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Let f : R rarr R be a function defined a...

Let `f : R rarr R` be a function defined as
`f(x) = {{:(3(1-(|x|)/(2)),"if",|x| le 2),(0,"if",|x| ge 2):}`
Let `g : R rarr R` be given by `g(x) = ƒ(x + 2) – ƒ(x – 2)`. If n and m denote the number of points in R where g is not continuous and not differentiable, respectively, then n + m is equal to _______.

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JEE MAINS PREVIOUS YEAR-JEE MAINS 2021-MATHEMATICS (SECTION-B)
  1. The sum of all the elements in the set {n in {(1, 2, ……., 100} | H.C.F...

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  2. The area (in sq. units) of the region bounded by the curves x^(2) + 2y...

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  3. Let f : R rarr R be a function defined as f(x) = {{:(3(1-(|x|)/(2))...

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  4. If the constant term, in binomial expansion of (2x^(r) + (1)/(x^(2)))^...

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  5. Let y = y(x) be the solution of the differential equation ((x+2)e^(((y...

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  6. The number of elements in the set {n in {1, 2, 3,…, 100} | (11)^(n) gt...

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  7. Let n in N and [x] denote the greatest integer less than or equal to ...

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  8. Consider the function {:( f(x) (P(X))/(sin (x-2)), x ne 2 ),(=7,x=2)...

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  9. Equation of circle Re(z^2)+2(img(z))^2+2Re(z)=0 where z=x+iy .A line p...

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  10. If a rectangle is inscribed in an equilateral triangle of side length ...

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  11. If (veca + 3 vecb) is perpendicular to ( 7 veca - 5 vecb) and ...

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  12. Let a curve y = f(x) pass through the point (2, (loge 2)^2) and have...

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  13. If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a^4...

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  14. A coin is tossed n times, if the probability of getting at least one h...

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  15. If the coefficients of x^(7) and x^(8) in the expansion of (2+(x)/(3))...

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  16. If the lines (x-k)/(1) = (y-2)/(2) = (z-3)/(3) and (x+1)/(3) = (y ...

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  17. For real numbers alpha and beta, consider the following system of line...

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  18. Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) and vec(c )= hat(j)-hat(...

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  19. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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  20. Find the domain of function f(x)=(log)4[(log)5{(log)3(18 x-x^2-77}]

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