Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Answer the following questions in one word or one sentence or as per exact requirement of the question.  

If in a ∆ABC, \[\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}\] then find the measures of angles A, B, C. 

Answer the following questions in one word or one sentence or as per exact requirement of the question. 

In any triangle ABC, find the value of \[a\sin\left( B - C \right) + b\sin\left( C - A \right) + c\sin\left( A - B \right)\ 

Answer the following questions in one word or one sentence or as per exact requirement of the question. 

In any ∆ABC, find the value of

\[\sum^{}_{}a\left( \text{ sin }B - \text{ sin }C \right)\]

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In any ∆ABC, \[\sum^{}_{} a^2 \left( \sin B - \sin C \right)\] = 

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In a ∆ABC, if a = 2, \[\angle B = 60°\]  and\[\angle C = 75°\] 

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If the sides of a triangle are in the ratio \[1: \sqrt{3}: 2\] then the measure of its greatest angle is 

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In any ∆ABC, 2(bc cosA + ca cosB + ab cosC) = 

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In a triangle ABC, a = 4, b = 3, \[\angle A = 60°\]   then c is a root of the equation 

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In a ∆ABC, if  \[\left( c + a + b \right)\left( a + b - c \right) = ab\] then the measure of angle C is 

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In any ∆ABC, the value of  \[2ac\sin\left( \frac{A - B + C}{2} \right)\]  is 

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In any ∆ABC, \[a\left( b\cos C - c\cos B \right) =\]  

Find the value of `(1 + cos  pi/8)(1 + cos  (3pi)/8)(1 + cos  (5pi)/8)(1 + cos  (7pi)/8)`

If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`, then find the value of xy + yz + zx.

If x = sec Φ – tan Φ and y = cosec Φ + cot Φ then show that xy + x – y + 1 = 0
[Hint: Find xy + 1 and then show that x – y = –(xy + 1)]

The industrial revolution in England and Western Europe more than two centuries ago was triggered by some key scientific and technological advances. What were these advances?

The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?

The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 10¹¹m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?

The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of Jupiter

The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively, are shown in the figure. Choose the correct entries in the brackets below;

1. (A/B) lives closer to the school than (B/A)
2. (A/B) starts from the school earlier than (B/A)
3. (A/B) walks faster than (B/A)
4. A and B reach home at the (same/different) time
5. (A/B) overtakes (B/A) on the road (once/twice).