Which of the following compounds will show the maximum
Question: Which of the following compounds will show the maximum 'enol' content?$\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{COOC}_{2} \mathrm{H}_{5}$$\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{COCH}_{3}$$\mathrm{CH}_{3} \mathrm{COCH}_{3}$$\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{CONH}_{2}$Correct Option: , 2 Solution: Enol content $\propto$ Acidity of active methylene hydrogens. Maximum enol content...
Read More →Two gases-argon atomic radius 0.07 nm,
Question: Two gases-argon (atomic radius $0.07 \mathrm{~nm}$, atomic weight 40) and xenon (atomic radius $0.1 \mathrm{~nm}$, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:(1) $3.67$(2) $1.09$(3) $2.3$(4) $4.67$Correct Option: , 2 Solution: (2) Mean free path of a gas molecule is given by $\lambda=\frac{1}{\sqrt{2} \pi d^{2} n}$ Here, $n=$ number of collisions per unit volume $d=$ diameter of the molecu...
Read More →A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden,
Question: A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden. Solution: Let the length and breadth of the rectangular garden be $x$ and $y$ metre, respectively. Given: $x y=180$ sq m $\quad \ldots$ (i) and $2 y+x=39$ $\Rightarrow x=39-2 y$ Putting the value of $x$ in (i), we get: $(39-2 y) y=180$ $\Rightarrow 39 y-2 y^{2}=180$...
Read More →The IUPAC name of the following compound is :
Question: The IUPAC name of the following compound is : 4, 4-Dimethyl-3-hydroxybutanoic acid2-Methyl-3-hydroxypentan-5-oic acid3-Hydroxy-4-methylpentanoic acid4-Methyl-3-hydroxypentanoic acidCorrect Option: , 3 Solution: 3 -Hydroxy-4-methyl pentanoic acid...
Read More →The IUPAC name of the following compound is :
Question: The IUPAC name of the following compound is : 4, 4-Dimethyl-3-hydroxybutanoic acid2-Methyl-3-hydroxypentan-5-oic acid3-Hydroxy-4-methylpentanoic acid4-Methyl-3-hydroxypentanoic acidCorrect Option: Solution: 3 -Hydroxy-4-methyl pentanoic acid...
Read More →Consider two ideal diatomic gases A and B at some temperature T.
Question: Consider two ideal diatomic gases $A$ and $B$ at some temperature T. Molecules of the gas A are rigid, and have a mass $\mathrm{m}$. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the specific heats $\left(C_{V}^{A}\right.$ and $\left.C_{V}^{B}\right)$ of gas $A$ and $B$, respectively is:(1) $7: 9$(2) $5: 9$(3) $3: 5$(4) $5: 7$Correct Option: , 4 Solution: (4) Specific heat of gas at constant volume $C_{v}=\frac{1}{2} f R ; f=$ d...
Read More →Consider two ideal diatomic gases A and B at some temperature T.
Question: Consider two ideal diatomic gases $A$ and $B$ at some temperature T. Molecules of the gas A are rigid, and have a mass $\mathrm{m}$. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the specific heats $\left(C_{V}^{A}\right.$ and $\left.C_{V}^{B}\right)$ of gas $A$ and $B$, respectively is:(1) $7: 9$(2) $5: 9$(3) $3: 5$(4) $5: 7$Correct Option: , 4 Solution: (4) Specific heat of gas at constant volume $C_{v}=\frac{1}{2} f R ; f=$ d...
Read More →The length of a rectangle is thrice as long as the side of a square.
Question: The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than width of a the rectangle. Their areas being equal, find their dimensions. Solution: Let the breadth of rectangle be $x \mathrm{~cm}$. According to the question: Side of the square $=(x+4) \mathrm{cm}$ Length of the rectangle $=\{3(x+4)\} \mathrm{cm}$ It is given that the areas of the rectangle and square are same. $\therefore 3(x+4) \times x=(x+4)^{2}$ $\Rightarrow 3 x^{2}+12 x...
Read More →The number of
Question: The number of $s p^{2}$ hybrid orbitals in a molecule of benzene is:2461812Correct Option: , 3 Solution: In benzene each carbon atom is $s p^{2}$ hybridised. Therefore total $18 \mathrm{sp}^{2}$ hybrid orbitals are present in benzene....
Read More →The sum of the areas of two squares is 640 m2.
