Free Class 11 Solutions and Answers - All Boards, Books and Exams 2021

In a group of \(65\) people, \(40\) like cricket, \(10\) like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Math|Class 11

Correct5

In a survey it was found that \(21\) people liked product \(A, 26\) liked product \(B\) and \(29\) liked product \(C\). If \(14\) people liked products \(A\) and \(B, 12\) people liked products \(C\) and \(A, 14\) people liked products \(B\) and \(C\) and \(8\) liked all the three products. Find how many liked product \(C\) only.

Math|Class 11

Correct41

Convert the following products into the sum or difference of sines and cosines: \(\text{2 sin}\; 5x\;\text {cos}\; x\)

Math|Class 11

Correct44

Convert the following products into the sum or difference of sines and cosines: \(2 \cos 4 x \cos 3 x\)

Math|Class 11

Correct23

Convert each of the following products into the sum or difference of sines and cosines:\(2 \sin \;3x \;\sin x \)

Math|Class 11

Correct10

Convert the following product into the sum or difference of sine and cosine:
\(\sin \frac{5 \pi}{12} \cos \frac{\pi}{12}\)

Math|Class 11

Correct45

Convert each of the following products into the sum or differences of sines and cosines : \(\cos \frac{5 \pi}{12} \cos \frac{\pi}{12}\)

Math|Class 11

Correct44

Prove that: \(2 \cos \frac{\pi}{13} \cos \frac{9 \pi}{13}+\cos \frac{3 \pi}{13}+\cos \frac{5 \pi}{13}=0.\)

Math|Class 11

Correct23

Prove that: \(\cos 20^{\circ }\cos 40^{\circ }\cos 60^{\circ }\cos 80^{o}=\frac {1}{16}\)

Math|Class 11

Correct33

Prove that: \(\sin 10^{\circ }\sin 30^{\circ }\sin 50^{\circ }\sin 70^{\circ }=\frac {1}{16}\)

Math|Class 11

Correct8

Prove that: \(\sin 20^{\circ }\sin 40^{\circ }\sin 60^{\circ }\sin 80^{\circ }=\frac {3}{16}\)

Math|Class 11

Correct30

Prove that: \(4\cos 12^{\circ }\cos 48^{\circ }\cos 72^{\circ }=\cos 36^{\circ}\)

Math|Class 11

Correct43

Prove that: \(\sin A\sin (\frac {\pi }{3}-A)\sin (\frac {\pi }{3}+A)=\frac {1}{4}\sin 3A\)

Math|Class 11

Correct41

Prove that: \(\cos A \cos \left(\frac{\pi}{3}-A\right) \cos \left(\frac{\pi}{3}+A\right)=\frac{1}{4} \cos 3 A.\)

Math|Class 11

Correct33

Prove that: \(4 \sin x \sin (\frac {\pi}{3}+x)\sin (\frac {2\pi }{3}+x)=\sin 3x.\)

Math|Class 11

Correct44

Show that: \( \tan \left(\frac{\pi}{3}+x\right) \tan \left(\frac{\pi}{3}-x\right)=\frac{2 \cos 2 x+1}{2 \cos 2 x-1}.\)

Math|Class 11

Correct2

If \(\alpha+\beta=90^{\circ},\) find the maximum and minimum values of \(\sin \alpha \sin \beta.\)

Math|Class 11

Correct45

Express each of the following as the sum or difference-of sines and cosines:
\(2 \sin 3x\cos x\)

Math|Class 11

Correct44

Express each of the following as the sum or difference of sines and cosines:
\(2\;\cos 3x \;\sin 2x\)

Math|Class 11

Correct12

Express the following as the sum or difference of sines and cosines:
\(2\; \sin 4 x\; \sin 3 x\)

Math|Class 11

Correct16

Class 11

Important Questions for Class 11

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