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A DAS GUPTA-Miscellaneous Exercises-Exercise
- If z is a complex number such that zbarz = 1 and amp frac{z}{bar z}= ...
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- If 4 sin^(-1)x + cos^(-1)x=pi, then: x=
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- The solution set of f'(x)>g'(x) where f(x)=(1/2)5^(2x+1) and g(x)=5^x+...
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- lim(n to ∞) frac{a^n}{n!} is equal to .
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- The differential coefficient of 2^x w.r.t. x^2 is.
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- A natural number less than or equal to 200 is written down at random....
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- A box contains 100 tickets numbered 1, 2, 3, ... ,100. Two tickets ar...
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- Prove that two parabolas having the same focus and their axes in oppos...
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- If a, b, c and d are positive real numbers such that a+b+c+d= 1 then p...
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- A vertical lamp-post of height h stands at a point on the boundary of...
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- Find the equations of straight lines which pass through the intersecti...
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- The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...
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- Solve - frac{sin^(3) frac{x}{2} -cos^(3) frac{x}{2}}{2 +sinx} = cosx/3
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- let f(x) be the polynomial function. It satisfies the equation 2 +f(x)...
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- Evaluate int(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx.
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- Find the co-ordinates of all the points P on the ellipse, x^2/a^2+y^2/...
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- Find the equation of a curve passing through the point (1.1) if the pe...
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- Solve: (x^2 + 4y^2 + 4xy) dy = (x + 2y + 1) dx.
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- If the normal to the ellipse (x^(2))/9+(y^(2))/4=1 which is farthest f...
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- sum(n=0)^oo1/(n !)[sum(k=0)^n(k+1)int0^1 2^(-(k+1)x)dx]
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