NCERT 2022 | पूर्णांक - L4 | पूर्णांकों का योग | Integers | Class 6 NCERT गणित | 7 PM | Kamal Sir

NCERT EXERCISE-6.2 (प्रश्न)|त्रिभुज का कोण योग गुण |प्रमेय 6.8

Previous Class Revision|NCERT प्रश्नावली 7.5 का हल भाग-2|सारांश

सारणिक तथा आव्यूहों के अनुप्रयोग|आव्यूह के व्युत्क्रम द्वारा रैखिक समीकरणों के निकाय का हल|NCERT प्रश्नावली 4.6|Summary

सारणिक तथा आव्यूहों के अनुप्रयोग|आव्यूह के व्युत्क्रम द्वारा रैखिक समीकरणों के निकाय का हल|NCERT प्रश्नावली 4.6|Summary

Consider the marks, out of 100, obtained by 51 students of a class in a test, given in Table 14.9. M a r k s"N u m b e r o f S t u d e n t s"0-10 5 10-20 10 20-30 4 30-40 6 40-50 7 50-60 3 60-70 2 70-80 2 80-90 3 90-100 9Tot a l 51 Draw a freque

The difference of two positive numbers is 1020. If 7.6% of the greater number is 12.4% of the smaller number, then the sum of the two numbers is equal to: दो धनात्मक संख्याओं का अंतर 1020 है। यदि बड़ी संख्या का 7.6% छोटी संख्या का 12.4% है, तो दोनों संख्याओं का योग ज्ञात करें |

Let L denote antilog 320.6 and M denote the number of positive integers which have the characteristic 4, when the base of log is 5, and N denote the value of 49^((1-log_(7)2))+5^(-log_(5)4) Find the value of (LM)/(N) .

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of (tan^(2)""(pi)/(7) + tan^(2)""(2pi)/(7) + tan^(2)""(3pi)/(7))xx (cot^(2)""(pi)/(7) + cot^(2)""(2pi)/(7) + cot^(2)""(3pi)/(7)) is