A series AC circuit containing an inductor
Question: A series AC circuit containing an inductor $(20 \mathrm{mH})$, a capacitor $(120 \mu \mathrm{F})$ and a resistor $(60 \Omega)$ is driven by an $\mathrm{AC}$ source of $24 \mathrm{~V} / 50 \mathrm{~Hz}$. The energy dissipated in the(1) $5.65 \times 10^{2} \mathrm{~J}$(2) $2.26 \times 10^{3} \mathrm{~J}$(3) $5.17 \times 10^{2} \mathrm{~J}$(4) $3.39 \times 10^{3} \mathrm{~J}$Correct Option: , 3 Solution: (3) Given: $R^{\prime}=60 \Omega, f=50 H z, \omega=2 \pi f=100 \pi$ and $v=24 v$ $\ma...
Read More →The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm.
Question: The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid. Solution: Let the length, breadth and height (or depth) of the cuboid belcm,bcm andhcm, respectively.l+b+h= 19 .....(1)Also,Length of the diagonal = 11 cm $\Rightarrow \sqrt{l^{2}+b^{2}+h^{2}}=11$ $\Rightarrow l^{2}+b^{2}+h^{2}=121$ ......(2) Squaring (1), we get(l+b+h)2= 192⇒l2+b2+h2+ 2(lb+bh+hl) = 361⇒ 121+ 2(lb+bh+hl) = 361 [Using (2)]⇒2(lb+bh+hl) =...
Read More →An unsaturated hydrocarbon X absorbs two hydrogen?
Question: An unsaturated hydrocarbon $X$ absorbs two hydrogen? molecules on catalytic hydrogenation, and also gives following reaction: $\mathrm{B}(3-\mathrm{oxo}-\mathrm{hexanedicarboxylic~acid~})$Correct Option: , 3 Solution:...
Read More →Consider the LR circuit shown in the figure.
Question: Consider the LR circuit shown in the figure. If the switch S is closed at $\mathrm{t}=0$ then the amount of charge that passes through the battery between $\mathrm{t}=0$ and $t=\frac{L}{R}$ is : (1) $\frac{2.7 E L}{R^{2}}$(2) $\frac{E L}{2.7 R^{2}}$(3) $\frac{7.3 E L}{R^{2}}$(4) $\frac{E L}{7.3 R^{2}}$Correct Option: , 2 Solution: (2) We have, $i=i_{0}\left(1-e^{-t / c}\right)=\frac{\varepsilon}{R}\left(1-e^{-t / c}\right)$ Charge, $q=\int_{0}^{\tau} i d t$ $=\frac{\varepsilon}{R} \int...
Read More →The major product in the following reaction is:
Question: The major product in the following reaction is: Correct Option: , 4 Solution:...
Read More →Find the length of the longest pole that can be put in a room of dimensions
Question: Find the length of the longest pole that can be put in a room of dimensions (10m 10 m 5 m). Solution: Length of the longest pole = length of the diagonal of the room $=\sqrt{l^{2}+b^{2}+h^{2}} \mathrm{~m}$ $=\sqrt{10^{2}+10^{2}+5^{2}} \mathrm{~m}$ $=\sqrt{100+100+25}$ $=\sqrt{225}=15 \mathrm{~m}$...
Read More →Let f(x)=ex-x and g(x)=x2-x
Question: Let $f(x)=e^{x}-x$ and $g(x)=x^{2}-x, \forall x \in \mathbf{R}$. Then the set of all $x \in \mathbf{R}$, where the function $h(x)=(f \circ g)(x)$ is increasing, is :(1) $\left[-1, \frac{-1}{2}\right] \cup\left[\frac{1}{2}, \infty\right)$(2) $\left[0, \frac{1}{2}\right] \cup[1, \infty)$(3) $[0, \infty)$(4) $\left[\frac{-1}{2}, 0\right] \cup[1, \infty)$Correct Option: , 2 Solution: Given functions are, $f(x)=e^{x}-x$ and $g(x)=x^{2}-x$ $f(g(x))=e^{\left(x^{2}-x\right)}-\left(x^{2}-x\righ...
Read More →Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube.
Question: Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed. Solution: Three cubes of metal with edges 3cm, 4cm and 5 cm are melted to form a single cube. Volume of the new cube = sum of the volumes the old cubes $=\left(3^{3}+4^{3}+5^{3}\right) \mathrm{cm}^{3}$ $=(27+64+125) \mathrm{cm}^{3}=216 \mathrm{~cm}^{3}$ Suppose the edge of the new cube =xcmThen we have: Then $216=x^{3}$ $\Rightarrow x=...
