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 alpha=\ \ ^m C_2,\ then find the value of \ ^(alpha)C_2dot

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. .^(m)C_(1) + ^(m+1)C_(2) + ^(m+2)C_(3) + "…." + ^(m+n-1)C_(n) d. .^(m+n)C_(m) - 1

There are 2n points in a plane in which m are collinear. Number of quadrilaterals formed by joining these lines: a. is equal to .^(2n)C_(4)-.^(m)C_(4) b. is greater than .^(2n)C_(4)_.^(m)C_(4) c. is less than .^(2n)C_(4)-.^(m)C_(4) d. None of these

Using binomial theorem (without using the formula for .^n C_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_4dot

If m in N and mgeq2 prove that: |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|=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

If \ ^m C_1=\ \ ^n C_2 then which is correct a. 2m=n b. 2m=n(n+1) c. 2m=(n-1) d. 2n=m(m-1)

The set of values of alpha for which the point (alpha,1) lies inside the curves c_1: x^2+y^2-4=0 and c_2: y^2=4x is (a) |alpha| < sqrt(3) (b) |alpha|<2 (c) 1/4 < alpha < sqrt(3) (d) none of these

Prove that ^m C_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-=(-1)^(m-1)n^mdot

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to