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Consider f: R rarr [-5,oo) given by f(x...

Consider `f: R rarr [-5,oo)` given by `f(x)=9x^2+6x-5` . Show that `f` is invertible with `f^(-1)(y)=((sqrt(y+6)-1)/3)dot`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ...

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  2. Let A = R × R and * be the binary operation on A defined by (a, b) ...

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  3. Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is...

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  4. Evaluate: int(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

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  5. Find the vector equation of the line passing through the point (1,2...

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  6. Find the area of the region bounded by the parabola y=x^2 and y=|x| .

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  7. Find the particular solution of the differential equation(tan^(-1)y-x)...

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  8. Using elementary transformations, find the inverse of the matrix : [...

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  9. If vec a= hat i-\ hat j+7 hat k and vec b=5 hat i-\ hat j+lambda h...

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  10. Use product [[1,-1, 2],[ 0, 2,-3],[ 3,-2, 4]] [[-2, 0, 1],[ 9, 2,-3],[...

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  11. Find the angle between the line (x+1)/2=(3y+5)/9=(3-z)/(-6) and the ...

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  12. Solve the following differential equation: cos^2x(dy)/(dx)+y=tanx

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  13. Solve the following differential equation: e^xtany\ dx+(1-e^x)sec^2y...

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  14. Find the value of a for which the function f defined by f(x)={asin(pi...

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  15. int2/((1-x)(1+x^2))dx

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  16. Consider the binary operation ** on the set {1, 2, 3, 4, 5} defined by...

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  17. Write the intercept cut off by the plane 2x+y-z=5 on x-axis

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  18. Using properties of determinants, prove that |-a^2a b a c b a-b^2b cc...

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  19. Write the principal value of t a n^(-1)[t a n(3pi)/4]dot

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  20. Show that the right circular cylinder, open at the top, and of give...

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