Choose the correct order of basic nature of the above amines.
Question: A. Phenyl methanamine B. $N$, N-Dimethylaniline C. N-Methyl aniline D. Benzenamine Choose the correct order of basic nature of the above amines.$DCBA$$DBCA$$ACBD$$ABCD$Correct Option: , 4 Solution:...
Read More →A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height
Question: A Tennis ball is released from a height $\mathrm{h}$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by: (graph are drawn schematically and on not to scale)Correct Option: , 3 Solution: (3) For uniformly accelerated/ deaccelerated motion : $v^{2}=u^{2} \pm 2 g h$ As equation is quadratic, so, $v-h$ graph will be a parabola Initially velocity is downwards (-ve...
Read More →If the mean and variance of eight numbers
Question: If the mean and variance of eight numbers $3,7,9,12,13$, $20, x$ and $y$ be 10 and 25 respectively, then $x \cdot y$ is equal to___________. Solution: Mean $=\bar{x}=\frac{3+7+9+12+13+20+x+y}{8}=10$ $\Rightarrow x+y=16$...(i) Variance $=\sigma^{2}=\frac{\Sigma\left(x_{i}\right)^{2}}{8}-(\bar{x})^{2}=25$ $\sigma^{2}=\frac{9+49+81+144+169+400+x^{2}+y^{2}}{8}-100=25$ $\Rightarrow x^{2}+y^{2}=148$ From eqn. (i), $(x+y)^{2}=(16)^{2}$ $\Rightarrow x^{2}+y^{2}+2 x y=256$ Using eqn. (ii), $148...
Read More →Match List-I with List-II
Question: Match List-I with List-II Choose the correct answer from the option given below:$(a)-(i i),(b)-(i),(c)-(i v),(d)-(i i i)$$(a)-(i i i),(b)-(i v),(c)-(i),(d)-(i i)$$(a)-(i i),(b)-(i v),(c)-(i),(d)-(i i i)$$(a)-(i i i),(b)-(i),(c)-(i v),(d)-(i i)$Correct Option: , 3 Solution:...
Read More →If the variance of the first n
Question: If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , then $m+n$ is equal to__________. Solution: $\operatorname{Var}(1,2, \ldots . ., n)=10$ $\Rightarrow \frac{1^{2}+2^{2}+\ldots . .+n^{2}}{n}-\left(\frac{1+2+\ldots . .+n}{n}\right)^{2}=10$ $\Rightarrow \frac{(n+1)(2 n+1)}{6}-\left(\frac{n+1}{2}\right)^{2}=10$ $\Rightarrow n^{2}-1=120 \Rightarrow n=11$ $\operatorname{Var}(2,4,6, \ldots . ., 2 m)=16 \Rightarrow \operatorna...
Read More →Consider the data on x taking
Question: Consider the data on $x$ taking the values $0,2,4,8, \ldots, 2^{\text {n }}$ with frequencies ${ }^{n} C_{0},{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ respectively. If the mean of this data is $\frac{728}{2^{n}}$, then $n$ is equal to Solution: Mean $=\frac{\Sigma x_{i} f_{i}}{\Sigma f_{i}}$ $=\frac{0 \cdot{ }^{n} C_{0}+2 \cdot{ }^{n} C_{1}+2^{2} \cdot{ }^{n} C_{2}+\ldots+2^{n} \cdot{ }^{n} C_{n}}{{ }^{n} C_{0}+{ }^{n} C_{1}+\ldots .+{ }^{n} C_{n}}$ To find sum of numerator co...
Read More →An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution.
Question: An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by ammonolysis of ethyl chloride. The correct structure of amine is:$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \stackrel{\mathrm{H}}{\mathrm{N}}-\mathrm{CH}_{2} \mathrm{CH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NHCH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}$Correct Option: 1 Solution: According to the question the am...
Read More →An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution.
Question: An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by ammonolysis of ethyl chloride. The correct structure of amine is:$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \stackrel{\mathrm{H}}{\mathrm{N}}-\mathrm{CH}_{2} \mathrm{CH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NHCH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}$Correct Option: Solution: According to the question the amin...
Read More →Train A and train B are running on parallel tracks in the opposite directions
Question: Train $A$ and train $B$ are running on parallel tracks in the opposite directions with speeds of $36 \mathrm{~km} /$ hour and $72 \mathrm{~km} /$ hour, respectively. A person is walking in $\operatorname{train} A$ in the direction opposite to its motion with a speed of $1.8 \mathrm{~km} /$ hour. Speed (in $\mathrm{ms}^{-1}$ ) of this person as observed from $\operatorname{train} B$ will be close to : (take the distance between the tracks as negligible)(1) $29.5 \mathrm{~ms}^{-1}$(2) $2...
