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Questions(204)
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if $p,~q,~r$ are in arithmetic progression, then $m^p,~m^q,~m^r$ are in geometric progression or harmonic progression or arithmetic progression?
If angles of a triangle are in arithmetic progression with common difference equal to smallest angle, then what are the angles of the triangle?
Consider a sequence $\{a_i\}$ of natural numbers. $a_1,~ a_2,~ a_3,\cdots$ are given by $a_k= 11k+2 + 122k+11$. When the product $a_1.a_2.a_3 \cdots a_{2012}.a_{2013}$ is divided by 11, what is the remainder?
At the foot of the mountain the angle of elevation of its summit is found to be 45° by a climber. When he climbs 1000 m up the mountain inclined at an angle of 30°, he finds the angle of elevation of its summit to be 60°. Find the height of the mountain.
The digits of three digit number are in arithmetic progression. If the number is subtracted from the number formed by reversing the digits, the result is 396. What could be the original number?
if $21(a^2+b^2+c^2)=(a+2b+4c)^2$ then prove that a,b,c are in G.P.
What digit should be put in place of 'c' in 38c to make it divisible by
(1) 2
(2) 3
(3) 4
(4) 5
(5) 6
(6) 9
(7) 10
A number 15B is divisible by 6. Which of the following will be true about the positive integer B?

a)B will be even
b)B will be odd
c)B will be divisble by 6
d)both a and c
If an integer is divisible by both 8 and 15,then the integer also must be divisible by which of the following?
a)16  b)24 c)32 d)36 e)45
Find the maximum value of n such that
42 × 57 × 92 × 91 × 52 × 62 × 63 × 64 × 65 × 66 × 67
is perfectly divisible by $(42)^n$.

a)4
b)3
c)5
d)6