1. Let N = 2 + 22 + 222 + ... upto 30000 terms.

a) last digit of N is 0

b) last four digits of N are 580

c) last four digits of N are 9580

d) All of the Above

Explanation:

2. Let \[\left(1+x\right)^{2}\left(1+\frac{x}{2}\right)^{2}\left(1+\frac{x}{2^{2}}\right)^{2}\left(1+\frac{x}{2^{3}}\right)^{2}... \infty\]

\[=a_{0}+a_{1}x+a_{2}x_{2}+... \infty\]

then

a) \[a_{1}=4\]

b) \[a_{2}=20/3\]

c) \[a_{2}=16/3\]

d) Both a and b

Explanation:

3. If a, b, c, d are in G.P., then value of
\[\left(a – c\right)^{2} + \left(c – b\right)^{2} + \left(b – d\right)^{2} –\left(d – a\right)^{2}\]

is independent of

a) a

b) b

c) c

d) All of the Above

Explanation: Let common ratio be r. Given expression equals

4. If sum of the infinite G.P. p, 1, 1/p, 1/p^{2}, .... is 9/2, then value of then value of p is

a) 2

b) 3/2

c) 3

d) Both b and c

Explanation:

5. If a, b, c are in A.P., and \[a^{2} , b^{2} , c^{2} \] are in H.P., then

a) a = b = c

b) – a, 2b, 2c are in G.P.

c) a, b, c are in G.P.

d) All of the Above

Explanation:

6. Let \[\log x=\log_{10}x\forall x>0\]

suppose x,y,z>1, then least value of

\[E=\log\left(xyz\right)=\left[\frac{\log x}{\log y \log z}+\frac{\log y}{\log z \log x}+\frac{\log z}{\log x \log y}\right]\]

is

a) 3

b) 6

c) 9

d) 18

Explanation:

7. Number of solution of \[e\log_{e}x=x\]

is

a) 0

b) 1

c) 2

d) infinite

Explanation: It is defined for x > 0

It has exactly one solution

8. If a,b \[\geq\] 1, a+b=10 ,then minimum value of \[\log_{3}a+\log_{3}b\] is

a) 2

b) \[2\log_{3}5\]

c) \[\frac{1}{2}\log_{3}5\]

d) 1

Explanation:

9. If \[5^{x}=7^{x+1}\] , then x is equal to

a) \[\frac{1}{\log_{5}7+1}\]

b) \[\frac{1}{\log_{7}5-1}\]

c) \[\log_{7}5\]

d) \[\log_{5}7\]

Explanation:

10. Let \[\left(x_{0},y_{0}\right)\] be the solution of the following system of equations

\[\left(2x\right)^{ln2}=\left(3y\right)^{ln3}\]

\[3^{lnx}=2^{lny}\]

then \[x_{0}\] is equals to

a) 1/6

b) 1/3

c) 1/2

d) 2

Explanation: