Differentiation & Applications · JEE Main previous year questions

2019 11 questions

1. Q82019 · 12 Apr 2019 · Shift 1

   If m is the minimum value of k for which the function $f(x)=x\sqrt{kx-x^2}$ is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when $k=m$, then the ordered pair (m, M) is equal to :

   1. A.$\left(5,3\sqrt{6}\right)$
   2. B.$\left(4,3\sqrt{3}\right)$
   3. C.$\left(4,3\sqrt{2}\right)$
   4. D.$\left(3,3\sqrt{3}\right)$
   Show answer

   Answer: B

2. Q192019 · 12 Apr 2019 · Shift 2

   The equation of common tangent to the curves $y^2=16x$ and $xy=-4$, is :

   1. A.$x-y+4=0$
   2. B.$x+y+4=0$
   3. C.$x-2y+16=0$
   4. D.$2x-y+2=0$
   Show answer

   Answer: A

3. Q262019 · 12 Apr 2019 · Shift 2

   The tangents to the curve $y=(x-2{)}^2-1$ at its points of intersection with the line $x-y=3$, intersect at the point :

   1. A.$\left(\frac{5}{2},-1\right)$
   2. B.$\left(-\frac{5}{2},-1\right)$
   3. C.$\left(\frac{5}{2},1\right)$
   4. D.$\left(-\frac{5}{2},1\right)$
   Show answer

   Answer: A

4. Q282019 · 10 Apr 2019 · Shift 2

   If the tangent to the curve $y=\frac{x}{x^2-3}$ , $x\in \rho$, $(x\ne \pm \sqrt{3})$, at a point $(\alpha ,\beta )\ne (0,0)$ on it is parallel to the line $2x+6y-11=0$, then :

   1. A.$|6\alpha +2\beta |=9$
   2. B.$|2\alpha +6\beta |=11$
   3. C.$|2\alpha +6\beta |=19$
   4. D.$|6\alpha +2\beta |=19$
   Show answer

   Answer: D

5. Q272019 · 9 Apr 2019 · Shift 1

   If the tangent to the curve, $y=x^3+ax-b$ at the point (1, −5) is perpendicular to the line, −x + y + 4 = 0, then which one of the following points lies on the curve ?

   1. A.(2, −2)
   2. B.(2, −1)
   3. C.(−2, 2)
   4. D.(−2, 1)
   Show answer

   Answer: A

6. Q162019 · 8 Apr 2019 · Shift 2

   If $f(1)=1$, $f^{\prime }(1)=3$, then the derivative of $f(f(f(x)))+(f(x){)}^2$ at x = 1 is :

   1. A.33
   2. B.12
   3. C.9
   4. D.15
   Show answer

   Answer: A

7. Q212019 · 8 Apr 2019 · Shift 2

   The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

   1. A.$\sqrt{3}$
   2. B.$2\sqrt{3}$
   3. C.$\sqrt{6}$
   4. D.$\frac{2}{3}\sqrt{3}$
   Show answer

   Answer: B

8. Q192019 · 12 Jan 2019 · Shift 1

   The maximum value of $3\cos \theta +5\sin \left(\theta -\frac{\pi }{6}\right)$ for any real value of $\theta$ is :

   1. A.$\sqrt{34}$
   2. B.$\sqrt{31}$
   3. C.$\sqrt{19}$
   4. D.$\frac{\sqrt{79}}{2}$
   Show answer

   Answer: C

9. Q42019 · 12 Jan 2019 · Shift 2

   If a curve passes through the point $(1,-2)$ and has slope of the tangent at any point (x, y) on it as $\frac{x^2-2y}{x}$, then the curve also passes through the point :

   1. A.$(-1,2)$
   2. B.$(-\sqrt{2},1)$
   3. C.$(\sqrt{3},0)$
   4. D.$(3,0)$
   Show answer

   Answer: C

10. Q172019 · 11 Jan 2019 · Shift 2

    Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression $\frac{x^m{y}^n}{(1+x^{2m})(1+y^{2n})}$ is :

    1. A.$\frac{1}{2}$
    2. B.$\frac{1}{4}$
    3. C.$\frac{m+n}{6mn}$
    4. D.1
    Show answer

    Answer: B

11. Q152019 · 9 Jan 2019 · Shift 1

    The maximum volume (in cu.m) of the right circular cone having slant height $3\text{ m}$ is :

    1. A.$2\sqrt{3}\pi$
    2. B.$3\sqrt{3}\pi$
    3. C.$6\pi$
    4. D.$\frac{4}{3}\pi$
    Show answer

    Answer: A