An alternating voltage
Question: An alternating voltage $v(t)=220 \sin 100 \pi t$ volt is applied to a purely resistive load of $50 \Omega$. The time taken for the current to rise from half of the peak value to the peak value is :(1) $5 \mathrm{~ms}$(2) $2.2 \mathrm{~ms}$(3) $7.2 \mathrm{~ms}$(4) $3.3 \mathrm{~ms}$Correct Option: , 4 Solution: (4) As $V(t)=220 \sin 100 \pi t$ so, $I(t)=\frac{220}{50} \sin 100 \pi \mathrm{t}$ i.e., $I=I_{m}=\sin (100 \pi \mathrm{t})$ For $I=I_{m}$ $t_{1}=\frac{\pi}{2} \times \frac{1}{1...
Read More →The volume of a cuboid is 1536 m3. Its length is 16 m, and its breadth and height are in the ratio 3 : 2.
Question: The volume of a cuboid is 1536 m3. Its length is 16 m, and its breadth and height are in the ratio 3 : 2. Find the breadth and height of the cuboid. Solution: Length of the cuboid = 16 mSuppose that the breadth and height of the cuboid are 3xm and 2xm, respectively. Then $1536=16 \times 3 x \times 2 x$ $\Rightarrow 1536=16 \times 6 x^{2}$ $\Rightarrow x^{2}=\frac{1536}{96}=16$ $\Rightarrow x=\sqrt{16}=4$ The breadth and height of the cuboid are 12 m and 8 m, respectively....
Read More →The increasing order of the reactivity of the following compounds in nucleophilic addition reaction is :
Question: The increasing order of the reactivity of the following compounds in nucleophilic addition reaction is : Propanal, Benzaldehyde, Propanone, ButanoneBenzaldehyde $$ Butanone $$ Propanone $$ PropanalButanone $$ Propanone $$ Benzaldehyde $$ PropanalPropanal $$ Propanone $$ Butanone $$ BenzaldehydeBenzaldehyde $$ Propanal $$ Propanone $$ ButanoneCorrect Option: , 2 Solution: Rate of Nucleophillic addition reaction is directly proportional to the $-I$ and $-M$ effect of the substituents pre...
Read More →If the tangent to the curve,
Question: If the tangent to the curve, $y=x^{3}+a x-b$ at the point $(1,-5)$ is perpendicular to the line, $-x+y+4=0$, then which one of the following points lies on the curve?(1) $(-2,1)$(2) $(-2,2)$(3) $(2,-1)$(4) $(2,-2)$Correct Option: 4, Solution: $y=x^{3}+a x-b$ Since, the point $(1,-5)$ lies on the curve. $\Rightarrow 1+a-b=-5$ $\Rightarrow a-b=-6$ ...........(1) Now, $\frac{d y}{d x}=3 x^{2}+a$ $\Rightarrow\left(\frac{d y}{d x}\right)_{\text {at } x=1}=3+a$ Since, required line is perpen...
Read More →A box made of sheet metal costs ₹ 6480 at ₹ 120 per square metre.
Question: A box made of sheet metal costs ₹ 6480 at ₹ 120 per square metre. If the box is 5 m long and 3 m wide, find its height. Solution: Length of the box =5 mBreadth of the box =3 m Area of the sheet required $=\frac{\text { total cost }}{\text { cost per metre square }}$ Lethm be the height of the box.Then area of the sheet = total surface area of the box $=2(l b+l h+b h) \mathrm{m}^{2}$ $=2(5 \times 3+5 \times h+3 \times h) \mathrm{m}^{2}$ $=2(15+8 h)=(30+16 h) \mathrm{m}^{2}$ Now, $30+16 ...
Read More →The increasing order of the following compounds towards HCN addition is :
Question: The increasing order of the following compounds towards HCN addition is : (1) (i) $($ iii $)($ iv $)($ ii $) (2) (iii) $($ iv $)($ i $)($ ii $)$ (3) (iii) $($ i $)$ (iv) $$ (ii) (4) (iii) $($ iv $)($ ii $)($ i $)$Correct Option: , 3 Solution: -I effect of $\mathrm{NO}_{2}$ increases reactivity towards nucleophilic addition reaction with $\mathrm{HCN} .-\mathrm{OCH}_{3}$ group is electron donating due to resonance effect which decreases the reactivity towards nucleophillic addition....
Read More →In LC circuit the inductance L=40 mH and capacitance
Question: In LC circuit the inductance $\mathrm{L}=40 \mathrm{mH}$ and capacitance $\mathrm{C}=100 \mu \mathrm{F}$. If a voltage $\mathrm{V}(t)=10 \sin (314 t)$ is applied to the circuit, the current in the circuit is given as:(1) $0.52 \cos 314 \mathrm{t}$(2) $10 \cos 314 t$(3) $5.2 \cos 314 \mathrm{t}$(4) $0.52 \sin 314 \mathrm{t}$Correct Option: 1 Solution: (1) Given, Inductance, $L=40 \mathrm{mH}$ Capacitance, $C=100 \mu F$ Impedance, $Z=X_{C}-X_{L}$ $\Rightarrow Z=\frac{1}{\omega C}-\omega ...
