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If f:R to R is the function defined by f...

If `f:R to R` is the function defined by `f(x)=4x^(3) +7`, then show that f is a bijection.

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SHARAM PUBLICATION-MODEL QUESTION PAPER -15-EXERCISE
  1. What is the solution of the equation (d^2y)/(dx^2)=e^-(2x)?

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  2. What is the equation of the line passing through the point (1,2,3)and ...

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  3. If f:R to R is the function defined by f(x)=4x^(3) +7, then show that ...

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  4. If R and S are two equivalence relation on the set then prove that Rca...

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  5. If ** is a binary operation on set Q of rational numbers such tht a**b...

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  6. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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  7. [[1,-2],[3,2]][[x,2],[1,y]]=[[-3,4],[-1,4]]Find x and y.

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  8. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  9. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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  10. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  11. For what value of lambda,is the function f(x)={(lambdax^2-2x,if xle0),...

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  12. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  13. If y^2cot x = x^2 coty then find (dy)/(dx)

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  14. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  15. Find two positive numbers whose product is 256 and whose sum is least.

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  16. Integrate:inta/(b+ce^x)dx

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  17. Integrate:int sec(sqrtx)/(sqrtx)dx

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  18. Prove that int0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

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  19. Find the area bounded by y=sinx,y=0,x=pi/2

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  20. Solve : (x+y)dy +(x-y)dx = 0.

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