Read More →Prove the following
Question: If $\sum_{i=1}^{n}\left(x_{i}-a\right)=n$ and $\sum_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a,(n, a1)$, then the standard deviation of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is :(1) $a-1$(2) $n \sqrt{a-1}$(3) $\sqrt{n(a-1)}$(4) $\sqrt{a-1}$Correct Option: , 4 Solution: Standard deviation $=\sqrt{\frac{\sum_{i=1}^{n}\left(x_{i}-a\right)^{2}}{n}-\left(\frac{\sum_{i=1}^{n}\left(x_{i}-a\right)}{n}\right)^{2}} \quad[\because n, a1]$ $=\sqrt{\frac{n a}{n}-\left(\frac{n}{n}\right)^{2}}=\s...
Read More →Correct statement about the given chemical reaction is :
Question: Correct statement about the given chemical reaction is :Reaction is possible and compound (A) will be major product.The reaction will form sulphonated product instead of nitration.$-\mathrm{NH}_{2}$ group is ortho and para directive, so product (B) is not possibleReaction is possible and compound (B) will be the major product.Correct Option: 1 Solution:...
Read More →If the mean and the standard deviation
Question: If the mean and the standard deviation of the data $3,5,7, a$, $b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation:(1) $x^{2}-10 x+18=0$(2) $2 x^{2}-20 x+19=0$(3) $x^{2}-10 x+19=0$(4) $x^{2}-20 x+18=0$Correct Option: , 3 Solution: Mean $=\frac{3+5+7+a+b}{5}=5 \Rightarrow a+b=10$ Variance $=\frac{3^{2}+5^{2}+7^{2}+a^{2}+b^{2}}{5}-(5)^{2}=4$ $\Rightarrow a^{2}+b^{2}=62$ $\Rightarrow(a+b)^{2}-2 a b=62$ $\Rightarrow a b=19$ Hence, $a$ and $b$ are the roots of the e...
Read More →A scooter accelerates from rest for time
Question: A scooter accelerates from rest for time $t_{1}$ at constant rate $a_{1}$ and then retards at constant rate $\mathrm{a}_{2}$ for time $\mathrm{t}_{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be:(1) $\frac{a_{1}+a_{2}}{a_{2}}$(2) $\frac{a_{2}}{a_{1}}$(3) $\frac{a_{1}+a_{2}}{a_{1}}$(4) $\frac{a_{1}}{a_{2}}$Correct Option: , 2 Solution: (2) From given information: For $1^{\text {st }}$ interval $a_{1}=\frac{v_{0}}{t_{1}}$ $v_{0}=a_{1} t_{1} \quad \ldots . .(1)$ ...
Read More →The mean and variance of 7
Question: The mean and variance of 7 observations are 8 and 16 , respectively. If five observations are $2,4,10,12,14$, then the absolute difference of the remaining two observations is :(1) 1(2) 4(3) 2(4) 3Correct Option: , 3 Solution: Let two remaining observations are $x_{1}, x_{2}$. So, $\bar{x}=\frac{2+4+10+12+14+x_{1}+x_{2}}{7}=8$ (given) $\Rightarrow x_{1}+y_{1}=14$ ......(i) Now, $\sigma^{2}=\frac{\sum x_{i}^{2}}{N}-\left(\frac{\sum x_{i}}{N}\right)^{2}=16$ (given) $=\frac{4+16+100+144+1...
Read More →Carbylamine test is used to detect the presence of primary amino group in an organic compound.
Question: Carbylamine test is used to detect the presence of primary amino group in an organic compound. Which of the following compound is formed when this test is performed with aniline?Correct Option: , 2 Solution:...
Read More →A person standing on a spring balance inside a stationary lift measures
Question: A person standing on a spring balance inside a stationary lift measures $60 \mathrm{~kg}$. The weight of that person if the lift descends with uniform downward acceleration of $1.8 \mathrm{~m} / \mathrm{s}^{2}$ will be N. $\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$ Solution: $\mathrm{Mg}-\mathrm{N}=\mathrm{Ma}$ $\mathrm{N}=\mathrm{M}(\mathrm{g}-\mathrm{a})$ $\mathrm{N}=60(10-1.8)$ $\mathrm{N}=60 \times 8.2=492 \mathrm{~N}$ $\mathrm{~N}=492$...
Read More →Which of the following reaction/s will not give p-aminoazobenzene?