Read More →The increasing order of the following compounds towards HCN addition is :
Question: The increasing order of the following compounds towards HCN addition is : (1) (i) $($ iii $)($ iv $)($ ii $) \quad$ (2) $\quad$ (iii) $($ iv $)($ i $)($ ii $)$ (3) (iii) $($ i $)$ (iv) $$ (ii) $\quad$ (4) $\quad$ (iii) $($ iv $)($ ii $)($ i $)$Correct Option: , 3 Solution: -I effect of $\mathrm{NO}_{2}$ increases reactivity towards nucleophilic addition reaction with $\mathrm{HCN} .-\mathrm{OCH}_{3}$ group is electron donating due to resonance effect which decreases the reactivity towa...
Read More →How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm,
Question: How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cm3of iron weighs 15 g, find the weight of the empty box in kilograms. Solution: The external dimensions of the box are36 cm, 25 cm and 16.5 cm.Thickness of the iron = 1.5 cmInner length of the box = 36 1.51.5 = 33 cmInner breadth of the box = 25 1.51.5 = 22 cmInner height of the box = 16.5 1.5 = 15 cmNow,Volume of iron in the ...
Read More →a non-zero polynomial of degree four, having local extreme points at
Question: If $\mathrm{f}(\mathrm{x})$ isa non-zero polynomial of degree four, having local extreme points at$x=-1,0,1$; then the set $S=\{x \in R: f(x)=f(0)\}$ contains exactly:(1) four irrational numbers.(2) four rational numbers.(3) two irrational and two rational numbers.(4) two irrational and one rational number.Correct Option: 4, Solution: Since, function $\mathrm{f}(\mathrm{x})$ have local extreem points at $\mathrm{x}=$ $-1,0,1$. Then $f(x)=K(x+1) x(x-1)$ $=\mathrm{K}\left(\mathrm{x}^{3}-...
Read More →A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring (22 cm × 12.5 cm × 7.5 cm).
Question: A wall $15 \mathrm{~m}$ long, $30 \mathrm{~cm}$ wide and $4 \mathrm{~m}$ high is made of bricks, each measuring $(22 \mathrm{~cm} \times 12.5 \mathrm{~cm} \times 7.5 \mathrm{~cm})$. If $\frac{1}{12}$ of the total volume of the wall consists of mortar, how many bricks are there in the wall? Solution: Length of the wall = 15 m = 1500 cmBreadth of the wall = 30 cmHeight of the wall = 4 m = 400 cm Volume of wall $==1500 \times 30 \times 400 \mathrm{~cm}^{3}=18000000 \mathrm{~cm}^{3}$ Now, ...
Read More →The dimensions of a room are (9 m × 8 m × 6.5 m). It has one door of dimensions (2 m × 1.5 m) and two windows,
Question: The dimensions of a room are (9 m 8 m 6.5 m). It has one door of dimensions (2 m 1.5 m) and two windows, each of dimensions (1.5 m 1 m). Find the cost of whitewashing the walls at Rs 25 per square metre. Solution: Length of the room,l= 9 mBreadth of the room,b= 8 mHeight of the room,h= 6.5 mNow,Area of the walls to be whitewashed= Curved surface area of the room Area of the door 2 Area of each window= 2h(l+b)2 m 1.5 m 21.5 m 1 m= 2 6.5 (9 + 8) 3 3= 221 6= 215 m2 Cost of whitewashing th...
Read More →The major aromatic product $mathrm{C}$ in the following reaction sequence will be :
Question: The major aromatic product $\mathrm{C}$ in the following reaction sequence will be : Correct Option: Solution:...
Read More →Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5 m.
Question: Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5 m. Also, find the area of the iron sheet required to make the cistern. Solution: Length of the cistern,l= 8 mBreadth of the cistern,b= 6 mHeight (or depth) of the cistern,h= 2.5 m Capacity of the cistern= Volume of the cistern=lbh= 8 6 2.5= 120 m3Also,Area of the iron sheet required to make the cistern= Total surface area of the cistern= 2(lb+bh+hl)= 2(8 6 + 6 2.5 + 2.5 8)= 2 83= 166 m2...
Read More →How many bricks will be required to construct a wall 8 m long,
Question: How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm 11.25 cm 6 cm)? Solution: Length of the wall = 8 m = 800 cmBreadth of the wall = 22.5 cmHeight of the wall = 6 m = 600 cm i.e., volume of wall $=800 \times 22.5 \times 600 \mathrm{~cm}^{3}=10800000 \mathrm{~cm}^{3}$ Length of the brick = 25 cmBreadth of the brick = 11.25 cmHeight of the brick = 6 cm i.e., volume of one brick $=25 \times 11.25 \times 6=1687.5 \mathrm{~...
