The circuit shown in the figure consists of a charged capacitor of capacity
Question: The circuit shown in the figure consists of a charged capacitor of capacity $3 \mu \mathrm{F}$ and a charge of $30 \mu \mathrm{C}$. At time $\mathrm{t}=0$, when the key is closed, the value of current flowing through the $5 \mathrm{M} \Omega$ resistor is ' $\mathrm{x}^{\prime} \mu-\mathrm{A}$. The value of ' $x$ to the nearest integer is Solution: (2) $\mathrm{i}_{0}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{30 / 3}{5 \times 10^{6}}=2 \times 10^{-6}$ $\therefore$ Ans. $=2.00$...
Read More →The base of a right-angled triangle measures 48 cm and its hypotenuse measures 50 cm.
Question: The base of a right-angled triangle measures 48 cm and its hypotenuse measures 50 cm. Find the area of the triangle. Solution: Let $\triangle P Q R$ be a right-angled triangle and $P Q \perp Q R$. Now, $P Q=\sqrt{P R^{2}-Q R^{2}}$ $=\sqrt{50^{2}-48^{2}}$ $=\sqrt{2500-2304}$ $=\sqrt{196}$ $=14 \mathrm{~cm}$ Area of triangle $=\frac{1}{2} \times Q R \times P Q$ $=\frac{1}{2} \times 48 \times 14$ $=336 \mathrm{~cm}^{2}$...
Read More →then which of the following relations is true?
Question: If the curves, $\frac{x^{2}}{a}+\frac{y^{2}}{b}=1$ and $\frac{x^{2}}{c}+\frac{y^{2}}{d}=1$ intersect each other at an angle of $90^{\circ}$, then which of the following relations is true?(1) $a+b=c+d$ (2) $a-b=c-d$(3) $a b=\frac{c+d}{a+b}$(4) $a-c=b+d$Correct Option: 2, Solution: $\frac{x^{2}}{a}+\frac{y^{2}}{b}=1$ diff : $\frac{2 x}{a}+\frac{2 y}{b} \frac{d y}{d x}=0 \Rightarrow \frac{y}{b} \frac{d y}{d x}=\frac{-x}{a}$ $\frac{d y}{d x}=\frac{-b x}{a y} \ldots(2)$ $\frac{x^{2}}{c}+\fr...
Read More →The height of an equilateral triangle measures 9 cm.
Question: The height of an equilateral triangle measures $9 \mathrm{~cm}$. Find its area, correct to 2 places of decimal. Take $\sqrt{3}=1.732$. Solution: Height of the equilateral triangle = 9 cmThus, we have: Height $=\frac{\sqrt{3}}{2} \times$ Side $\Rightarrow 9=\frac{\sqrt{3}}{2} \times$ Side $\Rightarrow$ Side $=\frac{18}{\sqrt{3}}=\frac{18}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=6 \sqrt{3} \mathrm{~cm}$ Also, Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}...
Read More →Each side of an equilateral triangle measures 8 cm.
Question: Each side of an equilateral triangle measures $8 \mathrm{~cm}$. Find (i) the area of the triangle, correct to 2 places of decimal and (ii) the height of the triangle, correct to 2 places of decimal. Take $\sqrt{3}=1.732$. Solution: Side of the equilateral triangle = 8 cm (i) Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$ $=\frac{\sqrt{3}}{4} \times(8)^{2}$ $=\frac{1.732 \times 64}{4}$ $=27.71 \mathrm{~cm}^{2}$ (ii) Height $=\frac{\sqrt{3}}{2} \times$ Side...
Read More →An organic compound 'A'
Question: An organic compound ' $\mathrm{A}$ ' $\left(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}\right)$ when treated with conc. HI undergoes cleavage to yield compounds ' $\mathrm{B}$ ' and ' $\mathrm{C}$ '. ' $\mathrm{B}$ ' gives yellow precipitate with $\mathrm{AgNO}_{3}$ where as ' $\mathrm{C}$ 'tautomerizes to 'D'. 'D' gives positive iodoform test. 'A' could be : Correct Option: , 3 Solution:...
