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Let f: R to R be defined as f(x)={{:(...

Let `f: R to R ` be defined as `f(x)={{:(x^(5) sin""((1)/(x))+5x^(2)",",x lt0),(" 0,", x=0),(x^(5) cos""((1)/(x))+ lambdax^(2)",",x gt 0):}` The value of ` lambda ` for which `f''(0) ` exists , is ____________

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JEE MAINS PREVIOUS YEAR-JEE MAINS 2020-MATHEMATICS
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  2. Set A has m element and Set B has n element . If the total numbers of ...

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  3. Let f: R to R be defined as f(x)={{:(x^(5) sin""((1)/(x))+5x^(2)","...

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  4. If veca and vecb are unit vectors, then the greatest value of sqrt(3)...

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  5. Let AD and BC be two vertical poles at A and B respectively on a horiz...

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  6. The angle of elevation of the top of a hill from a point on the horizo...

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  7. Let f:R rarr R be a function which satisfies f(x+y)=f(x)+f(y) AA x, ...

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  8. If the sum of first 11 terms of an A.P., a(1),a(2),a(3),.... is 0(a(1...

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  9. Let E^(C) denote the complement of an event E. Let E(1),E(2) and E(...

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  10. If the equation cos^(4)theta+sin^(4) theta+lambda=0 has real solutions...

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  11. An equilateral trinagle is inscribed in parabola y^2=8x whose one ver...

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  12. Find the imaginary part of ((3+2sqrt(-54))^(1/2)-(3-2sqrt(-54))^(1/2))

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  13. A plane passing through the point (3,1,1) contains two lines whose dir...

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  14. Let A={X=(x, y, z)^(T): PX=0" and "x^(2)+y^(2)+z^(2)=1}, where P=[(1,2...

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  15. The equation of the normal to the curve y=(1+x)^(2y)+cos^(2)(sin^(-1)...

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  16. Consider a region R={(x,y) in R^(2):x^(2) le y le 2x}. If a line y= al...

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  17. Let f:(-1,oo) rarr R be defined by f(0)=1 and f(x)=1/x log(e)(1+x), x ...

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  18. Which of the following is a tautology?

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  19. If f(x) be a quadratic polynomial such that f(x)=0 has a root 3 and f(...

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  20. Let S be the sum of the first 9 terms of the series : {x+ka}+{x^(2)...

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