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3 months ago

Class 11th Maths

Two vertical poles are 150m apart and the height of one is three times that of other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

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alok kumar singh

Contributor-Level 10

BC = CN = x = 75

$c o t θ = \frac{3 h}{75}$

$t a n θ = \frac{h}{75}$

$\frac{3 h^{2}}{75 * 75} = 1 \Rightarrow h = \frac{75}{\sqrt[]{3}} = 25 \sqrt[]{3}$

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3 months ago

Class 11th Physics Motion in Straight Line

A scooter accelerates from rest for time t₁ at constant rate a₁ and then retards at constant rate a₂ for time t₂ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be:

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Vishal Baghel

Contributor-Level 10

$t a n α = \frac{v_{m a x}}{t_{1}} = a_{1}$

$t a n β = \frac{v_{m a x}}{t_{2}} = a_{2}$

^{$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{t_{2}}{t_{1}} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{a_{2}}{a_{1}}$}

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Class 11th Physics

As shown in the figure, a block of mass $\sqrt[]{3} k g$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt[]{3}} .$ The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that it does not move, will be 3x. The value of x will be-------------.

[g = 10m/s² ; sin 60° = $\frac{\sqrt[]{3}}{2};$ cos60° = $\frac{1}{2}]$

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Payal Gupta

Contributor-Level 10

N = mg + F sin 60°

$f_{l i m} = F c o s 60 ° \Rightarrow μ N = F c o s 60 °$

$μ m g = F [c o s 60 ° - μ s i n 60 °]$

$F = \frac{μ m g}{c o s 60 ° - μ s i n 60 °} = \frac{\frac{1}{3 \sqrt[]{3}} * \sqrt[]{3} * 10}{\frac{1}{2} - \frac{1}{3 \sqrt[]{3}} * \frac{\sqrt[]{3}}{2}} = \frac{10 / 3}{\frac{1}{2} - \frac{1}{6}} = \frac{10 / 3}{1 / 3} = 10 N = 3 * (\frac{10}{3}) N$

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3 months ago

Class 11th Physics Oscillations

A particle executes S.H.M., the graph of velocity as a function of displacement is:

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Vishal Baghel

Contributor-Level 10

$v = ω \sqrt[]{A^{2} - x^{2}} \Rightarrow \frac{v^{2}}{A^{2} ω^{2}} + \frac{x^{2}}{A^{2}} = 1$ Path is ellipse.

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Class 11th Physics

A boy pushes a box of mass 2kg with a force $\vec{F} = (20 \hat{i} + 10 \hat{j}) N$ on a frictionless surface. If the box was initially at rest, then-------------m is displacement along the x – axis after 10s.

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Payal Gupta

Contributor-Level 10

$a_{x} = \frac{F_{x}}{m} = \frac{20}{2} = 10 m / s^{2}$

$S_{x} = \frac{1}{2} a_{x} t^{2} = \frac{1}{2} * 10 * 1 0^{2}$

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3 months ago

Class 11th Maths

Let p and q be two positive numbers such that p + q = 2 and p⁴ + q⁴ = 272. Then p and q are roots of the equation:

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alok kumar singh

Contributor-Level 10

p + q = 2

p⁴ + q⁴ = 272

${(p^{2} + q^{2})}^{2} - 2 p^{2} q^{2} = 272$

${[{(p + q)}^{2} - 2 p q]}^{2} - 2 p^{2} q^{2} = 272$

Let pq = t Þ (4 – 2t)² – 2t² = 272

2t² – 16 t – 256 = 0

->t = pq = 16

Required equation x² – 2x + 16 = 0

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3 months ago

Class 11th Laws of Motion

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be:

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Vishal Baghel

Contributor-Level 10

Let the spring is in extension state and $a_{B} > a_{A}, {\vec{a}}_{A B} = - a_{A} \hat{i} - (- a_{B} \hat{i}) = (- a_{A} + a_{B}) \hat{i}$ $_{}_{}_{}_{}_{}_{}_{}$

Hence we can say that block moves away from block B in the frame of B

F – kx = MaB . (1)

kx = Ma. (2)

$\Rightarrow a_{B} = \frac{F}{M} - a$

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Class 11th Maths

The statement among the following that is a tautology is:

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alok kumar singh

Contributor-Level 10

A	B		A B			A -> B
T	T	T	T	T	T	T	T
T	F	T	F	T	T	F	F
F	T	T	F	F	F	T	F
F	F	F	F	F	F	T	F

A (A -> B) -> B is a tautology

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3 months ago

Class 11th Physics Thermodynamics

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contains 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x * 10^-1 atm. Value of x is----------.

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Payal Gupta

Contributor-Level 10

$P = \frac{P_{1} V_{1} + P_{2} V_{2}}{V_{1} + V_{2}} = \frac{2 * 4.5 + 3 * 5.5}{10} = \frac{9 + 16.5}{10} = 25.5 * 1 0^{- 1} a t m$

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3 months ago

Class 11th Maths

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of the line on the coordinate axes is $\frac{1}{4} .$ Three stones A, B and C are placed at the point (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is / are on the path of the man?

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alok kumar singh

Contributor-Level 10

According to question,

$\frac{1}{2} (\frac{1}{a} + \frac{1}{b}) = \frac{1}{4}$

$\frac{1}{a} + \frac{1}{b} = \frac{1}{2} . . . . . . . . (i)$

Equation of required line is $\frac{x}{a} + \frac{y}{b} = 1$

Obviously B (2, 2) satisfying condition (i)

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