The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)⁴  and of (1−αx )⁶  is the same if α equals

• -5/3

• 3/5

• -3/10

• -3/10

The coefficient of xⁿ in expansion of (1+x)(1-x)ⁿ is

• (n-1)

• (-1)ⁿ(1-n)

• (-1)^n-1(n-1)²

• (-1)^n-1(n-1)²

• 
• 

• n-1

• n-1

Let T be the rth term of an A.P. whose first term is a and the common difference is d. If for r some positive integers m, n, m ≠ n, T_m = 1/n  and T_n = 1/m, then a-b equals

• 0

• 1

• 1/mn

• 1/mn

The sum of the first n terms of the series  when n is even. When n is odd the sum is

The sum of series 

Let α, β be such that π < α - β < 3π. If sinα + sinβ = -21/65 and cosα + cosβ = -27/65, then the value of cos α-β/2 is

• 
• 

• 6/65

• 6/65

If  then the difference between the maximum and minimum values of 2 u is given by

• 2(a² + b²)

• 2(a²-b²)

• (a+b)²

• (a+b)²

19.

The sides of a triangle are sinα, cosα and  for some 0 < α < π/2 . Then the greatest angle of the triangle is

• 60^o

• 120^o

• 360^o

• 360^o

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60^o and when he retires 40 meters away from the tree the angle of elevation becomes 30^o. The breadth of the river is

• 20 m

• 30 m

• 40 m

• 40 m