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Question Bank - Algebra - Hemant Malhotra

Amar Rajput last edited by @hemant_malhotra

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B

badalravi last edited by @hemant_malhotra

@hemant_malhotra x=4, y=2, z=4
96
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra said in Question Bank - Algebra - Hemant Malhotra:

If a^2 = 5a - 3 and b^2 = 5b - 3 then find the quadratic eqn whose roots are a/b and b/a

3x^2-19x+3=0
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra d.......
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra said in Question Bank - Algebra - Hemant Malhotra:

Let a < b < c be the three real roots of the equation √2014 x^3 - 4029 x^2 + 2 = 0. Find b(a + c).

@zabeer sir help
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra (8/3)^4 ( 5) ^5
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra ...........d............
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Amar Rajput last edited by @hemant_malhotra

@hemant_malhotra 20 .....................
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Anurag MN last edited by @hemant_malhotra

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Anurag MN last edited by @hemant_malhotra

@hemant_malhotra said in Question Bank - Algebra - Hemant Malhotra:

Let a < b < c be the three real roots of the equation √2014 x^3 - 4029 x^2 + 2 = 0. Find b(a + c).

https://artofproblemsolving.com/wiki/index.php/2014_AIME_I_Problems/Problem_9
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cat questions86 quant - mixed bag73 question bank47 theory of equations14 permutation & combination11 time speed & distance10 cat questions lr10 set theory7

Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 1
Quant - Boosters • question bank theory of equations • • zabeer

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x^2 + y^2 - xy = x + y (x - y)^2 + (x -1)^2 + (y -1)^2 = 2 (0,0) (0,1) (1,0) (2,2) (1,2) (2,1) 6 integral solutions 3 positive integer solutions [credits : @Raman_Sharma]
Question Bank - Number of Integral/Positive/Non-Negative Solutions - Set 2
Quant - Boosters • question bank theory of equations • • zabeer

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@vikas_saini can u plz explain 2nd and 3rd+4th step again. 2nd step:what is -1-what are we reducing in it 3rd step: 3rd+4th step doesnt giv value in 2nd step. what are we missing in it. 3rd+4th= 2T-2
Quant Boosters - Geometry - Raman Sharma - Set 1
Quant - Boosters • question bank • • Raman_Sharma

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@raman_sharma BC =1 , CA =2 so AB =rt5using similarity in triangle ABC and ADCwe get CD= 2/rt5 and diameter of circle as 4/rt5 now using tangent secant theoremCD^2 = CE * AC4/5 = CE *2CE =0.4so AE=1.6hence 1.6/0.4 = 4
Quant Boosters - Rajesh Balasubramanian - Set 4
Quant - Boosters • question bank time speed & distance • • rajesh_balasubramanian

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@rajesh_balasubramanian Hello. I was just looking for an online CAT coaching and stumbled upon this. The answer seems to be 7. And i don't think 10 can be a value for B. Eg: Take the Track length as 300m. A will complete it in 50secs. And B will take 75 secs to overlap A for the first time(300/4). I can email you my solution if you'd like to give it a look. Thank you.
Quant Boosters - Kamal Lohia - Set 7
Quant - Boosters • quant - mixed bag question bank • • kamal_lohia

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Q30) Given f(x) = x - 1/x, solve the equation f(f(x)) = x.
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CAT Question Bank - Binomial Theorem
Quant - Boosters • question bank binomial theorem • • Rowdy Rathore

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General term - nCr * (x^2)^(n-r) (3y)^r It is given that 2n - 2r + r = 52n - r = 5n = 4 => r = 3 So the term we have here is 4C3 * (x^2)^1 (3y)^3Coefficient = 4C3 * 3^3 = 4 * 27 = 108
Quant Boosters - Hemant Yadav - Set 1
Quant - Boosters • quant - mixed bag question bank • • zabeer

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1/x + 1/y = 1/n=> xy = nx + ny=> (x - n)(y - n) = n² Now, n² must have 5 factors to get 5 ordered pairs=> n must be of form p², where p is prime number Hence all primes less than 20
Quant Boosters - Hemant Yadav - Set 3
Quant - Boosters • quant - mixed bag question bank • • zabeer

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Let students be x (X/2)-1 /x >=0.47 ( for x even)(X/2 -0.5)/x >=0.47 (x being odd case) It satisfies at x=17( min)

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