Read More →If the area of an equilateral triangle is
Question: If the area of an equilateral triangle is $81 \sqrt{3} \mathrm{~cm}^{2}$, find its height. Solution: Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$ $\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=81 \sqrt{3}$ $\Rightarrow$ (Side) $^{2}=324$ $\Rightarrow$ Side $=18 \mathrm{~cm}$ Now, we have: Height $=\frac{\sqrt{3}}{2} \times$ Side $=\frac{\sqrt{3}}{2} \times 18$ $=9 \sqrt{3} \mathrm{~cm}$...
Read More →If the area of an equilateral triangle is
Question: If the area of an equilateral triangle is $36 \sqrt{3} \mathrm{~cm}^{2}$, find its perimeter. Solution: Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$ $\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=36 \sqrt{3}$ $\Rightarrow$ (Side) $^{2}=144$ $\Rightarrow$ Side $=12 \mathrm{~cm}$ Thus, we have:Perimeter = 3 Side = 3 12 = 36 cm...
Read More →An AC source rated 220V, 50 Hz is connected to a resistor.
Question: An $\mathrm{AC}$ source rated $220 \mathrm{~V}, 50 \mathrm{~Hz}$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:(1) $2.5 \mathrm{~ms}$(2) $25 \mathrm{~ms}$(3) $2.5 \mathrm{~s}$(4) $0.25 \mathrm{~ms}$Correct Option: 1 Solution: (1) $\mathrm{i}=\mathrm{i}_{0} \cos (\omega t)$ $\mathrm{i}=\mathrm{i}_{0}$ at $\mathrm{t}=0$ $\mathrm{i}=\frac{\mathrm{i}_{0}}{\sqrt{2}}$ at $\omega \mathrm{t}=\frac{\pi}{4}$ $\mathrm{t}=\frac{\pi}{4 \ome...
Read More →Identify A in the given reaction
Question: Identify $\mathrm{A}$ in the given reaction Correct Option: , 2 Solution:...
Read More →In a scries LCR resonance circuit, if we change the resistance only, from a lower to higher value:
Question: In a scries LCR resonance circuit, if we change the resistance only, from a lower to higher value:(1) The bandwidth of resonance circuit will increase.(2) The resonance frequency will increase.(3) The quality factor will increase.(4) The quality factor and the resonance frequency will remain constant.Correct Option: 1 Solution: (1) Bandwidth $=\mathrm{R} / \mathrm{L}$ Bandwidth $\propto \mathrm{R}$ So bandwidth will increase...
Read More →Ceric ammonium nitrate and
Question: Ceric ammonium nitrate and $\mathrm{CHCl}_{3} /$ alc. $\mathrm{KOH}$ are used for the identification of functional groups present in _________ and ________________ respectively.alcohol, amineamine, alcoholalcohol, phenol amine, phenolCorrect Option: 1 Solution: Alcohol give positive test with ceric ammonium nitrate and primary amines gives carbyl amine test with $\mathrm{CHCl}_{3}, \mathrm{KOH}$....
Read More →Ceric ammonium nitrate and
Question: Ceric ammonium nitrate and $\mathrm{CHCl}_{3} /$ alc. $\mathrm{KOH}$ are used for the identification of functional groups present in _________ and ________________ respectively.(1) alcohol, amine(2) amine, alcohol(3) alcohol, phenol (4) amine, phenolCorrect Option: 1 Solution: Alcohol give positive test with ceric ammonium nitrate and primary amines gives carbyl amine test with $\mathrm{CHCl}_{3}, \mathrm{KOH}$....
