Processing math: 18%




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11.

 The solution  of the differential equation  dθdt=k(θθ0) where k is constant , is ...................

θ=θ0+aekt


A) θ=θ0+aekt

B) θ=θ0+aekt

C) θ=2θ0aekt

D) θ=2θ0aekt



12.

\int\frac{x^{2}+1}{x^{4}-x^{2}+1}dx=.......


A) \tan^{-1}\left(\frac{x^{2}+1}{2}\right)+c

B) \tan^{-1}(x^{2})+c

C) \tan^{-1}\left(\frac{x^{2}-1}{2}\right)+c

D) \tan^{-1}(2x^{2}-1)+c



13.

 Using differentiation , approximate value of  f(x)= x2-2x+1  at x=2.99 is


A) 3.96

B) 9.96

C) 4.98

D) 5.98



14.

 The vectors  x\hat{i}-3\hat{j}+7\hat{k} and    \hat{i}+y\hat{j}-z\hat{k} are collinear then the value of

  \frac{xy^{2}}{z} is equal 


A) \frac{9}{7}

B) \frac{-9}{7}

C) \frac{-7}{9}

D) \frac{7}{9}



15.

 The negation of '" \forall,n\in N, n+7>6 "  is ................


A) \exists n\in N, such that n+7 \leq6

B) \exists n\in N, such that n+7 \geq6

C) \forall n\in N, n+7 \leq 6

D) \exists n\in N, such that n+7 < 6



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