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If y=(x+sqrt(1+x^2))^n , then show that ...

If `y=(x+sqrt(1+x^2))^n` , then show that `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=n^2y`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
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  2. Find whether the following function is differentiable at x = 1 and x...

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  3. If y=(x+sqrt(1+x^2))^n , then show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(d...

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  4. Find the point on the curve 9y^2=x^3, where the normal to the curve ma...

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  5. Find the equation of a plane which passes through the point (3, 2, ...

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  6. The two vectors hat j+ hat k and 3 hat i- hat j+4 hat k represent t...

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  7. Evaluate : int(-pi/2)^(pi/2)(cosx)/(1+e^x)dx

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  8. Evaluate : int(x^2)/((x^2+4)(x^2+9))dx

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  9. Two numbers are selected at random (without replacement) from posit...

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  10. If A=[[2,-1],[-1, 2]] and I is the identity matrix of order 2, then ...

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  11. If A=[[1,-1],[ 2,-1]] and B=[[a,1],[b,-1]] and (A+B)^2=A^2+B^2, then f...

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  12. Three machinesE1, E2 and E3 in a certain factory producing electric...

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  13. A shopkeeper has 3 varieties of pens ‘A’, ‘B’ and ‘C’. Meenu purcha...

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  14. Using properties of determinants, show that ABC is isosceles if |(1,1,...

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  15. A trust invested some money in two type of bonds. The first bond pays...

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  16. If cos^(-1)(x/a) + cos^(-1) (y/b) = a show that : (x^2)/(a^2) - (2xy...

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  17. Find : int(3x+1)sqrt(4-3x-2x^2)dx

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  18. Form the differential equation of the family of circles in the second ...

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  19. Solve the differential equation : y+x(dy)/(dx)=x-y(dy)/(dx)

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  20. Prove that the least perimeter of an isosceles triangle in which a cir...

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