Read More →The perimeter of an isosceles triangle is 42 cm and its base is
Question: The perimeter of an isosceles triangle is $42 \mathrm{~cm}$ and its base is $1 \frac{1}{2}$ times each of the equal sides. Find (i) the length of each side of the triangle, (ii) the area of the triangle, and (iii) the height of the triangle. Solution: Let the equal sides of the isosceles triangle beacm each. $\therefore$ Base of the triangle, $b=\frac{3}{2} \mathrm{a} \mathrm{cm}$ (i) Perimeter $=42 \mathrm{~cm}$ or, $a+a+\frac{3}{2} a=42$ or, $2 a+\frac{3}{2} a=42$ $\Rightarrow 2 a+\f...
Read More →The triangular side walls of a flyover have been used for advertisements.
Question: The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m, 15 m. The advertisements yield an earning of Rs 2000 per m2a year. A company hired one of its walls for 6 months. How much rent did it pay? Solution: The sides of the triangle are of length 13 m, 14 m and 15 m. Semi-perimeter of the triangle is $s=\frac{13+14+15}{2}=\frac{42}{2}=21 \mathrm{~m}$ By Heron's formula, Area of $\Delta=\sqrt{s(s-a)(s-b)(s-c)}$ $=\sqrt{21(21-13)(21...
Read More →The perimeter of triangle is 50 cm. One side of the triangle is 4 cm longer than the smallest side and the third side is 6 cm less than twice the smallest side.
Question: The perimeter of triangle is 50 cm. One side of the triangle is 4 cm longer than the smallest side and the third side is 6 cm less than twice the smallest side. Find the area of the triangle. Solution: LetABCbe any triangle with perimeter 50 cm.Let the smallest side of the triangle bex.Then the other sides bex+ 4 and 2x 6. Now,x+x+ 4 + 2x 6 = 50 (∵ perimeter is 50 cm)⇒ 4x 2 = 50⇒ 4x= 50 + 2⇒ 4x= 52⇒x= 13 The sides of the triangle are of length 13 cm, 17 cm and 20 cm. Semi-perimeter of ...
Read More →Identify the major products A and B respectively in the following reaction of phenol:
Question: Identify the major products $A$ and $B$ respectively in the following reaction of phenol: Correct Option: 1 Solution:...
Read More →What happens to the inductive reactance and
Question: What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?(1) Both, inductive reactance and current will be halved.(2) Inductive reactance will be halved and current will be doubled. (3) Inductive reactance will be doubled and current will be halved.(4) Both, inducting reactance and current will be doubled.Correct Option: 2, Solution: (2) $X_{L}=\omega L$ $i=\frac{v_{0}}{\omega L}$...
Read More →If Rolle's theorem holds for the function
Question: If Rolle's theorem holds for the function $f(x)=x^{3}-a x^{2}+b x-4, x \in[1,2]$ with $f^{\prime}\left(\frac{4}{3}\right)=0$, then ordered pair $(a, b)$ is equal to :(1) $(-5,8)$ (2) $(5,8)$(3) $(5,-8)$(4) $(-5,-8)$Correct Option: 2, Solution: $f(1)=f(2)$ $\Rightarrow 1-a+b-4=8-4 a+2 b-4$ $3 a-b=7$ $f^{\prime}(x)=3 x^{2}-2 a x+b$ $\Rightarrow f^{\prime}\left(\frac{4}{3}\right)=0 \Rightarrow 3 \times \frac{16}{9}-\frac{8}{3} a+b=0$ $\Rightarrow-8 a+3 b=-16$ $a=5, b=8$...
Read More →The perimeter of an isosceles triangle is 32 cm.
Question: The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle. Solution: The ratio of the equal side to its base is 3 : 2.⇒Ratio of sides = 3 : 3 : 2.Let the three sides of triangle be 3x,3x, 2x.The perimeter of isosceles triangle = 32 cm. $\Rightarrow 3 x+3 x+2 x=32 \mathrm{~cm}$ $\Rightarrow 8 x=32$ $\Rightarrow x=4 \mathrm{~cm}$ Therefore, the three side of triangle are 3x,3x, 2x =12 cm, 12 cm, 8 cm. Let $S$ be the s...
