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If f(x)= f(a+x) then prove that the valu...

If f(x)= f(a+x) then prove that the value of `overset(a+t)underset(a)int f(x)dx` is independent of a.

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UNITED BOOK HOUSE-QUESTION PAPER 2017-EXERCISE
  1. A particle starts with the velocity u and moves in a straight line, i...

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  2. Find the interval where f(x) = 1/(1+x^2) decrease.

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  3. If f(x)= f(a+x) then prove that the value of overset(a+t)underset(a)in...

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  4. If vec a= 3hati+hatj+9 hat k and vecb = hati +lambda hat j+3 hat k the...

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  5. Find the vector equation of a plane through the point hati+ hat j+hat ...

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  6. If P(A)=2/3,P(B)=1/2 and P(AnnB)=1/6 then find the value of P(AnnB^C).

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  7. Solve: tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)(8/31).

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  8. If A=([2,-1],[1,3]) then show that A^2-5A+7I2=0 hence find A^(-1)

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  9. Solve by Cramer's rule: x+3y= 4,y+3z = 7, 4x+z= 6.

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  10. Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2.

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  11. If f(x)= ((a+x)/(b+x))^(a+b+2x) then prove that f'(0)= [2log(a/b)+(b...

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  12. Evaluate: int (xdx)/(x^4-x^2+1)

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  13. Solve: ydx-(x+2y^2)dy=0.

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  14. In a certain culture the rate of increment of bacterial at any instant...

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  15. The position vectors of four points A,B,C and D are 4hati+8 hat j+12ha...

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  16. If a vector 2 i ^ +3 j ^ ​ +8 k ^ is perpendicular to the vecto...

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  17. Evaluate: overset(pi/4)underset(0)intlog(1+tan theta)d theta.

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  18. find the value of overset(2)underset(1)int 5x^2dx.

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  19. A man is known to speak the truth 3 out of 4 times. HE throws an unbia...

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  20. If the sum of the mean and variance of a binomial distribution for 5 r...

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