If `alpha=^m C_2,t h e n^(alpha)C_2` is equal to a. `^m+1C_4` b. `^m-1C_4` c. `3^(m+2)C_4` d. `3^(m+1)C_4`

If a : b=3:4, b : c4:7, t h e n(a+b+c)/c is equal to 1 b. 2 c. 3 d. 7

If a :(b+c)=1:3 a n d c :(a+b)=5:7, t h e b :(a+c) is equal to 1:2 b. 1:3 c. 2:3 d. 2:1

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then(a^2)/8 is equal to (a)m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c)m_1^2+m_3^2-2m_2^2 (d) none of these

The value of determinant |1 1 1^m C_1^(m+1)C_1^(m+2)C_1^m C_2^(m+1)C_2^(m+2)C_2| is equal to 1 b. -1 c. 0 d. none of these

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m , B C=4c m , C A=2 c m D E F : D E=2 c m , E F=3 c m a n d F D=4 c m P Q R : P Q=17 c m , Q R=15 c m , P R=18 c m D E F : D E=18 c m , E F=17 c m , D F=15 c m .

If the given equation: |x^2-2x-3|=m has three solutions, then a. m in (0,oo) b. m in "{"4"]" c. m in (0,4) d. m in (-1,3)

Using binomial theorem (without using the formula for sim nC_(r)), prove that ^nC_(4)+^(m)C_(2)-^(m)C_(1)^(n)C_(2)=^(m)C_(4)-^(m+n)C_(1)^(m)C_(3)+^(m+n)C_(2)^(m)C_(2)-^(m+n)C_(3)^(m)C_(1)+^(m+n)C_(4)

The value of the determinant |(1,1,1),(.^(m)C_(1),.^(m +1)C_(1),.^(m+2)C_(1)),(.^(m)C_(2),.^(m +1)C_(2),.^(m+2)C_(2))| is equal to