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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 19-EXERCISE
  1. Find the distance of the plane 6x- y + 3z = 3 from the origin.

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  2. Find the least positive integer r such that 185 in [r]7

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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 ** is the binary operation on N given by a**b= L. C. M of a and b. ...

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  5. Show that 2 tan^-1(1/4) + 2 tan^-1 (2/9) = tan^-1(4/3).

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  6. Evaluate int1/(sqrt(x)sqrt(x-a^2))dx.

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  7. Evaluate int (x+3)/sqrt(9-x^2)dx.

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  8. Evaluate intcos(2-7x)dx

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  9. Solve(d^2y)/dt^2=e^(2t)+e^-t.

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  10. Using integration, find the area of the region bounded by the curves ...

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  11. Find the value of a such that the function f defined by f(x)={((sinax...

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  12. Find (dx)/dy when y=(sinx)^x.

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  13. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  14. Find the points on the curve y = x^3 - 11x + 5 at which the equation o...

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  15. If A=[[-1,3,5],[1,-3,-5],[-1,3,5]]Show that A^2=A.

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  16. If [[x+y,x-2],[2x-z,0]]=[[2,5],[3,1]] then the values of x,y,z.

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  17. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

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  18. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  19. If A=[[2,1],[-1,3]] B=[[2,5],[-3,2]] find AB and BA.

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  20. If the sum of two unit vectors is a unit vectors find the magnitude of...

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