45 - Algebra Questions Answers

Mathematics >> Algebra >> Sequence and Series IIT JEE

Find Sum to n terms

x/1-x² + x²/1-x⁴ + x⁴/1-x⁸ + ....

Asked By: LUFFY

is this question helpfull: 3 0 submit your answer

Joshi sir comment

$\frac{x}{1 - x^{2}} = \frac{1}{1 - x} - \frac{1}{1 - x^{2}} b r e a k a l l t e r m s s i m i l a r l y a n d s o l v e$

Maths >> Algebra >> Equation and Enequalities IIT JEE

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

Asked By: VAIBHAV GUPTA

is this question helpfull: 18 3 submit your answer

Joshi sir comment

two times sign change so 2 positive roots

Maths >> Algebra >> Equation and Enequalities IIT JEE

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)²+3*(n-2)² +...+n .

Asked By: RESHU SINGH

is this question helpfull: 10 3 submit your answer

Joshi sir comment

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

now put sigma then solve

Maths >> Algebra >> Binomial Theorem IIT JEE

If x+y = 1 ,then ∑ r ⁿC_rx^ry^n-requals nx....How??

Asked By: RESHU SINGH

is this question helpfull: 6 1 submit your answer

Joshi sir comment

∑ r ⁿC_rx^ry^n-r

= ∑ r ⁿC_rx^r(1-x)^n-r

= ∑ r n!/r!(n-r)! x^r(1-x)^n-r

= n (n-1)!/(r-1)!(n-r)! x^r(1-x)^n-r

= n ⁽^n-1)C₍_r-1)x^r(1-x)^n-r

= n ⁽^n-1)C_rx^r+1(1-x)^n-r-1let r = r+1

= nx ⁽^n-1)C_rx^r(1-x)^n-r-1

^{now solve}

Maths >> Algebra >> Binomial Theorem Others

What is the value of 0⁄0? if its otherthan 1, then how this can be true: lim (e^x-1)/x = 1

^{x −−>0}

Asked By: BONEY HAVELIWALA

is this question helpfull: 2 1 submit your answer

Joshi sir comment

exact 0 and lim tends to 0 are different

Maths >> Algebra >> Permutation and Combination IIT JEE

what will be the rank of word OPTION in the dictionary of words formed by letters of the word OPTION

Asked By: JIGYASA KUMAR

is this question helpfull: 13 6 submit your answer

Joshi sir comment

OPTION

ordered way INOOPT

total words = 6!/2! = 360

so rank = (360/6)*2+([60*2]/5)*3+(24/4)*3+(6/3)*0+(2/2)*1+1 = 120+72+18+0+1+1 = 212

Maths >> Algebra >> Matrices and Determinant Engineering Exam

prove using property of determinant

1. a+b+c -c -b

-c a+b+c -a = 2(a+b)( b+c ) (c+a)

-b -a a+b+c

Asked By: SONAM SHARMA

is this question helpfull: 12 4 submit your answer

Joshi sir comment

first use C1 = C1+C2+C3

then R1 = R1+R2 and R2 = R2+R3

after it solve mathematically

Maths >> Algebra >> Permutation and Combination IIT JEE

rank of the number 3241?(digits cannot be repeated)

Asked By: HARSHITH

is this question helpfull: 7 2 read solutions ( 1 ) | submit your answer

Joshi sir comment

total numbers = 4*3*2*1 = 24

on arranging these numbers in order we get 1234

so rank = [24/4]*2+[6/3]*1+[2/2]*1+1 = 16

Maths >> Algebra >> Matrices and Determinant Engineering Exam

which is the 4 digit number whose second digit is thrice the first digit and 3'rd digit is sum of 1'st and 2'nd and last digit is twice the second digit.

Asked By: SAURABH TIWARI

is this question helpfull: 6 2 read solutions ( 2 ) | submit your answer

Joshi sir comment

let the 4 digit number is 1000a+100b+10c+d

then according to the given condition b=3a, c=a+b, d=2b

so c=4a, d=6a and b=3a

on putting all the values we get number = 1000a+100(3a)+10(4a)+6a = 1346a

on putting a =1, number = 1346

45 - Algebra Questions Answers

which is the 4 digit number whose second digit is thrice the first digit and 3'rd digit is sum of 1'st and 2'nd and last digit is twice the second digit.

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