Read More →How many planks of dimensions (5 m × 25 cm × 10 cm) can be stored in a pit which is 20 m long,
Question: How many planks of dimensions (5 m 25 cm 10 cm) can be stored in a pit which is 20 m long, 6 m wide and 80 cm deep? Solution: Number of planks $=\frac{\text { volume of the pit in } \mathrm{cm}^{3}}{\text { volume of } 1 \text { plank in } \mathrm{cm}^{3}}$ Volume of one plank $=(l \times b \times h) \mathrm{cm}^{3}$ $=500 \times 25 \times 10 \mathrm{~cm}^{3}$ $=125000 \mathrm{~cm}^{3}$ Volume of the pit $=(l \times b \times h) \mathrm{cm}^{3}$ Here, $l=20 \mathrm{~m}=2000 \mathrm{~cm}...
Read More →As shown in the figure, a battery of emf in is connected to an inductor L and resistance R in series.
Question: As shown in the figure, a battery of emf $\in$ is connected to an inductor $L$ and resistance $R$ in series. The switch is closed at $t=0$. The total charge that flows from the battery, between $t=0$ and $t=t_{c}\left(t_{c}\right.$ is the time constant of the circuit) is:(1) $\frac{\in}{e L}$(2) $\frac{\in L}{R^{2}}\left(1-\frac{1}{e}\right)$(3) $\frac{\in L}{R^{2}}$(4) $\frac{\in R}{e L^{2}}$Correct Option: 1, Solution: (1) For series connection of a resistor and inductor, time variat...
Read More →Considering the above reaction, the major product among the following is:
Question: Considering the above reaction, the major product among the following is:Correct Option: , 3 Solution:...
Read More →The height of a right circular cylinder of maximum
Question: The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is : (1) $\sqrt{6}$(2) $\frac{2}{3} \sqrt{3}$(3) $2 \sqrt{3}$(4) $\sqrt{3}$Correct Option: , 3 Solution: Let radius of base and height of cylinder be $r$ and $h$ respectively. $\therefore r^{2}+\frac{h^{2}}{4}=9$ ...........(1) Now, volume of cylinder, $V=\pi r^{2} h$ Substitute the value of $\mathrm{r}^{2}$ from equation (i), $V=\pi h\left(9-\frac{h^{2}}{4}\right) \Rightarrow V=9 \pi h-\frac{\p...
Read More →Identify A in the given chemical reaction.
Question: Identify A in the given chemical reaction. Correct Option: 1 Solution:...
Read More →Given that the slope of the tangent to a curve
Question: Given that the slope of the tangent to a curve $y=y(x)$ at any point $(x, y)$ is $\frac{2 y}{x^{2}}$. If the curve passes through the centre of the circle $x^{2}+y^{2}-2 x-2 y=0$, then its equation is :(1) $x \log _{e}|y|=2(x-1)$(2) $x \log _{e}|y|=-2(x-1)$(3) $x^{2} \log _{e}|y|=-2(x-1)$(4) $x \log _{e}|y|=x-1$Correct Option: 1, Solution: Given $\frac{d y}{d x}=\frac{2 y}{x^{2}}$ Integrating both sides, $\int \frac{d y}{y}=2 \int \frac{d x}{x^{2}}$ $\Rightarrow \ln |y|=-\frac{2}{x}+C$...
Read More →A godown measures 40 m × 25 m × 15 m.
Question: A godown measures 40 m 25 m 15 m. Find the maximum number of wooden crates, each measuring 1.5 m 1.25 m 0.5 m, that can be stored in the godown. Solution: Volume of the godown =40 m 25 m 15 m = 15000 m3Volume of each wooden crate =1.5 m 1.25 m 0.5 m = 0.9375 m3 Maximum number of wooden crates that can be stored in the godown $=\frac{\text { Volume of the godown }}{\text { Volume of each wooden crate }}$ $=\frac{15000}{0.9375}$ $=16000$...
Read More →Identify A in the following chemical reaction.
Question: Identify A in the following chemical reaction. Correct Option: , 3 Solution:...
Read More →The capacity of a cuboidal tank is 50000 litres of water.
Question: The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank if its length and depth are respectively 10 m and 2.5 m. (Given, 1000 litres = 1 m3.) Solution: Capacity of the tank $=50000 \mathrm{~L}=\frac{50000}{1000}=50 \mathrm{~m}^{3}$ $\left(1000 L=1 \mathrm{~m}^{3}\right)$ Length of the tank = 10 mHeight (or depth) of the tank = 2.5 mNow,Volume of the cuboidal tank = Length Breadth Height $\therefore$ Breadth of the tank $=\frac{\text { Volume of the tank }...
Read More →A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep.
Question: A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (Given, 1 m3= 1000 litres.) Solution: Volume of water in the tank = Length Breadth Height = 65 4.5 = 135 m3 Volume of water in litres = 135 1000 = 135000 L (1 m3= 1000 L)Thus, the water tank can hold 135000 L of water....
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