Two ideal polyatomic gases at temperatures
Question: Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed so that there is no loss of energy. If $\mathrm{F}_{1}$ and $\mathrm{F}_{2}, \mathrm{~m}_{1}$ and $\mathrm{m}_{2}, \mathrm{n}_{1}$ and $\mathrm{n}_{2}$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :(1) $\frac{\mathrm{n}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~T}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$(2) $\frac{\m...
Read More →The regions of the atmosphere, where clouds are formed and where we live,
Question: The regions of the atmosphere, where clouds are formed and where we live, respectively, are :Troposphere and StratosphereStratosphere and TroposphereTroposphere and TroposphereStratosphere and StratosphereCorrect Option: , 3 Solution: The lowest region of atmosphere in which human beings live and clouds form is known as troposphere. It extends up to a height of $10 \mathrm{~km}$ from sea level....
Read More →A dealer sells an article for ₹75 and gains as much percent as the cost price of the article.
Question: A dealer sells an article for ₹75 and gains as much percent as the cost price of the article. Find the cost price of the article. Solution: Let the cost price of the article be ₹x. Gain percent =x%According to the given condition, $₹ X+₹\left(\frac{x}{100} \times x\right)=₹ 75$ (Cost price + Gain = Selling price) $\Rightarrow \frac{100 x+x^{2}}{100}=75$ $\Rightarrow x^{2}+100 x=7500$ $\Rightarrow x^{2}+100 x-7500=0$ $\Rightarrow x^{2}+150 x-50 x-7500=0$ $\Rightarrow x(x+150)-50(x+150)=...
Read More →The values of
Question: The values of $\lambda$ and $\mu$ for which the system of linear equations $x+y+z=2$ $x+2 y+3 z=5$ $x+3 y+\lambda z=\mu$ has infinitely many solutions are, respectively: (1) 6 and 8(2) 5 and 7(3) 5 and 8(4) 4 and 9Correct Option: , 3 Solution: $D=\left|\begin{array}{lll}1 1 1 \\ 1 2 3 \\ 1 3 \lambda\end{array}\right|=0 \Rightarrow \lambda=5$ $D_{x}=\left|\begin{array}{lll}2 1 1 \\ 5 2 3 \\ \mu 3 5\end{array}\right|=0 \Rightarrow \mu=8$...
Read More →The layer of atmosphere between
Question: The layer of atmosphere between $10 \mathrm{~km}$ to $50 \mathrm{~km}$ above the sea level is called as:tropospherethermospherestratospheremesosphereCorrect Option: , 3 Solution: Stratosphere lies between $10-50 \mathrm{~km}$ above sea level....
Read More →A polyatomic ideal gas has 24 vibrational modes.
Question: A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$ ?(1) $1.03$(2) $1.3$(3) $1.37$(4) $10.3$Correct Option: 1 Solution: (1) Since each vibrational mode has 2 degrees of freedom hence total vibrational degrees of freedom $=48$ $\mathrm{f}=3+3+48=54$ $\gamma=1+\frac{2}{\mathrm{f}}=\frac{28}{27}=1.03$...
Read More →Excessive release of
Question: Excessive release of $\mathrm{CO}_{2}$ into the atmosphere results in:global warmingpolar vortexformation of smogdepletion of ozoneCorrect Option: Solution: Global warming is caused by the emission of green house gases. $72 \%$ of the totally emitted green house gases is $\mathrm{CO}_{2}$. Therefore, excessive release of $\mathrm{CO}_{2}$ is the main cause of global warming....
Read More →A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less.
Question: A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less. How many pens did he buy? Solution: Let number of pens bought =xLet the price per pen = RsyIt is given that the price ofx pens is Rs 180 $\Rightarrow x y=180 \quad \ldots(i)$ $\Rightarrow x=\frac{180}{y}$ Also, given that if 3 more pens are purchased for the same amount, the price per pen gets reduced by Rs 3 $\Rightarrow(y-3)(x+3)=180 \quad \ldots(i i)$ Put t...
Read More →The maximum prescribed concentration of copper in drinking water is:
Question: The maximum prescribed concentration of copper in drinking water is:$5 \mathrm{ppm}$$0.05 \mathrm{ppm}$$0.5 \mathrm{ppm}$$3 \mathrm{ppm}$Correct Option: , 4 Solution: Maximum prescribed concentration of $\mathrm{Cu}$ in drinking water is $3 \mathrm{ppm}$....
Read More →Solve the following
Question: If $a+x=b+y=c+z+1$, where $a, b, c, x, y, z$ are non-zero distinct real numbers, then $\left|\begin{array}{lll}x a+y x+a \\ y b+y y+b \\ z c+y z+c\end{array}\right|$ is equal to :(1) $y(b-a)$(2) $y(a-b)$(3) 0(4) $y(a-c)$Correct Option: 2, Solution: (2) Use properties of determinant $\left|\begin{array}{lll}x a+y x+a \\ y b+y y+b \\ z c+y z+c\end{array}\right|=\left|\begin{array}{lll}x a x+a \\ y b y+b \\ z c z+c\end{array}\right|+y\left|\begin{array}{ccc}x 1 x+a \\ y 1 y+b \\ z 1 z+c\e...
Read More →The maximum prescribed concentration of copper in drinking water is:
Question: The maximum prescribed concentration of copper in drinking water is:$5 \mathrm{ppm}$$0.05 \mathrm{ppm}$$0.5 \mathrm{ppm}$$3 \mathrm{ppm}$Correct Option: , 4 Solution: Maximum prescribed concentration of $\mathrm{Cu}$ in drinking water is $3 \mathrm{ppm}$....
Read More →Calculate the value of mean free path
Question: Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} \mathrm{C}$ and pressure $1.01 \times 10^{5} \mathrm{~Pa}$. Assume the molecular diameter $0.3 \mathrm{~nm}$ and the gas is ideal. $\left(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$(1) $58 \mathrm{~nm}$(2) $32 \mathrm{~nm}$(3) $86 \mathrm{~nm}$(4) $102 \mathrm{~nm}$Correct Option: , 4 Solution: (4) $\lambda=\frac{\mathrm{RT}}{\sqrt{2} \pi \mathrm{d}^{2} \mathrm{~N}_{\mathrm{A}...
Read More →Assertion : Ozone is destroyed by CFCs in the upper stratosphere.
Question: Assertion : Ozone is destroyed by CFCs in the upper stratosphere. Reason : Ozone holes increase the amount of UV radiation reaching the earth.Assertion and reason are incorrect.Assertion and reason are both correct, and the reason is the correct explanation for the assertion.Assertion and reason are correct, but the reason is not the explanation for the assertion.Assertion is false, but the reason is correct.Correct Option: , 3 Solution: CFC's are responsible for depletion of ozone lay...
Read More →If the system of linear equations
Question: If the system of linear equations $x+y+3 z=0$ $x+3 y+k^{2} z=0$ $3 x+y+3 z=0$ has a non-zero solution $(x, y, z)$ for some $k \in \mathbf{R}$, then $x+\left(\frac{y}{z}\right)$ is equal to : (1) $-3$(2) 9(3) 3(4) $-9$Correct Option: 1 Solution: (1) Since, system of linear equations has non-zero solution $\therefore \Delta=0$' $\Rightarrow\left|\begin{array}{ccc}1 1 3 \\ 1 3 k^{2} \\ 3 1 3\end{array}\right|=0$ $\Rightarrow 1\left(9-k^{2}\right)-1\left(3-3 k^{2}\right)+3(1-9)=0$ $\Righta...
Read More →The volume V of an enclosure contains a
Question: The volume $\mathrm{V}$ of an enclosure contains a mixture of three gases, $16 \mathrm{~g}$ of oxygen, $28 \mathrm{~g}$ of nitrogen and $44 \mathrm{~g}$ of carbon dioxide at absolute temperature $\mathrm{T}$. Consider $\mathrm{R}$ as universal gas constant. The pressure of the mixture of gases is:(1) $\frac{88 \mathrm{RT}}{\mathrm{V}}$(2) $\frac{3 \mathrm{RT}}{\mathrm{V}}$(3) $\frac{5}{2} \frac{\mathrm{RT}}{\mathrm{V}}$(4) $\frac{4 \mathrm{RT}}{\mathrm{V}}$Correct Option: , 3 Solution:...
Read More →In a class test, the sum of the marks obtained by P in mathematics and science is 28.
Question: In a class test, the sum of the marks obtained byPin mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained him in the two subjects separately. Solution: Let the marks obtained byPin mathematics and science bexand (28 x), respectively.According to the given condition, $(x+3)(28-x-4)=180$ $\Rightarrow(x+3)(24-x)=180$ $\Rightarrow-x^{2}+21 x+72=180$ $...
Read More →Which is wrong with respect to our responsibility as a human being to protect our environment?
Question: Which is wrong with respect to our responsibility as a human being to protect our environment?Restricting the use of vehiclesAvoiding the use of floodlighted facilitiesSetting up compost tin in gardens.Using plastic bags.Correct Option: , 4 Solution: Use of plastic bags is hazardous to our environment...
Read More →Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm):
Question: Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm):for sustaining life in a water body.by bacteria to break-down organic waste in a certain volume of a water sample.for the photochemical breakdown of waste present in 1 $\mathrm{m}^{3}$ volume of a water body.by anaerobic bacteria to breakdown inorganic waste present in a water body.Correct Option: , 2 Solution: Biochemical oxygen demand is the amount of oxygen required by bacteria to break down the organic matter...
Read More →A person on tour has ₹10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹90.
Question: A person on tour has ₹10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹90. Find the original duration of the tour. Solution: Let the original duration of the tour bexdays. $\therefore$ Original daily expenses $=₹ \frac{10,800}{x}$ If he extends his tour by 4 days, then his new daily expenses $=₹ \frac{10,800}{x+4}$ According to the given condition, $₹ \frac{10,800}{x}-₹ \frac{10,800}{x+4}=₹ 90$ $\Rightarrow \frac{10800 x+43200-10800 x}...
Read More →Among the gases (a)-(e), the gases that cause greenhouse effect are:
Question: Among the gases (a)-(e), the gases that cause greenhouse effect are: (a) $\mathrm{CO}_{2}$ (b) $\mathrm{H}_{2} \mathrm{O}$ (c) $\mathrm{CFCs}$ (d) $\mathrm{O}_{2}$ (e) $\mathrm{O}_{3}$(a), (b), (c) and (d)(a), (b), (c) and (e)(a) and (d)(a), (c), (d) and (e)Correct Option: , 2 Solution: $\mathrm{CO}_{2}, \mathrm{O}_{3}, \mathrm{H}_{2} \mathrm{O}$ vapours and $\mathrm{CFC}^{\prime}$ s are the gases that cause green house effect....
Read More →The system of linear equations
Question: Let $\lambda \in R$. The system of linear equations $2 x_{1}-4 x_{2}+\lambda x_{3}=1$ $x_{1}-6 x_{2}+x_{3}=2$ $\lambda x_{1}-10 x_{2}+4 x_{3}=3$(1) exactly one negative value of $\lambda$(2) exactly one positive value of $\lambda$(3) every value of $\lambda$(4) exactly two value of $\lambda$Correct Option: 1 Solution: $\because\left|\begin{array}{ccc}2 -4 \lambda \\ 1 -6 1 \\ \lambda -10 4\end{array}\right|=0 \Rightarrow 3 \lambda^{2}-7 \lambda-12=0$ $\Rightarrow \lambda=3$ or $-\frac{...
Read More →The condition that indicates a polluted environment is:
Question: The condition that indicates a polluted environment is:eutrophication$0.03 \%$ of $\mathrm{CO}_{2}$ in the atmosphereBOD value of $5 \mathrm{ppm}$$\mathrm{pH}$ of rain water to be $5.6$Correct Option: 1 Solution: The process in which nutrient enriched water bodies support a dense plant population which kill animal life by depriving it of oxygen results in subsequent loss of biodiversity is known as Eutrophication. So, this condition indicates a polluted environment....
Read More →Suppose the vectors x1, x2 and x3 are the solutions
Question: Suppose the vectors $x_{1}, x_{2}$ and $x_{3}$ are the solutions of the system of linear equations, $A x=b$ when the vector $b$ on the right side is equal to $b_{1}, b_{2}$ and $b_{3}$ respectively. If $x_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], x_{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], x_{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], b_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], b_{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\...
Read More →The incorrect statement(s) among (1) - (4) regarding acid rain is (are):
Question: The incorrect statement(s) among (1) - (4) regarding acid rain is (are): (a) It can corrode water pipes. (b) It can damage structures made up of stone. (c) It cannot cause respiratory ailments in animals (d) It is not harmful for trees(a), (c) and (d)(c) only(a), (b) and (d)(c) and (d)Correct Option: , 4 Solution: Acid rain is harmful for trees and animal life. It can also cause respiratory ailments in animals....
Read More →If the price of a book is reduced by ₹5, a person can buy 4 more books for ₹600.
Question: If the price of a book is reduced by ₹5, a person can buy 4 more books for ₹600. Find the original price of the book. Solution: Let the original price of the book be ₹x. $\therefore$ Number of books bought at original price for ₹ $600=\frac{600}{x}$ If the price of a book is reduced by ₹5, then the new price of the book is ₹(x 5). $\therefore$ Number of books bought at reduced price for ₹ $600=\frac{600}{x-5}$ According to the given condition, $\frac{600}{x-5}-\frac{600}{x}=4$ $\Righta...
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