If the system of linear equations
Question: If the system of linear equations $2 x+2 a y+a z=0$ $2 x+3 b y+b z=0$ $2 x+4 c y+c z=0$ where $a, b, c \in \boldsymbol{R}$ are non-zero and distinct; has a non-zero solution, then:(1) $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in A.P.(2) $a, b, c$ are in G.P.(3) $a+b+c=0$(4) $a, b, c$ are in A.P.Correct Option: 1 Solution: For non-zero solution $\left|\begin{array}{lll}2 2 a a \\ 2 3 b b \\ 2 4 c c\end{array}\right|=0$ $\Rightarrow\left|\begin{array}{lll}1 2 a a \\ 1 3 b b \\ 1 4 c c\...
Read More →The compound that is NOT a common component of photochemical smog is :
Question: The compound that is NOT a common component of photochemical smog is :$\mathrm{O}_{3}$$\mathrm{CH}_{2}=\mathrm{CHCHO}$$\mathrm{CF}_{2} \mathrm{Cl}_{2}$Correct Option: , 4 Solution: Acrolein, PAN (produced by the oxidation of unburnt hydrocarbons present in the polluted air) and ozone are the main components of photochemical smog. While $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ is not a common component of photochemical smog....
Read More →Two years ago, a man's age was three times the square of his son's age.
Question: Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages. Solution: Let son's age 2 years ago bexyears. Then,Man's age 2 years ago = 3x2years Son's present age = (x+ 2) yearsMan's present age = (3x2+ 2) yearsIn three years time,Son's age = (x+ 2 + 3) years = (x+ 5) yearsMan's age = (3x2+ 2 + 3) years = (3x2+ 5) yearsAccording to the given condition,Man's age = 4 Son's age3x2+ 5 = 4(x+ ...
Read More →n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes -
Question: $\mathrm{n}$ mole of a perfect gas undergoes a cyclic process $\mathrm{ABCA}$ (see figure) consisting of the following processes - $\mathrm{A} \rightarrow \mathrm{B}$ : Isothermal expansion at temperature $\mathrm{T}$ so that the volume is doubled from $\mathrm{V}_{1}$ to $\mathrm{V}_{2}=2 \mathrm{~V}_{1}$ and pressure changes from $\mathrm{P}_{1}$ to $\mathrm{P}_{2}$. $\mathrm{B} \rightarrow \mathrm{C}$ : Isobaric compression at pressure $\mathrm{P}_{2}$ to initial volume $\mathrm{V}_...
Read More →The higher concentration of which gas in air can cause stiffness of flower buds?
Question: The higher concentration of which gas in air can cause stiffness of flower buds?$\mathrm{NO}_{2}$$\mathrm{CO}_{2}$$\mathrm{SO}_{2}$$\mathrm{CO}$Correct Option: , 3 Solution: High concentration of $\mathrm{SO}_{2}$ leads to stiffness of flower buds....
Read More →The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30.
Question: The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age. Solution: Let the present age of Meena be $x$ years. According to the question: $(x-5)(x+8)=30$ $\Rightarrow x^{2}+3 x-40=30$ $\Rightarrow x^{2}+3 x-70=0$ $\Rightarrow x^{2}+(10-7) x-70=0$ $\Rightarrow x^{2}+10 x-7 x-70=0$ $\Rightarrow x(x+10)-7(x+10)=0$ $\Rightarrow(x+10)(x-7)=0$ $\Rightarrow x+10=0$ or $x-7=0$ $\Rightarrow x=-10$ or $x=7$ $\Rightarrow x=7 \quad(\because$ Age canno...
Read More →Taj Mahal is being slowly disfigured and discoloured.
Question: Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :Global warmingAcid rainWater pollutionSoil pollutionCorrect Option: , 2 Solution: Acid rain....
Read More →Peroxyacetyl nitrate (PAN),
Question: Peroxyacetyl nitrate (PAN), an eye irritant, is produced by :Classical smogAcid rainOrganic wastePhotochemical smogCorrect Option: , 4 Solution: P.A.N is produced by photochemical smog....
Read More →The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126.
Question: The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages. Solution: Let the present ages of the boy and his brother be $x$ years and $(25-x)$ years. According to the question: $x(25-x)=126$ $\Rightarrow 25 x-x^{2}=126$ $\Rightarrow x^{2}-(18+7) x+126=0$ $\Rightarrow x^{2}-18 x-7 x+126=0$ $\Rightarrow x(x-18)-7(x-18)=0$ $\Rightarrow(x-18)(x-7)=0$ $\Rightarrow x-18=0$ or $x-7=0$ $\Rightarrow x=18$ or $x=7$ $\Rightarrow x=18 ...
Read More →The reaction that is NOT involved in the ozone layer
Question: The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is:Correct Option: , 3 Solution: The reaction, $\mathrm{CH}_{4}+2 \mathrm{O}_{3}^{-} \rightarrow 3 \mathrm{CH}_{2}=\mathrm{O}+3 \mathrm{H}_{2} \mathrm{O}$, not involved in the ozone layer depletion mechanism....
Read More →The reaction that is NOT involved in the ozone layer
Question: The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is:Correct Option: Solution: The reaction, $\mathrm{CH}_{4}+2 \mathrm{O}_{3}^{-} \rightarrow 3 \mathrm{CH}_{2}=\mathrm{O}+3 \mathrm{H}_{2} \mathrm{O}$, not involved in the ozone layer depletion mechanism....
Read More →Water filled in two glasses
Question: Water filled in two glasses $\mathrm{A}$ and $\mathrm{B}$ have $\mathrm{BOD}$ values of 10 and 20 , respectively. The correct statement regarding them, is:$\mathrm{B}$ is more polluted than $\mathrm{A}$.$\mathrm{A}$ is suitable for drinking, whereas $\mathrm{B}$ is not.Both A and B are suitable for drinking.$\mathrm{A}$ is more polluted than $\mathrm{B}$.Correct Option: 1 Solution: BOD indicates the amount of putrescible organic matter plesent in water. Therefore, a low BOD is an indic...
Read More →The pH of rain water, is approximately:
Question: The $\mathrm{pH}$ of rain water, is approximately:5.67.57.06.5Correct Option: Solution: $\mathrm{pH}$ of rain water is around $5.6$....
Read More →The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is
Question: The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is $\frac{1}{3}$. Find her present age. Solution: Let the present age of Meena bexyears.Meena's age 3 years ago = (x 3) yearsMeena's age 5 years hence = (x+ 5) yearsAccording to the given condition, $\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}$ $\Rightarrow \frac{x+5+x-3}{(x-3)(x+5)}=\frac{1}{3}$ $\Rightarrow \frac{2 x+2}{x^{2}+2 x-15}=\frac{1}{3}$ $\Rightarrow x^{2}+2 x-15=6 x+6$ $\Rightarrow x^{2}-4 x-21=...
Read More →Which of the following conditions in drinking water causes methemoglobinemia?
Question: Which of the following conditions in drinking water causes methemoglobinemia? $50 \mathrm{ppm}$ of lead$50 \mathrm{ppm}$ of chloride$50 \mathrm{ppm}$ of nitrate$100 \mathrm{ppm}$ of sulphateCorrect Option: , 3 Solution: Methemoglobinemia is caused by drinking water which is contaminated with nitrate....
Read More →Consider a sample of oxygen behaving like an ideal gas.
Question: Consider a sample of oxygen behaving like an ideal gas. At $300 \mathrm{~K}$, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is $\left.32 \mathrm{~g} / \mathrm{mol} ; \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$(1) $\sqrt{\frac{3}{3}}$(2) $\sqrt{\frac{8}{3}}$(3) $\sqrt{\frac{3 \pi}{8}}$(4) $\sqrt{\frac{8 \pi}{3}}$cCorrect Option: , 3 Solution: (3) $\mathrm{v}_{\mathrm{ms}}=\sqrt{\frac...
Read More →A water sample has ppm level concentration of the following metals:
Question: A water sample has ppm level concentration of the following metals: $\mathrm{Fe}=0.2 ; \mathrm{Mn}=5.0 ; \mathrm{Cu}=3.0 ; \mathrm{Zn}=5.0$. The metal that makes the water sample unsuitable for drinking is:CuMnFeZnCorrect Option: Solution: The water sample containing $\mathrm{Mn}=5 \mathrm{ppm}$ is unsuitable for drinking as the prescribed level for Mn in drinking water is $0.5 \mathrm{ppm}$....
