JEE MAIN Parabola Previous Year Questions (PYQs) – Page 1 of 4
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If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment $AB$ subtends an angle equal to:
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The area (in sq. units) of the region described by $\{(x,y):y^{2}\le2x,\;y\ge4x-1\}$ is:
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Let $PQ$ be a chord of the parabola $y^{2}=12x$ and the midpoint of $PQ$ be at $(4,1)$.
Then, which of the following points lies on the line passing through the points $P$ and $Q$?
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The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances $\sqrt{2}$ and $2\sqrt{2}$ units from the origin, respectively. If the point $(1,k)$ lies on the parabola, then a possible value of $k$ is:
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The length of the chord of the parabola $x^2=4y$ having equation $x-\sqrt{2}\,y+4\sqrt{2}=0$ is –
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Let the shortest distance from $(a,0)$, $a>0$, to the parabola $y^{2}=4x$ be $4$.
Then the equation of the circle passing through the point $(a,0)$ and the focus of the parabola, with centre on the axis of the parabola, is:
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Let P be the parabola, whose focus is $(-2,1)$ and directrix is $2 x+y+2=0$. Then the sum of the ordinates of the points on P, whose abscissa is $-$2, is
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$f:R \to R$ be defined as$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$ Let A = {x $ \in $ R : f is increasing}. Then A is equal to :
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If the shortest distance of the parabola $y^2=4x$ from the centre of the circle
$x^2+y^2-4x-16y+64=0$ is $d$, then $d^2$ is equal to:
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Let $S=\{1,2,\ldots,20\}$. A subset $B$ of $S$ is said to be “nice”, if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is “nice” is :
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