A survey shows that
Question: A survey shows that $63 \%$ of the people in a city read newspaper $A$ whereas $76 \%$ read newspaper $B$. If $x \%$ of the people read both the newspapers, then a possible value of $x$ can be :(1) 29(2) 37(3) 65(4) 55Correct Option: , 4 Solution: Let $n(U)=100$, then $n(A)=63, n(B)=76$ $n(A \cap B)=x$ Now, $n(A \cup B)=n(A)+n(B)-n(A \cap B) \leq 100$ $=63+76-x \leq 100$ $\Rightarrow x \geq 139-100 \Rightarrow x \geq 39$ $\because n(A \cap B) \leq n(A)$ $\Rightarrow x \leq 63$ $\theref...
Read More →Reagent, 1 -naphthylamine and sulphanilic acid in acetic acid is used for the detection of
Question: Reagent, 1 -naphthylamine and sulphanilic acid in acetic acid is used for the detection of$\mathrm{N}_{2} \mathrm{O}$$\mathrm{NO}_{3}^{-}$NO$\mathrm{NO}_{2}^{-}$Correct Option: , 4 Solution:...
Read More →Prove the following
Question: Let $R_{1}$ and $R_{2}$ be two relations defined as follows : $R_{1}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \in Q\right\}$ and $R_{2}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \notin Q\right\}$, where $Q$ is the set of all rational numbers. Then :(1) Neither $R_{1}$ nor $R_{2}$ is transitive.(2) $R_{2}$ is transitive but $R_{1}$ is not transitive.(3) $R_{1}$ is transitive but $R_{2}$ is not transitive.(4) $R_{1}$ and $R_{2}$ are both transitive.Correct Option: 1 Solution: Fo...
Read More →Considering the above reaction, $X$ and $Y$ respectively are
Question: Considering the above reaction, $X$ and $Y$ respectively are Correct Option: , 2 Solution:...
Read More →The position, velocity and acceleration of a particle moving with a constant
Question: The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:(1) (2) (3) Correct Option: 2, Solution: Option (2) represent correct graph for particle moving with constant acceleration, as for constant acceleration velocity time graph is straight line with positive slope and $x-\operatorname{tg}$ graph should be an opening upward parabola....
Read More →Solve the following
Question: (A) In the above reaction, the structural formula ofCorrect Option: 1 Solution:...
Read More →The velocity of a particle
Question: The velocity of a particle is $v=v_{0}+g t+\mathrm{Ft}^{2}$ Its position is $x=0$ at $t=0$; then its displacement after time $(t=1)$ is :(1) $v_{0}+g+F$(2) $v_{0}+\frac{g}{2}+\frac{F}{3}$(3) $v_{0}+\frac{g}{2}+F$(4) $v_{0}+2 g+3 F$Correct Option: , 2 Solution: (2) $\mathrm{v}=\mathrm{v}_{0}+\mathrm{gt}+\mathrm{Ft}^{2}$ $\frac{\mathrm{ds}}{\mathrm{dt}}=\mathrm{v}_{0}+\mathrm{gt}+\mathrm{Ft}^{2}$ $\int \mathrm{ds}=\int_{0}^{1}\left(\mathrm{v}_{0}+\mathrm{gt}+\mathrm{Ft}^{2}\right) \mathr...
Read More →Consider the two sets :
Question: Consider the two sets : $A=\left\{m \in \mathbf{R}:\right.$ both the roots of $x^{2}-(m+1) x+m+4=0$ are real $\}$ and $B=[-3,5)$. Which of the following is not true?(1) $A-B=(-\infty,-3) \cup(5, \infty)$(2) $A \cap B=\{-3\}$(3) $B-A=(-3,5)$(4) $A \cup B=\mathbf{R}$Correct Option: 1 Solution: $A=\left\{m \in \mathbf{R}: x^{2}-(m+1) x+m+4=0\right.$ has real roots $\}$ $D \geq 0$ $\Rightarrow(m+1)^{2}-4(m+4) \geq 0$ $\Rightarrow m^{2}-2 m-15 \geq 0$ $A=\{(-\infty,-3] \cup[5, \infty)\}$ $B...
Read More →Primary, secondary and tertiary amines can be separated using :-
Question: Primary, secondary and tertiary amines can be separated using :-Para-Toluene sulphonyl chlorideChloroform and $\mathrm{KOH}$Benzene sulphonic acidAcetyl amideCorrect Option: 1 Solution: Primary amines react with Para Toluene sulfonyl chloride to form a precipitate that is soluble in $\mathrm{NaOH}$. Secondary amines reacts with para toluene sulfonyl chloride to give a precipitate that is insoluble in $\mathrm{NaOH}$. Tertiary amines do not react with para toluen....
Read More →A rubber ball is released from a height of 5 m above the floor.
Question: A rubber ball is released from a height of $5 \mathrm{~m}$ above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g=10 \mathrm{~ms}^{-2}$ )(1) $3.0 \mathrm{~ms}^{-1}$(2) $3.50 \mathrm{~ms}^{-1}$(3) $2.0 \mathrm{~ms}^{-1}$(4) $2.50 \mathrm{~ms}^{-1}$Correct Option: , 4 Solution: (4) $v_{0}=\sqrt{2 g h}$ $v=e \sqrt{2 g h}=\sqrt{2 g h}$ $\Rightarrow e=0.9$ $s=h+2 e^{2} h+2 e^{4} h+\ldo...
Read More →Which of the following reaction is an example of ammonolysis?
Question: Which of the following reaction is an example of ammonolysis?Correct Option: , 4 Solution: The process of cleavage of the $\mathrm{C}-\mathrm{X}$ bond by Ammonia molecule is known as ammonolysis. $\mathrm{Ex}: \mathrm{R}-\mathrm{CH}_{2}-\mathrm{Cl}+\ddot{\mathrm{N} H}_{3} \longrightarrow \mathrm{R}-\mathrm{CH}_{2}-\mathrm{NH}_{2}$...
Read More →Prove the following
Question: If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :(1) $\{-2,-1,1,2\}$(2) $\{0,1\}$(3) $\{-2,-1,0,1,2\}$(4) $\{-1,0,1\}$Correct Option: , 4 Solution: Since, $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ $\therefore R=\{(1,1),(2,1),(1,-1),(0,1),(1,0)\}$ $\Rightarrow D_{R^{-1}}=\{-1,0,1\}$...
Read More →A car accelerates from rest at a constant rate
Question: A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is:(1) $\frac{4 \alpha \beta}{(\alpha+\beta)} t^{2}$(2) $\frac{2 \alpha \beta}{(\alpha+\beta)} \mathrm{t}^{2}$(3) $\frac{\alpha \beta}{2(\alpha+\beta)} \mathrm{t}^{2}$(4) $\frac{\alpha \beta}{4(\alpha+\beta)} \mathrm{t}^{2}$Correct Option: , 3 Solution: (3) $\mathrm{v}_{0}=\alp...
Read More →Hoffmann bromomide degradation of benzamide gives product A,
Question: Hoffmann bromomide degradation of benzamide gives product $A$, which upon heating with $\mathrm{CHCl}_{3}$ and $\mathrm{NaOH}$ gives product $\mathrm{B}$. The structures of $\mathrm{A}$ and $\mathrm{B}$ are :Correct Option: , 2 Solution: Hoffmann bromamide degradation reaction :...
Read More →Prove the following
Question: Let $\mathrm{R}=\{\mathrm{P}, \mathrm{Q}) \mid \mathrm{P}$ and $\mathrm{Q}$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1,-1)$ is the set:(1) $S=\left\{(x, y) \mid x^{2}+y^{2}=1\right\}$(2) $S=\left\{(x, y) \mid x^{2}+y^{2}=4\right\}$(3) $S=\left\{(x, y) \mid x^{2}+y^{2}=\sqrt{2}\right\}$(4) $S=\left\{(x, y) \mid x^{2}+y^{2}=2\right\}$Correct Option: , 4 Solution: $\mathrm{P}(\mathrm{a}, \mathrm{b}), \mathrm{Q}(\mathrm{c}, \mathrm{d}), \...
