CAT4MBA

1) If log ₄ 5 =1 and log ₅ 6=b.Then log ₅ 2=?

2)Find the value of 1/log ₂ X +1/ log₃ X +1/log ₄ X +1/log ₅ X.

3)What is the number of zeros coming immediately after the decimal point in the value of (0.2)²⁵? (log ₁₀ 2=0.301303)

4)If log _y x=8 and log _10y 16x=4;y=?

5)[3log _(3x2) 27]-[2log _(3x) 9]=0;x=?

6)If log _e 2 * log _p 625 =log ₁₀ 16 *log _e 10. What is the value of p.

7)x ²+bx+c=0 has roots such that LCM of(a,b)=24 and HCF of (a,b)=2.What is the total number of such quadratic equation if a and b are natural number.

8) How many positive integers p,q,r exist such that p/q+q/r+r/p=2.

9) Sum of all the real roots of the equation mod(x-2) ² +mod(x-2) -2 =0 is?

10)If the pth,qth,rth terms of a G.P. be 27,8,12 respectively ,then the equation px²+2qx-2r=0 has
a) Only 1 root (0,1)
b) No root in (0,1)
c) Both roots in (0,1)
d) Integer roots

11)If a,b be the roots of the equation x²+ax+b=0 and m,n,p,q are discreet integers in A.P. such that the values of a,m,n,p,q,b are in ascending order and q= m ²+n ²+ p²,then which of the following is true?
a) b+1+mod a is greater than 0   b) b+1+mod a=0
c) b+mod a=0                          d) 1+b+mod a is smaller than 0 

12) ax²+bx+c is real for real values of x (a,b,c are rational nimbers)and imaginary for imaginary value of x,then
a) a is positive   b) a is negative  c) a=0  d) nothing can be said

13)If x+1/x=1 and p=x ⁴⁰⁰⁰+1/x⁴⁰⁰⁰ and q be the digit at unit place in the number ₂ 2ⁿ +1,n being a natural number greater than 1,then p+q=?

14) There are two quadratic expression a₁x+b₁x+c₁ and a₂x+b₂x+c₂.Both of them have the same roots.If the ratio of a₁ to a₂ is 1:2.What is the ratio of the maximum value of the two quadratic expression (a1,a2 are positive).

15)Given that P,Q are the roots of Ax²-4x+1=0 and R,S are the roots of the equation Bx²-6x+1=0.What is the value of  A so that P,Q,R,S are in H.P.?

16) If a+b+c=0; a,b,c are natural number then which of the following is true about the roots of the quadratic equation (b+c-a) x ²+(c+a-b) x+(a+b-c)=0 ?