Read More →One year ago, a man was 8 times as old as his son.
Question: (i) One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son's age. Find their present ages. (ii) A man is $3 \frac{1}{2}$ times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son. Solution: (i)Let the present age of the son bexyears. Present age of the man =x2yearsOne year ago,Age of the son = (x 1) yearsAge of the man = (x2 1) yearsAccording to the given condition,Age of the man = 8 Age ...
Read More →What will be the average value of energy along one degree
Question: What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $\mathrm{T}\left(\mathrm{k}_{\mathrm{B}}\right.$ is Boltzmann constant)(1) $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$(2) $\frac{2}{3} \mathrm{k}_{\mathrm{B}} \mathrm{T}$(3) $\frac{3}{2} k_{\mathrm{B}} \mathrm{T}$(4) $\mathrm{k}_{\mathrm{B}} \mathrm{T}$Correct Option: 1 Solution: (1) Energy associated with each degree of freedom per molecule $=\frac{1}{2} \...
Read More →The primary pollutant that leads to
Question: The primary pollutant that leads to photochemical smog is:acroleinnitrogen oxidesozonesulphur dioxideCorrect Option: , 2 Solution: In photochemical smog, $\mathrm{NO}_{2}$ and hydrocarbons are primary pollutants whereas ozone and acrolein are secondary pollutants....
Read More →The sum of distinct values of
Question: The sum of distinct values of $\lambda$ for whcih the system of equations $(\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0$ $(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0$ $2 x+(3 \lambda+1) y+3(\lambda-1) z=0$ has non-zero solutions, is___________. Solution: For non-zero solution, $\Delta=0$ $\Rightarrow\left|\begin{array}{ccc}\lambda-1 3 \lambda+1 2 \lambda \\ \lambda-1 4 \lambda-2 \lambda+3 \\ 2 3 \lambda+1 3(\lambda-1)\end{array}\right|=0$ $\Rightarrow 6 \lambda^{3}-36 \lambda^{2}+54 \...
Read More →If one mole of the polyatomic gas is having two vibrational modes
Question: If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{v}}}\right)$ then the value of $\beta$ is :(1) $1.02$(2) $1.2$(3) $1.25$(4) $1.35$Correct Option: Solution: (2) $f=4+3+3=10$ assuming non linear $\beta=\frac{C_{p}}{C_{v}}=1+\frac{2}{f}=\frac{12}{10}=1.2$...
Read More →The correct set of species responsible for the photochemical smog is :
Question: The correct set of species responsible for the photochemical smog is :$\mathrm{N}_{2}, \mathrm{NO}_{2}$ and hydrocarbons$\mathrm{CO}_{2}, \mathrm{NO}_{2}, \mathrm{SO}_{2}$ and hydrocarbons$\mathrm{NO}, \mathrm{NO}_{2}, \mathrm{O}_{3}$ and hydrocarbons$\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{O}_{3}$ and hydrocarbonsCorrect Option: Solution: Photochemical smog contains oxides of nitrogen, ozone and hydrocarbons. It is also called oxidation smog....
Read More →Air pollution that occurs in sunlight is :
Question: Air pollution that occurs in sunlight is :reducing smogacid rainoxidizing smogfogCorrect Option: , 3 Solution: Air pollution caused by sunlight is photochemical smog also knows as oxidising smog....
Read More →Solve the following
Question: Let $\theta=\frac{\pi}{5}$ and $\mathrm{A}=\left[\begin{array}{cc}\cos \theta \sin \theta \\ -\sin \theta \cos \theta\end{array}\right]$. If $\mathrm{B}=\mathrm{A}+\mathrm{A}^{4}$, then $\operatorname{det}(B):$(1) is one(2) lies in $(2,3)$(3) is zero(4) lies in $(1,2)$Correct Option: , 4 Solution: $\because A=\left[\begin{array}{cc}\cos \theta \sin \theta \\ -\sin \theta \cos \theta\end{array}\right]$ $\therefore A^{n}=\left[\begin{array}{cc}\cos n \theta \sin n \theta \\ -\sin n \thet...
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