Read More →Consider the following reactions:
Question: Consider the following reactions: Correct Option: , 4 Solution:...
Read More →The volume of a cube is 512 cm3. Find its surface area.
Question: The volume of a cube is 512 cm3. Find its surface area. Solution: Suppose that the side of the given cube isxcm.Volume of the cube = 512 cm3 Then $512=x^{3}$ $\Rightarrow x=\sqrt[3]{512}=8$ i. e., the side of the cube is $8 \mathrm{~cm}$. $\therefore$ Surface area of the cube $=6 x^{2} \mathrm{~cm}^{2}=6 \times 8^{2} \mathrm{~cm}^{2}=384 \mathrm{~cm}^{2}$...
Read More →The lateral surface area of a cube is 900 cm2.
Question: The lateral surface area of a cube is 900 cm2. Find its volume. Solution: Suppose that the side of cube isxcm.Lateral surface area of the cube = 900 cm2. Then $900=4 x^{2}$ $\Rightarrow x^{2}=\frac{900}{4}=225$ $\Rightarrow x=\sqrt{225}=15$ i.e., the side of the cube is 15 cm. $\therefore$ Volume of the given cube $=x^{3} \mathrm{~cm}^{3}=15^{3} \mathrm{~cm}^{3}=3375 \mathrm{~cm}^{3}$...
Read More →A coil of self inductance 10 mH and resistance
Question: A coil of self inductance $10 \mathrm{mH}$ and resistance $0.1 /$ is connected through a switch to a battery of internal resistance $0.9$. After the switch is closed, the time taken for the current to attain $80 \%$ of the saturation value is $[$ take $\ln 5=1.6]$(1) $0.324 \mathrm{~s}$(2) $0.103 \mathrm{~s}$(3) $0.002 \mathrm{~s}$(4) $0.016 \mathrm{~s}$Correct Option: , 4 Solution: (4) $I=I_{0}\left(1-e^{-\frac{R t}{L}}\right)$ Here $\mathrm{R}=\mathrm{R}_{\mathrm{L}}+\mathrm{r}=1 \Om...
Read More →A water tank has the shape of an inverted right circular cone,
Question: A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan ^{-1}\left(\frac{1}{2}\right)$. Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in $\mathrm{m} / \mathrm{min}$.), at which the level of water is rising at the instant when the depth of water in the tank is $10 \mathrm{~m}$; is:(1) $1 / 15 \pi$(2) $1 / 10 \pi$(3) $2 / \pi$(4) $1 / 5 \pi$Correct Option: Solution: ' Given that water is poured into the ta...
Read More →The major product [C] of the following reaction sequence will be:
Question: The major product [C] of the following reaction sequence will be: Correct Option: 1 Solution:...
Read More →The total surface area of a cube is 1176 cm2.
Question: The total surface area of a cube is 1176 cm2. Find its volume. Solution: Suppose that the side of cube isxcm.Total surface area of cube = 1176 sq cm Then $1176=6 x^{2}$ $\Rightarrow x^{2}=\frac{1176}{6}=196$ $\Rightarrow x=\sqrt{196}=14$ i.e., the side of the cube is 14 cm. $\therefore$ Volume of the cube $=x^{3}=14^{3} \mathrm{~cm}^{3}=2744 \mathrm{~cm}^{3}$...
Read More →The number of chiral centres present in [B] is
Question: The number of chiral centres present in $[\mathrm{B}]$ is ______________ Solution:...
Read More →A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power
Question: A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of $2.2 \mathrm{~kW}$. If the current in the secondary coil is $10 \mathrm{~A}$, then the input voltage and current in the primary coil are :(1) $220 \mathrm{~V}$ and $20 \mathrm{~A}$(2) $440 \mathrm{~V}$ and $20 \mathrm{~A}$(3) $440 \mathrm{~V}$ and $5 \mathrm{~A}$(4) $220 \mathrm{~V}$ and $10 \mathrm{~A}$Correct Option: , 3 Solution: (3) Power output $\left(\mathrm{V}_{2} \mathrm{I}...
Read More →Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m.
Question: Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures $9 \mathrm{~m}$. (Take $\sqrt{3}=1.73$.) Solution: Here,a= 9 m Volume of the cube $=a^{3}=9^{3} \mathrm{~m}^{3}=729 \mathrm{~m}^{3}$ Lateral surface area of the cube $=4 a^{2}=4 \times 9^{2} \mathrm{~m}^{2}=4 \times 81 \mathrm{~m}^{2}=324 \mathrm{~m}^{2}$ Total surface area of the cube $=6 a^{2}=6 \times 9^{2} \mathrm{~m}^{2}=6 \times 81 \mathrm{~m}^{2}=486 \mathrm...
