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

Correct38

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

Correct49

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

Math|Class 11

Correct49

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

Math|Class 11

Correct26

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

Math|Class 11

Correct13

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

Correct48

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

Correct47

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

Correct24

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

Math|Class 11

Correct35

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

Math|Class 11

Correct9

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

Math|Class 11

Correct31

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

Math|Class 11

Correct44

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

Math|Class 11

Correct42

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

Correct34

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

Math|Class 11

Correct45

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

Correct3

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

Math|Class 11

Correct46

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

Math|Class 11

Correct45

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

Math|Class 11

Correct13

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

Math|Class 11

Correct19

Class 11

Important Questions for Class 11

2 million+ students are checking solutions below