In the figure shown, a circuit contains two identical resistors with resistance
Question: In the figure shown, a circuit contains two identical resistors with resistance $\mathrm{R}=5 \Omega$ and an inductance with $\mathrm{L}=2 \mathrm{mH}$. An ideal battery of $15 \mathrm{~V}$ is connected in the circuit. What will be the current through the battery long after the switch is closed? (1) $5.5 \mathrm{~A}$(2) $7.5 \mathrm{~A}$(3) $3 \mathrm{~A}$(4) $6 \mathrm{~A}$Correct Option: , 4 Solution: (4)] Long time after switch is closed, the inductor will be idle so, the equivalent...
Read More →The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.
Question: The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3of wood has a mass of 0.6 g. Solution: Inner radius of the wooden pipe, $r=\frac{24}{2}=12 \mathrm{~cm}$ Outer radius of the wooden pipe, $R=\frac{28}{2}=14 \mathrm{~cm}$ Length of the wooden pipe,h= 35 cm $\therefore$ Volume of wood in the pipe $=\pi\left(R^{2}-r^{2}\right) h=\frac{22}{7} \times\left(14^{2}-12^{2}\right) \times 3...
Read More →The major product of the following reaction is ?
Question: The major product of the following reaction is ? Correct Option: , 4 Solution:...
Read More →The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres.
Question: The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. Find the area of the metal sheet needed to make it. Solution: Height of the cylinder,h= 1 mCapacity of the cylinder = 15.4 L = 15.4 0.001 m3= 0.0154 m3 $\therefore \pi r^{2} h=0.0154 \mathrm{~m}^{3}$ $\Rightarrow \frac{22}{7} \times r^{2} \times 1=0.0154$ $\Rightarrow r=\sqrt{\frac{0.0154 \times 7}{22}}=0.07 \mathrm{~m}$ Area of the metal sheet needed to make the cylinder= Total surface area of the cylinder $=2 \...
Read More →The lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm. Find
Question: The lateral surface area of a cylinder is 94.2 cm2and its height is 5 cm. Find (i) the radius of its base and (ii) its volume. (Take = 3.14.) Solution: Height of the cylinder,h= 5 cmLateral (or curved) surface area of cylinder = 94.2 cm2(i) Let the radius of the cylinder bercm. $\therefore 2 \pi r h=94.2 \mathrm{~cm}^{2}$ $\Rightarrow 2 \times 3.14 \times r \times 5=94.2$ $\Rightarrow r=\frac{94.2}{2 \times 3.14 \times 5}=3 \mathrm{~cm}$ Thus, the radius of the cylinder is 3 cm. (ii) V...
Read More →An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution.
Question: An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent and gives positive iodoform test. The compound is : Correct Option: , 4 Solution:...
Read More →The curved surface area of a right circular cylinder is 4.4 m2. If the radius of its base is 0.7 m, find its
Question: The curved surface area of a right circular cylinder is 4.4 m2. If the radius of its base is 0.7 m, find its (i) height and (ii) volume. Solution: Radius of the cylinder,r= 0.7 mCurved surface area of cylinder = 4.4 m2(i) Let the height of the cylinder behm. $\therefore 2 \pi r h=4.4$ $\Rightarrow 2 \times \frac{22}{7} \times 0.7 \times h=4.4$ $\Rightarrow h=\frac{4.4 \times 7}{2 \times 22 \times 0.7}=1 \mathrm{~m}$ Thus, the height of the cylinder is 1 m. (ii) Volume of the cylinder $...
Read More →the switch S1 is closed at time t=0
Question: the switch $S_{1}$ is closed at time $t=0$ and the switch $S_{2}$ is kept open. At some later time $\left(\mathrm{t}_{0}\right)$, the switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed. the behaviour of the current I as a function of time ' $\mathrm{t}$ ' is given by:(1) (2) (3) (4) Correct Option: , 2 Solution: The current will grow for the time $t=0$ to $\mathrm{t}=\mathrm{t}_{0}$ and after that decay of current takes place....
Read More →There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4 m.
Question: There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4 m. Find the cost of cleaning them at ₹ 14 per m2. Solution: Radius of each pillar, $r=\frac{50}{2}=25 \mathrm{~cm}=0.25 \mathrm{~m} \quad(1 \mathrm{~m}=100 \mathrm{~cm})$ Height of each pillar,h = 4 m $\therefore$ Surface area of each pillar $=2 \pi r h=2 \times \frac{22}{7} \times 0.25 \times 4 \mathrm{~cm}^{2}$ Surface area of 20 pillars = Surface area of each pillar $\times 20=2 \times \frac...
Read More →Consider the following reactions
Question: Consider the following reactions The mass percentage of carbon in $\mathrm{A}$ is _______________ Solution:...
Read More →Let f(x)=5-|x-2| and g(x)=|x+1|
Question: Let $f(x)=5-|x-2|$ and $g(x)=|x+1|, x \in$ R. If $f(x)$ attains maximum value at$\alpha$ and $g(x)$ attains minimum value at $\beta$, then $\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^{2}-5 x+6\right)}{x^{2}-6 x+8}$ is equal to :(1) $1 / 2$(2) $-3 / 2$(3) $-1 / 2$(4) $3 / 2$Correct Option: 1, Solution: $f(x)=5-|x-2|$ Graph of $y=f(x)$ By the graph $f(x)$ is maximum at $x=2 \therefore \alpha=2$ $g(x)=|x+1|$ Graph of $y=g(x)$ By the graph $g(x)$ is minimum at $x=-1$ $\therefore...
Read More →A soft drink is available in two packs:
Question: A soft drink is available in two packs: (i) a tin can with a rectangular base of length 5 cm, breadth 4 cm and height 15 cm, and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? Solution: (i)Length of tin can,l= 5 cmBreadth of tin can,b= 4 cmHeight of tin can,h= 15 cm Volume of soft drink in tin can =lbh= 5 4 15 = 300 cm3 (ii) Radius of plastic cylinder, $r=\frac{7}{2} \mathrm{~cm}$ Height of plastic cyl...
Read More →The pillars of a temple are cylindrically shaped. Each pillar has a circular base of radius 20 cm and height 10 m.
Question: The pillars of a temple are cylindrically shaped. Each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars? Solution: Radius of each pillar,r= 20 cm = 0.2 m (1 m = 100 cm)Height of each pillar,h= 10 m Volume of concrete mixture used in each pillar $=\pi r^{2} h=\frac{22}{7} \times(0.2)^{2} \times 10 \mathrm{~m}^{3}$ Amount of concrete mixture required to build 14 such pillars= Volume of concrete mixture used i...
Read More →In the following reaction A is:
Question: In the following reaction $\mathrm{A}$ is: Correct Option: 1 Solution:...
Read More →A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm.
Question: A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients? Solution: Radius of the bowl, $r=\frac{7}{2} \mathrm{~cm}$ Height of soup in the bowl,h= 4 cm Volume of soup in one bowl $=\pi r^{2} h=\frac{22}{7} \times\left(\frac{7}{2}\right)^{2} \times 4=154 \mathrm{~cm}^{3}$ Amount of soup the hospital has to prepare daily to serve 250 patien...
Read More →If m is the minimum value of k for which the function
Question: If $m$ is the minimum value of $k$ for which the function $f(x)=x \sqrt{k x-x^{2}}$ is increasing in the interval $[0,3]$ and $\mathrm{M}$ is the maximum value of $f$ in $[0,3]$ when $k=\mathrm{m}$, then the ordered pair $(m, \mathrm{M})$ is equal to :(1) $(4,3 \sqrt{2})$(2) $(4,3 \sqrt{3})$(3) $(3,3 \sqrt{3)}$(4) $(5,3 \sqrt{6)}$Correct Option: , 2 Solution: Given function $f(x)=x \sqrt{k x-x^{2}}=\sqrt{k x^{3}-x^{4}}$ Differentiating w. r. t. $x$, $f^{\prime}(x)=\frac{\left(3 k x^{2}...
Read More →The diameter of a cylinder is 28 cm and its height is 40 cm.
Question: The diameter of a cylinder is 28 cm and its height is 40 cm. Find the curved surface area, total surface area and the volume of the cylinder. Solution: Here,r= 28/2 = 14 cm;h= 40 cm Curved surface area of the cylinder $=2 \pi r h$ $=2 \times \frac{22}{7} \times 14 \times 40 \mathrm{~cm}^{2}$ $=2 \times 22 \times 2 \times 40 \mathrm{~cm}^{2}$ $=3520 \mathrm{~cm}^{2}$ Total surface area of the cylinder $=2 \pi r h+2 \pi r^{2}$ $=\left(3520+2 \times \frac{22}{7} \times 14^{2}\right) \math...
Read More →A solid metallic cuboid of dimensions (9 m × 8 m × 2 m) is melted and recast into solid cubes of edge 2 m
Question: A solid metallic cuboid of dimensions (9 m 8 m 2 m) is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed. Solution: Volume of the solid metallic cuboid =9 m 8 m 2m = 144 m3 Volume of each solid cube $=(\text { Edge })^{3}=(2)^{3}=8 \mathrm{~m}^{3}$ $\therefore$ Number of cubes formed $=\frac{\text { Volume of the solid metallic cuboid }}{\text { Volume of each solid cube }}=\frac{144}{8}=18$ Thus, the number of cubes so formed is 18....
Read More →Identify (A) in the following reaction sequence:
Question: Identify (A) in the following reaction sequence: Correct Option: , 2 Solution:...
Read More →A 2 m ladder leans against a vertical wall.
Question: A $2 \mathrm{~m}$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate $25 \mathrm{~cm} / \mathrm{sec}$., then the rate (in $\mathrm{cm} / \mathrm{sec}$.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1 \mathrm{~m}$ above the ground is:(1) $25 \sqrt{3}$(2) $\frac{25}{\sqrt{3}}$(3) $\frac{25}{3}$(4) 25Correct Option: , 2 Solution: According to the question, $\frac{d ...
Read More →Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate,
Question: Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate, if 9 cm of standing water is densired? Solution: Width of the canal = 30 dm = 3 m (1 m = 10 dm)Depth of the canal = 12 dm = 1.2 mSpeed of the water flow = 20 km/h = 20000 m/h Volume of water flowing out of the canal in 1 h = 3 1.2 20000 = 72000 m3Height of standing water on field = 9 cm = 0.09 m (1 m = 100 cm)Assume that water flows out of the canal for 1 h. Then,A...
Read More →If V is the volume of a cuboid of dimensions a, b, c and S is its surface area then prove that
Question: If $V$ is the volume of a cuboid of dimensions $a, b, c$ and $S$ is its surface area then prove that $\frac{1}{V}=\frac{2}{S}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$. Solution: Let the length, breadth and height of the cuboid bea,bandc, respectively.Surface area of the cuboid,S= 2(ab+bc+ca)Volume of the cuboid,V=abcNow, $\frac{S}{V}=\frac{2(a b+b c+c a)}{a b c}$ $\Rightarrow \frac{S}{V}=2\left(\frac{a b}{a b c}+\frac{b c}{a b c}+\frac{c a}{a b c}\right)$ $\Rightarrow \frac{S}{...
Read More →The major product Y in the following reactions is:
Question: The major product $(Y)$ in the following reactions is: Correct Option: , 4 Solution:...
Read More →Each edge of a cube is increased by 50%.
Question: Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube. Solution: Let the initial edge of the cube beaunits.Initial surface area of the cube = 6a2square units New edge of the cube $=a+50 \%$ of $a=a+\frac{50}{100} a=1.5 a$ units $\therefore$ New surface of the cube $=6(1.5 a)^{2}=13.5 a^{2}$ square units Increase in surface area of the cube $=13.5 a^{2}-6 a^{2}=7.5 a^{2}$ square units Percentage increase in the surface area of the cube $=\...
Read More →A spherical iron ball of radius
Question: A spherical iron ball of radius $10 \mathrm{~cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \mathrm{~cm}^{3} / \mathrm{min}$. When the thickness of the ice is $5 \mathrm{~cm}$, then the rate at which the thickness (in $\mathrm{cm} / \mathrm{min}$ ) of the ice decreases, is :(1) $\frac{1}{18 \pi}$(2) $\frac{1}{36 \pi}$(3) $\frac{5}{6 \pi}$(4) $\frac{1}{9 \pi}$Correct Option: 1 Solution: (1) Given that ice melts at a rate of $50 \mathrm{~cm}^{3} / \ma...
Read More →