If `2^(-m)\ xx1/(2^m)=1/4,` then `1/(14)\ {(4^m)^(1//2)+\ (1/(5^m))^(-1)}` is equal to

(a)`1/2`
(b) `2`
(c) `4`
(d) `-1/4`

1/((2 1/3))+1/((1 3/4)) is equal to (a) 7/(14) (b) (12)/(49) (c) 4 1/(12) (d) None of these

sum_(m=1)^(n) tan^(-1) ((2m)/(m^(4) + m^(2) + 2)) is equal to

The sum (2^(1))/(4^(1) - 1) + (2^(2))/(4^(2) - 1) + (2^(4))/(4^(4) - 1) + (2^(8))/(4^(8) - 1) +... oo is equal to (A) 2 (B) 1 (C) 3 (D) 5

The value of m for which [{(1/(7^2))^(-2)}^(1/3)]^(1/4)=7^m , is (a) 1/3 (b) 1/4 (c) -3\ (d) 2

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3 1/5)^2+4^2+(4 4/5)^2+. . . . . , is (16)/5 m, then m is equal to: (1) 102 (2) 101 (3) 100 (4) 99

The line y=m x+1 is a tangent to the curve y^2=4x , if the value of m is (a) 1 (b) 2 (c) 3 (d) 1/2

If tanA=m/(m-1)\ a n d tanB=1/(2m-1), then prove that A-B=\ pi/4

The quantum number of electrons are given below: Arrange then in order of increasing energies a. n= 4,l= 2,m_(1)= -2, m_(s)= -(1)/(2) b. n= 3,l= 2,m_(1) = 1, m_(s)= +(1)/(2) c. n= 4,l= 1,m_(1) = 0, m_(s)= +(1)/(2) e.n= 3,l= 2,m_(1)= -2, m_(s)= +(1)/(2) f. n= 4,l= 1,m_(1) = +1, m_(s)= +(1)/(2)

Multiply : 2m^(2) - 3m - 1 and 4m^(2) - m - 1