Read More →B reacts with Hydroxyl amine but does not give Tollen's test.
Question: $\mathrm{B}$ reacts with Hydroxyl amine but does not give Tollen's test. Identify $\mathrm{A}$ and $\mathrm{B}$. (1) 1, 1-Dichlorobutane and 2-Butanone(2) 2,2 - Dichlorobutane and Butan-2-one(3) 2,2 - Dichlorobutane and Butanal(4) 1,1 - Dichlorobutane and ButanalCorrect Option: , 2 Solution: Compound 'B' does not gives Tollen's test due to presence of kenotic group but react with hydroxyl amine....
Read More →For which of the following curves
Question: For which of the following curves, the line $x+\sqrt{3} y=2 \sqrt{3}$ is the tangent at the point $\left(\frac{3 \sqrt{3}}{2}, \frac{1}{2}\right) ?$(1) $x^{2}+9 y^{2}=9$(2) $2 x^{2}-18 y^{2}=9$(3) $y^{2}=\frac{1}{6 \sqrt{3}} x$(4) $x^{2}+y^{2}=7$Correct Option: 1, Solution: Tangent to $x^{2}+9 y^{2}=9$ at point $\left(\frac{3 \sqrt{3}}{2}, \frac{1}{2}\right)$ is $\times\left|\frac{3 \sqrt{3}}{2}\right|+9 y\left(\frac{1}{2}\right)=9$ $3 \sqrt{3} \mathrm{x}+9 \mathrm{y}=18 \Rightarrow \m...
Read More →The base of an isosceles triangle measures 80 cm and its area is 360 cm2.
Question: The base of an isosceles triangle measures 80 cm and its area is 360 cm2. Find the perimeter of the triangle. Solution: Let $\triangle P Q R$ be an isosceles triangle and $P X \perp Q R$. Now, Area of triangle $=360 \mathrm{~cm}^{2}$ $\Rightarrow \frac{1}{2} \times Q R \times P X=360$ $\Rightarrow h=\frac{720}{80}=9 \mathrm{~cm}$ Now, $Q X=\frac{1}{2} \times 80=40 \mathrm{~cm}$ and $P X=9 \mathrm{~cm}$ Also, $P Q=\sqrt{Q X^{2}+P X^{2}}$ $a=\sqrt{40^{2}+9^{2}}=\sqrt{1600+81}=\sqrt{1681}...
Read More →If the curve
Question: If the curve $y=a x^{2}+b x+c, x \in R$, passes through the point $(1,2)$ and the tangent line to this curve at origin is $y=x$, then the possible values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are :(1) $a=1, b=1, c=0$ (2) $a=-1, b=1, c=1$(3) $a=1, b=0, c=1$(4) $a=\frac{1}{2}, b=\frac{1}{2}, c=1$Correct Option: 1 Solution: $2=a+b+c \ldots \ldots(i)$ $\frac{d y}{d x}=2 a x+\left.b \Rightarrow \frac{d y}{d x}\right|_{(0,0)}=1$ $\Rightarrow b=1 \Rightarrow a+c=1$ $(0,0)$ lie on curve $\th...
Read More →Find the area of an isosceles triangle each of
Question: Find the area of an isosceles triangle each of whose equal sides measures 13 cm and whose base measures 20 cm. Solution: We have : $a=13 \mathrm{~cm}$ and $b=20 \mathrm{~cm}$ $\therefore$ Area of isosceles triangle $=\frac{b}{4} \sqrt{4 a^{2}-b^{2}}$ $=\frac{20}{4} \times \sqrt{4(13)^{2}-20^{2}}$ $=5 \times \sqrt{676-400}$ $=5 \times \sqrt{276}$ $=5 \times 16.6$ $=83.06 \mathrm{~cm}^{2}$...
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