121 - Mathematics Questions Answers

Find 

lim n→∞  ⁿ√(n!) / n

Asked By: LUFFY
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Joshi sir comment
Is there a way to do this in terms of area in a coordinate plane. Where difference of larger and smaller can be difference in x coordinate for 1st player and difference in y coordinate for 2nd player
Asked By: LUFFY
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Joshi sir comment

Probability to get following differences  difference     probability 0                   6/36 1                 10/36 2                   8/36 3                   6/36 4                   4/36 5                   2/36 So required probability =1-2636436+236+1036236 now solve problem is based on integral values so area is not very useful

Find Sum to n terms 

 

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

Asked By: LUFFY
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Joshi sir comment

x1-x2=11-x-11-x2 break all terms similarly and solve 

1 . Iₙ = ∫ ( 1/ ( x² + a²)ⁿ  )dx

 

How to do this by substituting x = a tan Α

 

2.  Is this true 

    ∫ f(x) d(kg(x)) = k ∫ f(x) d(g(x))

    where k is a constant

 

Asked By: LUFFY
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Solution by Joshi sir

d/dx((1+x^2+x^4)/(1+x+x^2))=ax+b

then a=?, b=?

Asked By: RAJIV
is this question helpfull: 21 9 read solutions ( 2 ) | submit your answer
Joshi sir comment

1+x2+x4 = (1+x+x2)(1-x+x2)

now solve

Maths >> Calculus >> Functions IIT JEE

Find a formula for a function g(x) satisfying the following conditions

a) domain of g is (-∞ , ∞ )     b) range of g is [-2 , 8]     c)  g has a period π   d)  g(2) = 3

Asked By: VAIBHAV GUPTA
is this question helpfull: 6 0 read solutions ( 1 ) | submit your answer
Joshi sir comment

g(x) = 3-5sin(2x-4)

 

Maths >> Calculus >> Functions IIT JEE

Let f(x) = x135 + x125 - x115 + x5 +1. If f(x) is divided by x3-x then the remainder is some function of x say g(x). Find the value of g(10)

Asked By: VAIBHAV GUPTA
is this question helpfull: 7 6 submit your answer
Joshi sir comment

for getting reminder put x3= x so

x135 + x125 - x115 + x5 +1 will give

 x45 + x41*x2 - x38*x +x*x2 +1

x15 + x13*x2*x2 - x12*x2*x +x*x2 +1

 x17 + x3 +1

x5*x2 + x + 1

x+ x + 1

x2*x + x +1 

x3 + x +1 

x+x+1

2x+1

now put x = 10

No. of integral roots of the eqn. x8 - 24 x7 - 18x5 + 39 x2 + 1155 = 0 .

Asked By: VAIBHAV GUPTA
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Joshi sir comment

two times sign change so 2 positive roots

 

let a,b,c be three distinct real numbers such that each of expression ax2+bx+c,bx2+cx+a,cx2+ax+b are positive for all x ε R and let

α=bc+ca+ab/a2+b2+c2 then

(A) α<4 (B) α<1 (C) α>1/4 (D) α>1

 

THIS IS MULTIPLE CHOICE QUESTION

Asked By: AKASH
is this question helpfull: 7 0 read solutions ( 1 ) | submit your answer
Joshi sir comment

if ax2+bx+c is positive for real x

then b2< 4ac similarly others

on adding all inequalities we get b2 + c2 + a2< 4(ac+ab+bc)

now get answer 

Maths >> Algebra >> Binomial Theorem Engineering Exam

Find sum of series..1*(n)2  + 2*(n-1)+3*(n-2)2 +...+n .

Asked By: RESHU SINGH
is this question helpfull: 9 3 submit your answer
Joshi sir comment

general term of the series = r(n+1-r)= r(n+1)2 + r3 - 2(n+1)r2

now put sigma then solve                                       

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