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7 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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7 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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7 months ago

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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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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7 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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7 months ago

Class 11th Physics Mechanical Properties of Solids

The normal density of a material its $ρ$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be

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Payal Gupta

Contributor-Level 10

From defined of bulk modulus

$K = - \frac{P}{(d V / V)} . . . . . . . (1)$

m = $ρ v = c o n s t a n t$

$ρ d V + V d ρ = 0$

$\frac{d V}{V} = - \frac{d ρ}{ρ} . . . . . . . . . (2)$

With the help of equations (1) and (2), we can write

$K = - \frac{P}{(- \frac{d ρ}{ρ})} = \frac{ρ P}{d ρ} \Rightarrow d ρ = \frac{ρ P}{K}$

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Class 11th Physics

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

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Vishal Baghel

Contributor-Level 10

Frequency increases on filing. So, initial frequency of A is 335 Hz.

f = 340 – 5 = 335 Hz

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7 months ago

Class 11th Physics

The length of metallic wire is $l_{1}$ $_{}$ when tension in it is $T_{1}$ $_{}$ . It is $l_{2}$ $_{}$ when the tension is T2. The original length of the wire will be:

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Vishal Baghel

Contributor-Level 10

Stress = Y * strain

=> $\frac{T_{1}}{A} = Y * - \frac{(l_{1} - l)}{l} (i)$

$\frac{T_{2}}{A} = Y * \frac{(l_{2} - l)}{l} (i i)$

=> $\frac{T_{1}}{T_{2}} = \frac{l_{1} - l}{l_{2} - l}$

$\Rightarrow l = \frac{T_{1} l_{2} - T_{2} l_{2}}{T_{1} - T_{2}} = \frac{T_{2} l_{1} - T_{1} l_{2}}{T_{2} - T_{1}}$

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7 months ago

Class 11th Relations and Functions

The function f(x) $= \frac{4 x^{3} - 3 x^{2}}{6} - 2 s i n x + (2 x - 1) c o s x :$

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alok kumar singh

Contributor-Level 10

$f (x) = \frac{4 x^{3} - 3 x^{2}}{6} - 2 s i n x + (2 x - 1) c o s x$

$f' (x) = 2 x^{2} - x - 2 c o s x + 2 c o s x - (2 x - 1) s i n x$

= $(2 x - 1) (x - s i n x) \geq 0 f o r x \geq 0$

$f' (x) \geq 0 \forall x \geq 1 / 2$

$∴ f (x)$ is increasing in $[\frac{1}{2}, \infty)$

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7 months ago

Class 11th Physics Motion in Plane

A planet revolving in elliptical orbit has:

(A) a constant velocity of revolution.

(B) has the least velocity when it is nearest to the sun.

(C) its areal velocity is directly proportional to its velocity.

(D) areal velocity in inversely proportional to its velocity.

(E) To follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below

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Payal Gupta

Contributor-Level 10

In elliptical orbit, areal velocity is constant

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