Read More →Define a relation
Question: Define a relation $\mathrm{R}$ over a class of $\mathrm{n} \times \mathrm{n}$ real matrices $\mathrm{A}$ and $\mathrm{B}$ as "ARB iff there exists a non-singular matrix $P$ such that $P A P^{-1}=B^{\prime \prime}$. Then which of the following is true?(1) $R$ is symmetric, transitive but not reflexive,(2) $\mathrm{R}$ is reflexive, symmetric but not transitive(3) $\mathrm{R}$ is an equivalence relation(4) $\mathrm{R}$ is reflexive, transitive but not symmetricCorrect Option: , 3 Solutio...
Read More →A swimmer can swim with velocity of 12 km/h in still water.
Question: A swimmer can swim with velocity of $12 \mathrm{~km} / \mathrm{h}$ in still water. Water flowing in a river has velocity $6 \mathrm{~km} / \mathrm{h}$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is - (Round off to the Nearest Integer) (find the angle in degree) Solution: (120) $12 \sin \theta=v_{r}$ $\sin \theta=\frac{1}{2}$ $\theta=30^{\circ}$ $\therefore \quad \alp...
Read More →The structure of $X$ is:
Question: The structure of $X$ is:Correct Option: , 4 Solution:...
Read More →In a school, there are three types of
Question: In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement? (1) $\mathrm{P}$ and $\mathrm{Q}$(2) $\mathrm{P}$ and $\mathrm{R}$(3) None of these(4) $\mathrm{Q}$ and $\mathrm{R}$Correct Option: , 3 Solution: $A \cap B \cap C$ is visible in all three venn diagram Hence, Option (3)...
Read More →Which of the following is least basic?
Question: Which of the following is least basic?$\left(\mathrm{CH}_{3} \mathrm{CO}\right) \ddot{\mathrm{NH}} \mathrm{C}_{2} \mathrm{H}_{s}$$\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3} \ddot{\mathrm{N}}$$\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \ddot{\mathrm{NH}}$$\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \ddot{\mathrm{N}} \mathrm{H}$Correct Option: , 4 Solution: (Hence least basic) (d) $\mathrm{CH}_{3}-\mathrm{CH}_{2}-\ddot{\mathrm{NH}}-\mathrm{CH}_{2}-\mathrm{CH}_{3}$; L.P. on Nitro...
Read More →Prove the following
Question: Let $\mathrm{A}=\{2,3,4,5, \ldots, 30\}$ and $^{\prime} \simeq^{\prime}$ be an equivalence relation on $\mathrm{A} \times \mathrm{A}$, defined by $(a, b) \simeq(c, d)$, if and only if $a d=b c$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to:(1) 5(2) 6(3) 8(4) 7Correct Option: , 4 Solution: $\mathrm{A}=\{2,3,4,5, \ldots,, 30\}$ $(\mathrm{a}, \mathrm{b}) \simeq(\mathrm{c}, \mathrm{d}) \quad \Rightarrow \mathrm{ad}=\mathrm{b...
Read More →Which of the following reaction DOES NOT
Question: Which of the following reaction DOES NOT involve Hoffmann Bromamide degradation?Correct Option: , 3 Solution: $\Rightarrow$ This reaction does not involve haffmann bromanide degradation. $\Rightarrow$ Rest all options involve haffimann bromamide degradation during the reaction of $\mathrm{Br}_{2}+\mathrm{NaOH}$ with amide....
Read More →In the above chemical reaction, intermediate
Question: In the above chemical reaction, intermediate "X" and reagent/condition "A" are :Correct Option: , 3 Solution:...
Read More →In the above chemical reaction, intermediate
Question: In the above chemical reaction, intermediate "X" and reagent/condition "A" are :Correct Option: Solution:...
Read More →The velocity-displacement graph describing the motion of a bicycle is shown in the figure.
Question: The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by : (2 )Correct Option: 1 Solution: (1) For $0 \leq x \leq 200$ $\mathrm{v}=\mathrm{m} \mathrm{x}+\mathrm{C}$ $v=\frac{1}{5} x+10$ $\mathrm{a}=\frac{\mathrm{vdv}}{\mathrm{dx}}=\left(\frac{\mathrm{x}}{5}+10\right)\left(\frac{1}{5}\right)$ $a=\frac{x}{25}+2 \Rightarrow$ Straight line till $x=200$ $a=\frac{x}{25}+2 \Right...
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