A DAS GUPTA-Miscellaneous Exercises-Exercise
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- If usin t + vcos t = 5 and ucos t - vsin t = 7 then (ddotu)(dotv) - ...
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- If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(pri...
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- Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(...
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- One diagonal of a square is the portion of the line 7x + 5y= 35 interc...
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- Let f(x) = 2sin^(2)beta + 4cos(x + beta)* sin x* sin beta + cos 2(x + ...
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- A positive integral power of the imaginary quantity i is taken at ran...
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- 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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