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A number is divisible by 25 if it ends with 00, 25, 50 or 75 . From the given set of number there are only two ways in which the number can be divisible by 25 either the last two digits are 2 and 5...

3! X 4 c 3 X 1! X 7 c 2 X 1! This can be obtained by first arranging O L and T in 3! Ways and then choosing any 3 places for A between them out of 4 in 4 c 3 ways and permuating them amongst...

It is well known that lim n—> inf (1 + 1/n)^n evaluates to e. So if we put n = 10000 (1 + 1/10000)^10000 And by binomial theorem, Using the binomial theorem: ( 1 + 1/10000 )^10000 = 10000C0 +...

The total number of words that can be formed

Logarithms are nothing but just the inverse of exponential function. For example, a x =b can be written as log a b=x

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Use Hermite’s identity: Then E =[50/3] = 16. Then the exponent of 2 in 16! = [16/2]+[16/4]+[16/8]+[16/16] = 8+4+2+1 = 15

The missing condition is that x+y+z = 10. Now, if the numbers were non-negative real numbers, then all we would have to do is use the AP-GP inequality, and in that case the maximum would have...

divide d given equation by and let y/x be slope m hence we get nw, let d roots of this equation be as given nw SOR = m1 + m2=-2h/b=4m2 POR=m1m2= = a/b therefore, ,

The general term is t n = n/(1+n 2 +n 4 ) = ½ [1/(n 2 -n+1) – 1/(n 2 +n+1)] Also n 2 +n+1 = (n+1) 2 -(n+1)+1. So, the summation may be written as ½ [1/1 2 -1+1) – 1/(2 2 -2+1)] + ½ [1/(2 2 -2+1) –...

We have n(n+1)(n+2)(n+3)+1 = (n 2 +3n)(n 2 +3n+2)+1 Let y = n 2 +3n Then, the given expression is y(y+2)+1 = y 2 +2y+1 = (y+1) 2 = (n 2 +3n+1) 2 . Hence, the square root is n 2 +3n+1 . Substitue n =...

18 * 3 , 9*3 , 4.5*3,......... this is the perimeter of triangles same way find the areas …........................................

a + b = 4

cosec(90° – θ) = sec θ cot(90° – θ) = tan θ sin 2 (90° – θ) = cos 2 θ Therefore, sec 2 θ – tan 2 θ + sin 2 55° + sin 2 35° => (1 + tan 2 θ) – tan 2 θ + cos 2 35° + sin 2 35° => 1 + 1 => 2 I hope u...

Dear Student, To find the coefficient of x 20 in the given exantion, we can replace the terms written in the bracket with the (e x -(higher power of x)) 3 . Now the coefficient of x 20 will lies in...

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