Q1. Given that x^3+y^3=72 and xy = 8 with x > y, then the value of x – y is:
(a) 2
(b) -2
(c) 4
(d) 5
Q3. If x+(1/x)=2, then the value of x^12-(1/x^12) is:
(a) 0
(b) 2
(c) -2
(d) 3
Q4. If x+(1/x)=1, then the value of (x^2+3x+1)/(x^2+7x+1) is:
(a) 1/2
(b) 2/5
(c) 7
(d) 0
Q5. If x+(1/x)=2, then the value of x^7+(1/x^5) is:
(a) 0
(b) 2^7
(c) 20
(d) 2
Q6. The term, that should be added to (4x^2+8x) so that resulting expression be a perfect square is:
(a) 2x
(b) 3x
(c) 4x
(d) 4
Q7. If 999x + 888y = 1332 and 888x + 999y = 555 then x + y = ?
(a) 1
(b) 999
(c) 888
(d) 0
Q8. If a^2+b^2+c^2=ab+bc+ca, then the value of (a+c)/b is
(a) 0
(b) 2
(c) 4
(d) 5
Q9. ABC is a right-angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b and c are the length of the sides BC, CA and AB respectively, then
(a) 1/p^2 =1/b^2 -1/a^2
(b) 1/p^2 =1/a^2 +1/b^2
(c) 1/p^2 +1/a^2 =1/b^2
(d) 1/p^2 =1/a^2 -1/b^2
Q10. The orthocenter of a right-angled triangle lies
(a) outside the triangle
(b) at the right angular vertex
(c) on its hypotenuse
(d) within the triangle
Solutions
S1. Ans.(a)
Sol. Given, x^3+y^3=72
xy = 8
(x > y)
If we take x = 4 and y = 2
4^3+2^3=72
(72 = 72)
And xy = 8
⇒ 4 × 2 = 8
So x – y = ?
4 – 2 = 2
S6. Ans.(d)
Sol. Given expression
⇒ 4x^2+8x
Let P should be added,
⇒ 4x^2+8x+p
⇒(2x)^2+2×(2x)×2 +2×2
[(a+b)^2=a^2+b^2+2ab]
Term that should be added =2^2=4
S8. Ans.(b)
Sol. According to the question,
a^2+b^2+c^2=ab+bc+ca
Put a = 1, b = 1, c = 1
∴1^2+1^2+1^2=1×1+1×1+1×1
1 + 1 + 1 = 1 + 1 + 1
3 = 3 [Satisfy]
∴(a+c)/b=(1+1)/1=2
S10. Ans.(b)
Sol. Orthocenter is the point of intersection of the altitudes. Each leg in a right triangle forms an altitude. So, in a right-angled triangle, the orthocenter lies at the vertex containing the right angle.
