Processing math: 28%




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31.

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now, 1 ball is drawn at random from U2

 

Given that the drawn ball from U2 is white. the probability that head appeared on the coin is


A) 1723

B) 1123

C) 1523

D) 1223



32.

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now, 1 ball is drawn at random from U2

The probability of the drawn ball from U2 being  white is


A) 1330

B) 2330

C) 1930

D) 1130



33.

Let f:RR be a function such that f(x + y)= f(x) + f(y),x,yϵR. If f(x) is  differentiable at x = 0, then


A) f(x) is differentiable only in a finite interval containing zero

B) f(x)is continuous,xϵR

C) f'(x) is constant xϵR

D) f(x)is differentiable except at finitely many points



34.

The vector(s) which is/are coplanar with vectors   \widehat{i}+\widehat{j}+2\widehat{k} and \widehat{i}+2\widehat{j}+\widehat{k} , are  perpendicular to the vector  \widehat{i}+\widehat{j}+\widehat{k} is/are 


A) \widehat{j}-\widehat{k}

B) -\widehat{i}+\widehat{j}

C) \widehat{i}-\widehat{j}

D) \widehat{-j}+\widehat{k}



35.

Let the eccentricity of the hyperbola  \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} =1 be reciprocal to that of the ellipse x2 + 4y2 = 4. If the hyperbola passes through a focus of the ellipse, then


A) the equation of the hyperbola is \frac{x^{2}}{3^{2}}-\frac{y^{2}}{2^{2}}=1

B) a focus of the hyperbola is (2, 0)

C) the eccentricity of the hyperbola is \sqrt{\frac{5}{3}}

D) the equation of the hyperbola is x^{2}-3y^{2}=3



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