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Question 1
If x + 1/x = √5 then the value of x3 + 1/x3 is:
Question 2
If a + b + c = 4
and a2 + b2 + c2 = 16, then the ratio a : b : c is
and a2 + b2 + c2 = 16, then the ratio a : b : c isQuestion 3
If x2 + y2 = 29 and xy = 10, where x>0, y>0, x>y then the value of 
is
isQuestion 4
If 
, then find the value of (a+b+c)3 - 27abc
Question 5
If α and β are two roots of the quadratic equation 9x2-60x+100 =0. Then frame a quadratic equation with roots -α and (α +β).
Question 6
If 
, then 
is ?
, then is ? Question 7
If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?
Question 8
If x = 2t and 
then what is the value of t for which x = y holds?
then what is the value of t for which x = y holds?Question 9
If a + b = 1, c + d = 1 and a – b = 
then, the value of c2 – d2 is
then, the value of c2 – d2 is Question 10
If a+b+c = 13, what is the maximum value of (a-3)(b-2)(c+1). It is given that (a-3),(b-2),(c+1) are all positive numbers.
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Jun 23CDS & Defence
