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/p2, .... 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:
