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Prove that (d)/(dx)[(sin2x+1/(cos^2x)]...

Prove that `(d)/(dx)[(sin2x+1/(cos^2x)]

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Show that the line passing through the points (a1,b1,c1) and (a2,b2,c2...

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  2. What is the number of line which are equally inclined to the axes?

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  3. Prove that (d)/(dx)[(sin2x+1/(cos^2x)]

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  4. If y=e^x+a^x+x^x, then find dy/dx at x=a

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  5. Show that the semivertical angle of a cone of given slant height is ta...

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  6. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  7. If a line in the space makes angles alpha, beta  and gamma  with the c...

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  8. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  9. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  10. Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc...

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  11. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  12. int(x^2+1)/(x^4+x^2+1)dx

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  13. Show that int0^1(Inx)/sqrt(1-x^2)dx=pi/2In1/2

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  14. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

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  15. If A is a non-singular square matrix of order n, then what is abs(adj ...

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  16. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

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  17. Find least non negative integer r such that 1936xx8789 -= r"(mod4)"

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  18. What is the number of independent constants in the equations of a plan...

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  19. What is the antiderivative of 5^(5+x)?

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  20. What is the order of the matrix B if [2 3 5 -1] B=[1 3 2 5 -4 1] .

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