Question: The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares. Solution: Let the length of the side of the first and the second square be $x$ and $y$, respectively. According to the question: $x^{2}+y^{2}=640 \quad \ldots$ (i) Also, $4 x-4 y=64$ $\Rightarrow x-y=16$ $\Rightarrow x=16+y$ Putting the value of $x$ in (i), we get: $x^{2}+y^{2}=640$ $\Rightarrow(16+y)^{2}+y^{2}=640$ $\Rightarrow 256+32 y+y^{2}+y^{2}=640$ $\Ri...
Read More →Consider a mixture of n moles of helium gas and 2 n
Question: Consider a mixture of $n$ moles of helium gas and $2 n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $C_{P} / C_{V}$ value will be:(1) $19 / 13$(2) $67 / 45$(3) $40 / 27$(4) $23 / 15$Correct Option: 1 Solution: (1) Helium is a monoatomic gas and Oxygen is a diatomic gas. For helium, $C_{V_{1}}=\frac{3}{2} R$ and $C_{R_{1}}=\frac{5}{2} R$ For oxygen, $C_{V_{2}}=\frac{5}{2} R$ and $C_{P_{2}}=\frac{7}{2} R$ $\gamma=\frac{N_{1} C_{P}+N_{2} C_{P_{2}}}{N_{1} C_{V_{1...
Read More →If the tangent to the parabola
Question: If the tangent to the parabola $y^{2}=x$ at a point $(\alpha, \beta),(\beta0)$ is also a tangent to the ellipse, $x^{2}+2 y^{2}=1$, then $\alpha$ is equal to:(1) $\sqrt{2}-1$(2) $2 \sqrt{2}-1$(3) $2 \sqrt{2}+1$(4) $\sqrt{2}+1$Correct Option: , 4 Solution: Let tangent to parabola at point $\left(\frac{1}{4 m^{2}},-\frac{1}{2 m}\right)$ is $y=m x+\frac{1}{4 m}$ and tangent to ellipse is, $y=m x \pm \sqrt{m^{2}+\frac{1}{2}}$ Now, condition for common tangency, $\frac{1}{4 m}=\pm \sqrt{m^{...
Read More →Which of the following reactions will not produce a racemic product?
Question: Which of the following reactions will not produce a racemic product?Correct Option: , 4 Solution:...
Read More →A rectangular field is 16 m long and 10 m wide.
Question: A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m2. Find the width of the path. Solution: Let the width of the path be $x \mathrm{~m}$. $\therefore$ Length of the field including the path $=16+x+x=16+2 x$ Breadth of the field including the path $=10+x+x=10+2 x$ Now, (Area of the field including path) $-$ (Area of the field excluding path) $=$ Area of the path $\Rightarrow(16+2 x)(10+2 x)-(16 \times 10)=120$ $\Rightar...
Read More →The plot that depicts the behavior of the mean free time
Question: The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $(T)$, qualitatively, is: (Graphs are schematic and not drawn to scale)Correct Option: , 3 Solution: (3) Relaxation time $(\tau) \propto \frac{\text { mean free path }}{\text { speed }} \Rightarrow \tau \propto \frac{1}{\mathrm{~V}}$ and, $v \propto \sqrt{T}$ $\therefore \tau \propto \frac{1}{\sqrt{T}}$ Hence graph betw...
Read More →The area (in sq. units) of the smaller of the
Question: The area (in sq. units) of the smaller of the two circles that touch the parabola, $y^{2}=4 x$ at the point $(1,2)$ and the $x$-axis is:(1) $8 \pi(2-\sqrt{2})$(2) $4 \pi(2-\sqrt{2})$(3) $4 \pi(3+\sqrt{2})$(4) $8 \pi(3-2 \sqrt{2})$Correct Option: , 4 Solution: The circle and parabola will have common tangent at $\mathrm{H}$ $(1,2)$. So, equation of tangent to parabola is, $y \times(2)=\frac{4(x+1)}{2} \Rightarrow 2 y=2 x+2 \Rightarrow y=x+1$ Let equation of circle (by family of circles)...
Read More →Which of the following has the shortest
Question: Which of the following has the shortest $\mathrm{C}-\mathrm{Cl}$ bond?$\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}_{2}$$\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{NO}_{2}$$\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}$$\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{OCH}_{3}$Correct Option: , 2 Solution: In $\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{NO}_{2}$ double bond character in carbon-chlorine bond is maximum due to resonance and so the bond length is shortest....
