}$ Let us prove this question by principle of mathematical induction (PMI) Let $\mathrm{P}(\math...

Solve this

Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when $y=x^{\cos x}+(\sin x)^{\tan x}$ Solution: let $y=x^{\cos x}+(\sin x)^{\tan x}$ $\Rightarrow y=a+b$ where $a=x^{\cos x} ; b=(\sin x)^{\tan x}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\mathrm{dx}}$ where $\mathrm{a}$ and $\mathrm{u}$ are any varia...

Find the amount of Rs 10000 after 2 years compounded annually;

Question: Find the amount of Rs 10000 after 2 years compounded annually; the rate of interest being 10% per annum during the first year and 12% per annum during the second year. Also, find the compound interest. Solution: Here, $A=P \times\left(1+\frac{p}{100}\right) \times\left(1+\frac{r}{100}\right)$ $=$ Rs. $10000 \times\left(1+\frac{10}{100}\right) \times\left(1+\frac{12}{100}\right)$ $=$ Rs. $10000 \times\left(\frac{110}{100}\right) \times\left(\frac{112}{100}\right)$ $=$ Rs. $10000 \times\...

Find the amount and the compound interest on Rs 3000 for 2 years

Question: Find the amount and the compound interest on Rs 3000 for 2 years at 10% per annum. Solution: Here, $A=P \times\left(1+\frac{R}{100}\right)^{\mathrm{n}}$ $=$ Rs. $3000 \times\left(1+\frac{10}{100}\right)^{2}$ $=$ Rs. $3000 \times\left(\frac{110}{100}\right)^{2}$ $=$ Rs. $3000 \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right)$ $=$ Rs. $(30 \times 11 \times 11)$ $=$ Rs. 3630 $\therefore C I=A-P=$ Rs. $(3630-3000)=$ Rs. 630 Hence, the amount is Rs. 3630 and the CI is Rs. 63...

Tick (✓) the correct answer

Question: Tick (✓) the correct answer: At what rate per cent per annum will a sum of Rs 7500 amount to Rs 8427 in 2 years, compounded annually? (a) 4% (b) 5% (c) 6% (d) 8% Solution: (c) 6% Here, $A=P \times\left(1+\frac{R}{100}\right)$ $=$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$ $=$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$ However, amount $=$ Rs. 8427 Now, Rs. $8427==$ Rs. $7500 \times\left(1+\frac{R}{100}\right)^{2}$ $\Rightarrow \frac{\text { Rs. } 8427}{\text { Rs. } 7500}=...

Tick (✓) the correct answer

Question: Tick (✓) the correct answer The sum that amounts to Rs 4913 in 3 years at $6 \frac{1}{4} \%$ per annum compounded annually, is (a) Rs 3096 (b) Rs 4076 (c) Rs 4085 (d) Rs 4096 Solution: (d) Rs 4096 We have Rs $4913=\left\{P \times\left(1+\frac{25}{100 \times 4}\right)^{3}\right\}$ $\Rightarrow \mathrm{Rs} 4913=\left\{P \times\left(\frac{16+1}{16}\right)^{3}\right\}$ $\Rightarrow \mathrm{Rs} 4913=\left\{P \times\left(\frac{17}{16}\right) \times\left(\frac{17}{16}\right) \times\left(\frac...

Solve this

Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when $y=(\sin x)^{x}+\sin ^{-1} \sqrt{x}$ Solution: Let $y=(\sin x)^{x}+\sin ^{-1} \sqrt{x}$ $\Rightarrow y=a+b$ where, $a=(\sin x)^{x} ; b=\sin ^{-1} \sqrt{x}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\mathrm{dx}}$ where $\mathrm{a}$ and $\mathrm{u}$ ...

Tick (✓) the correct answer:

Question: Tick (✓) the correct answer: If the compound interest on a sum for 2 years at $12 \frac{1}{2} \%$ per annum is Rs 510 , the simple interest on the same sum at the same rate for the same period of time is (a) Rs 400 (b) Rs 450 (c) Rs 460 (d) Rs 480 Solution: (d) Rs 480 We have : $510=\left\{P \times\left(1+\frac{25}{100 \times 2}\right)^{2}\right\}-P$ $\Rightarrow 510=\Rightarrow\left\{P \times\left(\frac{8+1}{8}\right)^{2}\right\}-P$ $\Rightarrow 510=\left\{P \times\left(\frac{9}{8}\ri...

What is the role of fuse,

Question: What is the role of fuse, used in series with any electrical appli-ances ? Why should a fuse with defined rating not be replaced by one with a larger rating ? Solution: Electric fuse is a safety device. It protects the electrical appliance due to short circuiting and overloading in the electric circuit. Fuse with defined rating means the maximum current that can flow through the fuse wire without melting it. As and when current exceeds this maximum value, the fuse melts and the circuit...