Read More →In a shower, 5 cm of rain falls.
Question: In a shower, 5 cm of rain falls. Find the volume of water that falls on 2 hectares of ground. Solution: Volume of the water that falls on the ground $=$ area of ground $\times$ depth $=20000 \times 0.05 \mathrm{~m}^{3}$ $=1000 \mathrm{~m}^{3}$...
Read More →The surface area of a cuboid is 758 cm2. Its length and breadth are 14 cm and 11 cm respectively.
Question: The surface area of a cuboid is 758 cm2. Its length and breadth are 14 cm and 11 cm respectively. Find its height. Solution: Length of the cuboid = 14 cmBreadth of the cuboid = 11 cmLet the height of the cuboid bexcm.Surface area of the cuboid = 758 cm2 Then $758=2(14 \times 11+14 \times x+11 \times x)$ $\Rightarrow 758=2(154+14 x+11 x)$ $\Rightarrow 758=2(154+25 x)$ $\Rightarrow 758=308+50 x$ $\Rightarrow 50 x=758-308=450$ $\Rightarrow x=\frac{450}{50}=9$ The height of the cuboid is 9...
Read More →A circuit connected to an a c source
Question: A circuit connected to an $a c$ source of $e m f e=e_{0} \sin (100 t)$ with $t$ in seconds, gives a phase difference of $\frac{\pi}{4}$ between the $e m f e$ and current $i$. Which of the following circuits will exhibit this?(1) $\mathrm{RL}$ circuit with $\mathrm{R}=1 \mathrm{k} \Omega$ and $\mathrm{L}=10 \mathrm{mH}$(2) $R L$ circuit with $R=1 \mathrm{k} \Omega$ and $L=1 \mathrm{mH}$(3) $R C$ circuit with $R=1 \mathrm{k} \Omega$ and $C=1 \mu F$(4) $R C$ circuit with $R=1 \mathrm{k} \...
Read More →The compound A in the following reactions is :
Question: The compound A in the following reactions is : Correct Option: , 3 Solution:...
Read More →A classroom is 10 m long, 6.4 m wide and 5 m high. If each student be given 1.6 m2 of the floor area,
Question: A classroom is 10 m long, 6.4 m wide and 5 m high. If each student be given 1.6 m2of the floor area, how many students can be accommodated in the room? How many cubic metres of air would each student get? Solution: Length of the classroom = 10 mBreadth of the classroom = 6.4 mHeight of the classroom = 5 m Area of the floor $=$ length $\times$ breadth $=10 \times 6.4 \mathrm{~m}^{2}$ No. of students $=\frac{\text { area of the floor }}{\text { area given to one student on the floor }}$ ...
Read More →Let S be the set of all values of x for which the tangent to the curve
Question: Let $S$ be the set of all values of $x$ for which the tangent to the curve $y=f(x)=x^{3}-x^{2}-2 x$ at $(x, y)$ is parallel to the line segment joining the points $(1, f(1))$ and $(-1, f(-1))$, then $S$ is equal to:(1) $\left\{\frac{1}{3}, 1\right\}$(2) $\left\{-\frac{1}{3},-1\right\}$(3) $\left\{\frac{1}{3},-1\right\}$(4) $\left\{-\frac{1}{3}, 1\right\}$Correct Option: , 4 Solution: $y=f(x)=x^{3}-x^{2}-2 x$ $\Rightarrow \frac{d y}{d x}=3 x^{2}-2 x-2$ $f(1)=1-1-2=-2, \quad f(-1)=-1-1+2...
Read More →How many persons can be accommodated in a dining hall of dimensions (20 m × 16 m × 4.5 m),
Question: How many persons can be accommodated in a dining hall of dimensions (20 m 16 m 4.5 m), assuming that each person requires 5 cubic metres of air? Solution: Volume of the dining hall $=(20 \times 16 \times 4.5) \mathrm{m}^{3}$ $=1440 \mathrm{~m}^{3}$ Volume of air required by each person $=5 \mathrm{~m}^{3}$ $\therefore$ Capacity of the dining hall $=\frac{\text { volume of dining hall }}{\text { volume of air required by each person }}=\frac{1440}{5}=288$ persons...
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