Class 12th

Read the information carefully and answer the questions given below.

Bus route no. 971 has exactly six stops on its route. Any bus plying on this route starts from the initial position, then stops first at stop one and then stops at two, three, four, five, and six respectively. After the bus reaches stop six, the bus turns and returns to its initial position and repeats the cycle. Buses are not allowed to carry people on its return journey.

Following are the six stops – Lokhand Wala, Saket Xing, Kanpur, Aligarh, Peetampura, and Rajghat in no particular order, Further, following observations have been made regarding the stops on this

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Contributor-Level 10

Following is the structure of the stops on this route:

Case I:

Aligarh	Rajghat		Peetampura	Kanpur	Lokhand wala	Saket Xingh
Stop 1	Stop 2		Stop 3	Stop 4	Stop 5	Stop 6
Case II:
Kanpur	Lokhand wala	Peetampura		Aligarh	Rajghat	Saket Xingh
Stop 1	Stop 2	Stop 3		Stop 4	Stop 5	Stop 6

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New answer posted

8 months ago

Class 12th Maths

Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If $\int_{0}^{x} \sqrt[]{1 - {(f (t))}^{2}} d t = \int_{0}^{x} f (t) d t,$ and f(0) = 0, then $\underset{x \to 0}{l i m} \frac{1}{x^{2}} \int_{0}^{x} f (t) d t :$

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Raj Pandey

Contributor-Level 9

Applying Leibniz theorem,

$\sqrt[]{1 - {(f' (x))}^{2}} = f (x) \Rightarrow \frac{f' (x)}{\sqrt[]{1 - {(f (x))}^{2}}} = 1$ on integrating both sides, we get

$f (x) = s i n x + C$ put x = 0 and f (0) = 0 we get C = 0

$N o w \underset{x \to 0}{l i m} \frac{\int_{0}^{x} f (t) d t}{x^{2}}, (\frac{0}{0})$ by L' Hospital rule $\underset{x \to 0}{l i m} \frac{f (x)}{2 x} = \underset{x \to 0}{l i m} \frac{s i n x}{2 x} = \frac{1}{2}$

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New answer posted

8 months ago

Read the information carefully and answer the questions given below.

Following are the six stops – Lokhand Wala, Saket Xing, Kanpur, Aligarh, Peetampura, and Rajghat in no particular order, Further, following observations have been made regarding the stops on this

0 Follower 1 View

Contributor-Level 10

Following is the structure of the stops on this route:

Case I:

Aligarh	Rajghat		Peetampura	Kanpur	Lokhand wala	Saket Xingh
Stop 1	Stop 2		Stop 3	Stop 4	Stop 5	Stop 6
Case II:
Kanpur	Lokhand wala	Peetampura		Aligarh	Rajghat	Saket Xingh
Stop 1	Stop 2	Stop 3		Stop 4	Stop 5	Stop 6

0 0

New answer posted

8 months ago

Read the information carefully and answer the questions given below.

Following are the six stops – Lokhand Wala, Saket Xing, Kanpur, Aligarh, Peetampura, and Rajghat in no particular order, Further, following observations have been made regarding the stops on this

0 Follower 1 View

Contributor-Level 10

Following is the structure of the stops on this route:

Case I:

Aligarh	Rajghat		Peetampura	Kanpur	Lokhand wala	Saket Xingh
Stop 1	Stop 2		Stop 3	Stop 4	Stop 5	Stop 6
Case II:
Kanpur	Lokhand wala	Peetampura		Aligarh	Rajghat	Saket Xingh
Stop 1	Stop 2	Stop 3		Stop 4	Stop 5	Stop 6

0 0

New answer posted

8 months ago

Directions for questions: Read the information carefully and answer the questions given below.

Following are the six stops – Lokhand Wala, Saket Xing, Kanpur, Aligarh, Peetampura, and Rajghat in no particular order, Further, following observations have been made re

0 Follower 1 View

Class 12th Physics Ray Optics and Optical Instruments

Contributor-Level 10

Following is the structure of the stops on this route:

Case I:

Aligarh	Rajghat		Peetampura	Kanpur	Lokhand wala	Saket Xingh
Stop 1	Stop 2		Stop 3	Stop 4	Stop 5	Stop 6
Case II:
Kanpur	Lokhand wala	Peetampura		Aligarh	Rajghat	Saket Xingh
Stop 1	Stop 2	Stop 3		Stop 4	Stop 5	Stop 6

0 0

New answer posted

8 months ago

Class 12th Maths

If $\frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y}}, y (0) = 1,$ then y(1) is equal to:

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Raj Pandey

Contributor-Level 9

$\frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y}} \Rightarrow \int \frac{2^{y} d y}{2^{y} - 1} = \int 2^{x} d x \Rightarrow p u t 2^{y} - 1 = t \Rightarrow 2^{y} l n 2 d y = d t$

$\frac{1}{l n 2} \int \frac{d t}{t} = \int 2^{x} d x \Rightarrow \frac{1}{l n 2} l n t = \frac{2^{x}}{l n 2} + \frac{C}{l n 2}$ put x = 0 and y = 1 we get C = -1

$∴ l n (2^{y} - 1) = 2^{x} - 1$ put x = 1 and we get y = log₂ (1 + e)

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New answer posted

8 months ago

Class 12th Physics

A parallel plate capacitor of capacitance 200 $μ F$ is connected to a battery of 200V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be_______J.

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Vishal Baghel

Contributor-Level 10

Battery is connected while dielectric is inserted so potential difference will be remains same.

$U_{i} = \frac{1}{2} c V^{2}$

$U_{f} = \frac{1}{2} K c V^{2}$

$\Rightarrow Δ U = \frac{1}{2} (K - 1) c V^{2} = \frac{1}{2} * 1 * 200 * 1 0^{- 9} * 20 0^{2} = 4$

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New answer posted

8 months ago

Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is_______* 10^-10s. (Given, speed of light in vacuum = 3 * 10⁸ m/s and cos30° = $\frac{\sqrt[]{3}}{2})$

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Vishal Baghel

Contributor-Level 10

from given information : I = A = 60°, r = $\frac{A}{2} = 30 °$ => $μ = \sqrt[]{3} = \frac{c}{v}$

$\Rightarrow v = \frac{c}{\sqrt[]{3}} \Rightarrow t i m e = \frac{(\frac{5 \sqrt[]{3}}{100})}{(\frac{3 * 1 0^{8}}{\sqrt[]{3}})} = 5 * 1 0^{- 10} s$

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New answer posted

8 months ago

Class 12th Physics

At very high frequencies, the effective impendance of the given circuit will be_______ $Ω .$

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Vishal Baghel

Contributor-Level 10

$X_{c} = \frac{1}{ω c}, X_{L} = ω L$ so at very high frequencies capacitor behaves as conduct and inductor behaves as open circuit. The effective impedance will be $2 Ω .$

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New answer posted

8 months ago

Mr. Deepak has five sons – Umesh, Vikash, Shivam, Raman and Riya, and three daughters – Tamanna, Kuntala and Janaki. Three sons of Mr. Deepak were born first followed by two daughters. Riya is the eldest child and Janki is the youngest. Three of the children are studying at Trinity School and three are studying at St. Stefan. Tamanna and Shivam study at St. Stefan School. Kuntala, the eldest daughter, plays chess. Mansorover School offers cricket only, while Trinity school offers chess, Beside, these schools offer no other games. The children who are at Mansorover School have been born in succession. Vikash and Raman are cricketers

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