Find the common difference of an A.P if \( t_{18}-t_{14}=3 L \). If \( 3+k, 18-k, 5 k+1 \) are in A.P, then find \( k \). If \( p \) and \( q \) are positive integers, then we write \( p=a^{2} b^{3} \) and \( q=a^{3} b \) if \( a \), \( b \) are numbers, then verify that L.C.M of \( (p, q) \times \) H.C.F of \( (p, q)=p q \).

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Correct Answer - (4, 2)

Correct Answer - (i) 0.57 (ii) 0.43

Correct Answer - (i) 0.28 (ii) 0.4 (iii) 0.32

Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)

The common difference is 9 - 4 = 5 If the first term is 6 and common difference is 5, then new AP is, 6, 6 + 5, 6 + 10… = 6,11,16….

Given that \(\vec a, \vec b\) and \(\vec c\)are unit vectors. i.e., |\(\vec a\)| = |\(\vec b\)|  = |\(\vec c\)| = 1 And \(\vec a\) + \(\vec b\) + \(\vec c\) = \(\vec 0\) Then \((\vec a+\vec b+\vec c).(\vec a+\vec b+\vec c)=\vec 0.\vec...

Correct option is (B) 3 Mode - Mean  = k (Median - Mean) Mode = Mean + K.Median - K.Mean Mode = K.Median + (1 - K)Mean We know formula Mode = 3 Median - 2...

Correct Answer - Domain ={1,2,3,……,20} Range={39,37,35,….,3,1} Relation is not reflexive, symmetric or transitive .

Let the numbers be ‘a’ and ‘b’.  Given, sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8.  ⇒ a + b = 8  ⇒ a...