The solution  of   $\frac{d^{2}x}{dy^{2}}-x=k$ , where k is a non-zero constant , vanishes  when y=0 and tends  of finite limit as y  tends to infinity , is 

A) $x=k(1+e^{-y})$

B) $x=k(e^{y}+e^{-y}-2)$

C) $x=k(e^{-y}-1)$

D) $x=k(e^{y}-1)$


Which of the following inequality is true for x>0 ?

A) $\log(1+x) < \frac{x}{1+x} < x$

B) $ \frac{x}{1+x} < x < \log(1+x) $

C) $ x < \log(1+x) < \frac{x}{1+x}$

D) $ \frac{x}{1+x} < \log(1+x) < x$


Using  Rolle's theorm , the equation 


 has atleast one root betwwen 0 and 1, if

A) $\frac{a_{0}}{n}+ \frac{a_{1}}{n-1}+.....+a_{n-1}=0$

B) $\frac{a_{0}}{n-1}+ \frac{a_{1}}{n-2}+.....+a_{n-2}=0$

C) $na_{0}+(n-1) a_{1}+.......+a_{n-1}=0$

D) $\frac{a_{0}}{n+1}+ \frac{a_{1}}{n}+.....+a_{n}=0$


 At t=0, the function   $f(t)=\frac{\sin t}{t}$ has 

A) a minimum

B) a discontinuity

C) a point of inflexion

D) a maximum


From the city population , the probabilty of  selecting a male or smoker is  $\frac{7}{10}$ , a male smoker is $\frac{2}{5}$ and a male, if a smoker is already selected , is $\frac{2}{3}$ . Then , the probability of 

A) selecting a male is $\frac{3}{2}$

B) selecting a smoker is $\frac{1}{5}$

C) selecting a non -smoker is $\frac{2}{5}$

D) selecting a smoker , if a male is first selected , is given by $\frac{8}{5}$