Read More →The perimeter of a rectangular plot is 60 m and its area is 200 sq metres
Question: The perimeter of a rectangular plot is 60 m and its area is 200 sq metres. Find the dimensions of the plot. Solution: Given:Perimeter ofa rectangular plot = 60 mArea =200 m2Let the length of rectangular plot bex m. Perimeter $=60$ $\Rightarrow 2($ Length $+$ Breadth $)=60$ $\Rightarrow$ Length $+$ Breadth $=30$ $\Rightarrow$ Breadth $=30$ - Length Then,the breadth is (30x)m.According to the question, Length $\times$ Breadth $=$ Area $\Rightarrow x(30-x)=200$ $\Rightarrow 30 x-x^{2}=200...
Read More →A thermodynamic cycle x y z x is shown on a V-T diagram.
Question: A thermodynamic cycle $x y z x$ is shown on a $V-T$ diagram. The $P-V$ diagram that best describes this cycle is: (Diagrams are schematic and not to scale)Correct Option: 1 Solution: (1) From the corresponding V-T graph given in question, Process $x y \rightarrow$ Isobaric expansion, Process $y z \rightarrow$ Isochoric (Pressure decreases) Process $z x \rightarrow$ Isothermal compression Therefore, corresponding $P V$ graph is as shown in figure...
Read More →If one end of a focal chord of the parabola,
Question: If one end of a focal chord of the parabola, $y^{2}=16 x$ is at $(1,4)$, then the length of this focal chord is:(1) 25(2) 22(3) 24(4) 20Correct Option: 1 Solution: $\because y^{2}=16 x$ $\Rightarrow a=4$ One end of focal of the parabola is at $(1,4)$ $\because \mathrm{y}$ - coordinate of focal chord is $2 a t$ $\therefore 2 a t=4$ $\Rightarrow t=\frac{1}{2}$ Hence, the required length of focal chord $=a\left(t+\frac{1}{t}\right)^{2}=4 \times\left(2+\frac{1}{2}\right)^{2}=25$...
Read More →Complex X of composition
Question: Complex X of composition $\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{\mathrm{n}}$ has a spin only magnetic moment of $3.83 \mathrm{BM}$. It reacts with $\mathrm{AgNO}_{3}$ and shows geometrical isomerism. The IUPAC nomenclature of $X$ is:Hexaaqua chromium (III) chlorideTetraaquadichlorido chromium (IV) chloride dihydrateDichloridotetraaqua chromium (IV) chloride dihydrateTetraaquadichlorido chromium (III) chloride dihydrateCorrect Option: , 4 Solution: $\mu=\sqr...
Read More →The length of a hall is 3 metres more than its breadth
Question: The length of a hall is 3 metres more than its breadth. If the area of the hall is 238 square metres, calculate its length and breadth. Solution: Let the breadth of the rectangular hall be $x$ metre. Therefore, the length of the rectangular hall will be $(x+3)$ metre. According to the question: $x(x+3)=238$ $\Rightarrow x^{2}+3 x=238$ $\Rightarrow x^{2}+3 x-238=0$ $\Rightarrow x^{2}+(17-14) x-238=0$ $\Rightarrow x^{2}+17 x-14 x-238=0$ $\Rightarrow x(x+17)-14(x+17)=0$ $\Rightarrow(x+17)...
Read More →The length of a rectangular field is three times its breadth.
Question: The length of a rectangular field is three times its breadth. If the area of the field by 147 sq metres, find the length of the field. Solution: Let the length and breadth of the rectangle be $3 x \mathrm{~m}$ and $x \mathrm{~m}$, respectively. According to the question: $3 x \times x=147$ $\Rightarrow 3 x^{2}=147$ $\Rightarrow x^{2}=49$ $\Rightarrow x=7$ or $x=-7$ $\Rightarrow x=7 \quad(\because x$ cannot be negative $)$ $\therefore$ Length $=3 \times 7=21 \mathrm{~m}$ Breadth $=7 \ma...
Read More →The tangent to the parabola
Question: The tangent to the parabola $y^{2}=4 x$ at the point where it intersects the circle $x^{2}+y^{2}=5$ in the first quadrant, passes through the point :(1) $\left(-\frac{1}{3}, \frac{4}{3}\right)$(2) $\left(\frac{1}{4}, \frac{3}{4}\right)$(3) $\left(\frac{3}{4}, \frac{7}{4}\right)$(4) $\left(-\frac{1}{4}, \frac{1}{2}\right)$Correct Option: , 3 Solution: To find intersection point of $x^{2}+y^{2}=5$ and $y^{2}=4 x$, substitute $y^{2}=4 x$ in $x^{2}+y^{2}=5$, we get $x^{2}+4 x-5=0 \Rightarr...
Read More →The number of chiral centres in penicillin is
Question: The number of chiral centres in penicillin is _________________. Solution: (3.00) There are three chiral centres in penicillin....
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