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1) Let a,b be the two positive numbers, where a > b and 4 x GM = 5 X HM for the nos. Then a is A) 4b B) 1/4 b C) 2b D) b 2) In the value of 100 factorial, the no. of 0s at the end is... A) 11 B) 22 C) 23 D) 24 3) The sum of all proper divisors of 9900 is A) 33851 B) 23952 C) 23951 D) none of these 4) In the sequence 1,2,2,3,3,3,4,4,4,4..., where n consecutive terms have value n, the 150th term is A) 17 B) 16 C) 18 D) none of these 5)log(5c/a), log(3b/5c) and log (a/3b) are in AP, where a, b and c are in GP, then a.a.c are the lengths of the sides of A) Isoceles Triangle B) equilateral C) scalene D) none 6) The co-efficiant of x^15 in the product (1 - x) ( 1 - 2x) (1 - 4x) ( 1 - 8x) ... (1- 2^15 x) is equal to A) 2^105 - 2^121 B) 2^121 - 2^105 C) 2^120 - 2^104 D) none of these 7) The co-efficent of x^49 in product (x - 1) (x - 3)...(x - 99) is A) -99^2 B) 1 C) -2500 d) none of these 8)The sum of n terms of the series 1^2 + 2.2^2 + 3^2 + 2.4^2 +.... is [n(n+1)^2]/2 when n is even. What is sum when n is odd? 9)Th esolution set of mod of [(x +1 )/x] + mod of (X + 1) = (x+1)^2 / mod of (x) is A) x>= 0 B) x > 0 and x = -1 C) X= -1 or 1 D) none of these 10) mod of [(Z - 1)/(z +1)]= 1 represents A) circle B) ellipse C) a straight line D) none of these

1) Let a,b be the two positive numbers, where a > b and 4 x GM = 5 X HM for the nos. Then a is

A) 4b
B) 1/4 b
C) 2b
D) b

2) In the value of 100 factorial, the no. of 0s at the end is...
A) 11
B) 22
C) 23
D) 24

3) The sum of all proper divisors of 9900 is
A) 33851
B) 23952
C) 23951
D) none of these

4) In the sequence 1,2,2,3,3,3,4,4,4,4..., where n consecutive terms have value n, the 150th term is
A) 17
B) 16
C) 18
D) none of these

5)log(5c/a), log(3b/5c) and log (a/3b) are in AP, where a, b and c are in GP, then a.a.c are the lengths of the sides of

A) Isoceles Triangle
B) equilateral
C) scalene
D) none

6) The co-efficiant of x^15 in the product (1 - x) ( 1 - 2x) (1 - 4x) ( 1 - 8x) ... (1- 2^15 x) is equal to

A) 2^105 - 2^121
B) 2^121 - 2^105
C) 2^120 - 2^104
D) none of these

7) The co-efficent of x^49 in product (x - 1) (x - 3)...(x - 99) is
A) -99^2
B) 1
C) -2500
d) none of these

8)The sum of n terms of the series 1^2 + 2.2^2 + 3^2 + 2.4^2 +.... is [n(n+1)^2]/2 when n is even. What is sum when n is odd?

9)Th esolution set of mod of [(x +1 )/x] + mod of (X + 1) = (x+1)^2 / mod of (x) is

A) x>= 0
B) x > 0 and x = -1
C) X= -1 or 1
D) none of these

10) mod of [(Z - 1)/(z +1)]= 1 represents
A) circle
B) ellipse
C) a straight line
D) none of these


Grade:11

4 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear Vishrant Vasvada

a,b be the two positive numbers, where a > b and

   4 x GM = 5 X HM

or 4(ab)^.5 =5*2ab/(a+b)

simplify

4(a/b)2 - 17 (a/b) +4 =0

solve

a/b = 4

a=4b

option a is correct

please post seperate question in seperate post

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Askiitians Experts
Badiuddin


neha
11 Points
7 years ago
4.G.M.=5.A.M.
4root(ab)=5(2ab/a+b)
5root(ab)(a+b)=10ab
squaring both side
16(a+b)square(ab)=100(ab)square
16(a+b)square=100ab
16(a+b)square-100ab+0
16asquare+16bsquare+32ab-100ab=0
16asquqre+16bsquqre-68ab+0
4asquare-17ab+4bsquare=0
4asquqre-16ab-ab+4bsquare=0
4a(a-4b)-b(a-4b)=0
(a-4b)(4a-b)=0
hence
a=4b
Vikaa
22 Points
5 years ago
If a and b are two positive numbers such that a+b=640, where a is 100 greater than b, then find a and b
Vikaa
22 Points
5 years ago
If a and b are two positive numbers such that a+b=640, where a is 100 greater than b, then find a and b.

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