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Given : A circle, 2x^2+""2y^2=""5 and a ...

Given : A circle, `2x^2+""2y^2=""5` and a parabola, `y^2=""4sqrt(5)""x` . Statement - I : An equation of a common tangent to these curves is `y="x+"sqrt(5)` Statement - II : If the line, `y=m x+(sqrt(5))/m(m!=0)` is their common tangent, then m satisfies `m^4-3m^2+""2""=0.` (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

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Consider : Statement I : (phat~""q)hat(~""phatq) is a fallacy. Statement II : (pvecq)harr(~""qvec~""p) is a tautology. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-x)) . Statement-1: f(c)""=1/3, for some c in R . Statement-2: 0""<""f(x)lt=1/(2sqrt(2)), for all x in R . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

If A is 2 x 2 invertible matrix such that A=adjA-A^-1 Statement-I 2A^2+I=O(null matrix) Statement-II: 2|A|=1 (i) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I. 3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true.

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x""""y""+""z""=""5 . Statement-2: The plane x x""""y""+""z""=""5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , where I is 2xx2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: T r(A)""=""0 Statement-2: |A|""=""1 (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

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Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

MCGROW HILL PUBLICATION-PARABOLA-QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
  1. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  2. Statement 1: An equation of a common tangent to the parabola y^2=16...

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  3. Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . ...

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  4. Statement-1: The slopw of the tangent at any point P on a parabola, wh...

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  5. Statement 1 : The line x-2y=2 meets the parabola, y^2 + 2x = 0 only at...

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  6. The point of intersection of the normals to the parabola y^2=4x at the...

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  7. The slope of the line touching both the parabolas y^2=4x and x^2=−32y ...

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  8. Area common to the circle x^(2)+y^(2)=9 an the parbola y^(1)=8x is

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  9. Two tangents are drawn from a point (-2, -1) to the curve y^(2)=4x. If...

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  10. A chord is drawn through the focus of the parabola y^(2)=6x such that ...

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  11. Let O be the vertex and Q be any point on the parabola,x^2=""8y . I...

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  12. Let PQ be a double ordinate of the parabola, y^2=-4x where P lies in t...

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  13. If the tangent to the conic, y - 6= x^2 at (2, 10) touches the circle,...

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  14. Let P be the point on the parabola, y^2=8x which is at a minimum dis...

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  15. The minimum distance of a point on the curve y=x^2 -4 from the origin ...

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  16. P and Q are two distinct points on the parabola, y^2 = 4x with paramet...

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  17. If the common tangents to the parabola x^2 = 4y and the circle x^2 + y...

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  18. If y=mx+c is the normal at a point on the parabola y^(2)=8x whose foca...

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  19. The radius of a circle, having minimum area, which touches the curve y...

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  20. Tangent and normal are drawn at P(16,16) on the parabola y^2=16x which...

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