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Grade: 11
        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


10 years ago

Answers : (4)

Badiuddin askIITians.ismu Expert
147 Points
							

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


Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
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 All the best vishrant .
 
Regards,
Askiitians Experts
Badiuddin


10 years ago
neha
11 Points
							
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
4 years ago
Vikaa
22 Points
							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
						
2 years ago
Vikaa
22 Points
							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.
						
2 years ago
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