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If the straight line xcosalpha+ysinalpha...

If the straight line `xcosalpha+ysinalpha=p` touches the curve `(x^2)/(a^2)+(y^2)/(b^2)=1` , then prove that `a^2cos^2alpha+b^2sin^2alpha=p^2dot`

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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
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  2. Let f,g : [-1,2] to be continuous functions which are twice different...

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  3. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

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  4. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

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  5. The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is ver...

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  6. On the ellipse 4x^2+9y^2=1, the points at which the tangents are paral...

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  7. If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >...

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  8. If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...

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  9. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

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  10. The length of the longest interval in which the function 3sinx-4sin^3x...

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  11. If f(x)=xe^(x(1-x)), then f'(x) is

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  12. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

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  13. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

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  14. The function f(x)=(log (pi+x))/(log (e+x))," is "

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  15. Let fa n dg be increasing and decreasing functions, respectively, from...

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  16. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

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  17. Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h ...

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  18. Let f(X) be a polynomila of degree four having extreme values at x =1 ...

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  19. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

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  20. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  21. The total number of local maxima and local minima of the function f...

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