Question: Which of the following reaction/s will not give p-aminoazobenzene? B only$\mathrm{A}$ and $\mathrm{B}$C onlyA onlyCorrect Option: 1 Solution:...
Read More →If a variance of the following frequency distribution :
Question: If a variance of the following frequency distribution : is 50, then $x$ is equal to_____. Solution: $\bar{x}=\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}=\frac{30+70+25 x}{4+x}=25$ $\sigma^{2}=\frac{\Sigma f_{i} x_{i}^{2}}{\Sigma f_{i}}-(\bar{x})^{2}$ $\Rightarrow 50=\frac{450+625 x+2450}{4+x}-625$ $\Rightarrow 675=\frac{2900+625 x}{4+x} \Rightarrow 50 x=200$ $\therefore x=4$...
Read More →The major product of the following chemical reaction is:
Question: The major product of the following chemical reaction is: $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}\right)_{2} \mathrm{O}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$ $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$Correct Option: , 2 Solution:...
Read More →The mean and variance of 8 observations are
Question: The mean and variance of 8 observations are 10 and $13.5$, respectively. If 6 of these observations are $5,7,10,12,14,15$, then the absolute difference of the remaining two observations is :(1) 9(2) 5(3) 3(4) 7Correct Option: , 4 Solution: Let the two remaining observations be $x$ and $y$. $\because \bar{x}=\frac{5+7+10+12+14+15+x+y}{8}$ $\Rightarrow 10=\frac{63+x+y}{8}$ $\Rightarrow x+y=80-63$ $\Rightarrow x+y=17$ ...(i) $\because \operatorname{var}(x)=13.5$ $=\frac{25+49+100+144+196+...
Read More →A stone is dropped from the top of a building.
Question: A stone is dropped from the top of a building. When it crosses a point $5 \mathrm{~m}$ below the top, another stone starts to fall from a point $25 \mathrm{~m}$ below the top, Both stones reach the bottom of building simultaneously. The height of the building is:(1) $45 \mathrm{~m}$(2) $35 \mathrm{~m}$(3) $25 \mathrm{~m}$(4) $50 \mathrm{~m}$Correct Option: 1 Solution: For particle (1) $20+h=10 t+\frac{1}{2} g t^{2} \quad \ldots . .(i)$ For particle (2) $h=\frac{1}{2} \mathrm{~g} t^{2} ...
Read More →The total number of amines among the following
Question: The total number of amines among the following which can be synthesized by Gabriel synthesis isCorrect Option: , 3 Solution: Only aliphatic amines can be prepared by Gabriel synthesis. $1.86 \mathrm{~g}$ of aniline completely reacts to form acetanilide. $10 \%$ of the product is lost during purification. Amount of acetanilide obtained after purification (in $\mathrm{g}$ ) is $\times 10^{-2}$....
Read More →The total number of amines among the following
Question: The total number of amines among the following which can be synthesized by Gabriel synthesis isCorrect Option: , 3 Solution: Only aliphatic amines can be prepared by Gabriel synthesis. $1.86 \mathrm{~g}$ of aniline completely reacts to form acetanilide. $10 \%$ of the product is lost during purification. Amount of acetanilide obtained after purification (in $\mathrm{g}$ ) is $\times 10^{-2}$....
Read More →Prove the following
Question: Let $x_{i}(1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10}\left(x_{i}-p\right)=3 \quad$ and $\quad \sum_{i=1}^{10}\left(x_{i}-p\right)^{2}=9 \quad$ where $0 \neq p \in \mathbf{R}$, then the standard deviation of these observations is :(1) $\sqrt{\frac{3}{5}}$(2) $\frac{4}{5}$(3) $\frac{9}{10}$(4) $\frac{7}{10}$Correct Option: , 3 Solution: S.D. $=\sqrt{\frac{\sum_{i=1}^{10}\left(x_{i}-p\right)^{2}}{10}-\left(\frac{\sum_{i=1}^{10}\left(x_{i}-p\right)...
Read More →An engine of a train, moving with uniform acceleration,
Question: An engine of a train, moving with uniform acceleration, passes the signal post with velocity $u$ and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :(1) $\sqrt{\frac{v^{2}-u^{2}}{2}}$(2) $\frac{\mathrm{v}-\mathrm{u}}{2}$(3) $\sqrt{\frac{v^{2}+u^{2}}{2}}$(4) $\frac{\mathrm{u}+\mathrm{v}}{2}$Correct Option: , 3 Solution: $\mathrm{a}=$ uniform acceleration $\mathbf{u}=$ velocity of first compartment $\mathrm{v}=$ velocity ...
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