BITSAT SERIES Mathematics
Sections Of A Cone
19 previous year questions.
Volume: 19 Ques
Yield: Medium
High-Yield Trend
1
2026 1
2021 2
2020 1
2018 1
2017 2
2016 1
2015 2
2014 3
2013 1
2012 2
2011 2
2010 Chapter Questions 19 MCQs
01
PYQ 2010
medium
mathematics ID: bitsat-2
The line ax+by=1 cuts ellipse cx²+dy²=1 only once if
1
ca²+db²=1
2
(c)/(a²)+(d)/(b²)=1
3
(a²)/(c)+(b²)/(d)=1
4
a²c+b²d=1
02
PYQ 2010
medium
mathematics ID: bitsat-2
If the line 2x-1=0 is the directrix of the parabola
y²-kx+6=0, then one of the values of k is
1
-6
2
6
3
1/4
4
-1/4
03
PYQ 2011
medium
mathematics ID: bitsat-2
The length of the latus-rectum of the parabola whose focus is ((u²)/(2g)\sin2α,-(u²)/(2g)\cos2α) and directrix is y=(u²)/(2g), is:
1
(u²)/(g)cos²α
2
(u²)/(g)\cos2α
3
(2u²)/(g)cos² 2α
4
(2u²)/(g)cos²α
04
PYQ 2011
medium
mathematics ID: bitsat-2
The equation of the ellipse with focus at (±5,0) and eccentricity =(5)/(6) is:
1
(x²)/(36)+(y²)/(25)=1
2
(x²)/(36)+(y²)/(11)=1
3
(x²)/(25)+(y²)/(11)=1
4
None of these
05
PYQ 2012
medium
mathematics ID: bitsat-2
Find the eccentricity of the conic represented by :
1
2
2
3
4
06
PYQ 2013
medium
mathematics ID: bitsat-2
S and T are the foci of an ellipse and B is an end of the minor axis. If is an equilateral triangle, then the eccentricity of the ellipse is
1
2
3
4
07
PYQ 2013
medium
mathematics ID: bitsat-2
An ellipse has OB as semi-minor axis, and its foci and the angle is a right angle. Then the eccentricity of the ellipse is
1
2
3
4
08
PYQ 2013
medium
mathematics ID: bitsat-2
If the line touches the parabola , then find the value of .
1
2
3
4
09
PYQ 2014
medium
mathematics ID: bitsat-2
Through the vertex of parabola , chords OP and OQ are drawn at right angles to one another. The locus of the midpoint of PQ is
1
2
3
4
10
PYQ 2014
medium
mathematics ID: bitsat-2
An arch of a bridge is semi-elliptical with major axis horizontal. If the length of the base is m and the highest part of the bridge is m from the centre of the horizontal axis, the best approximation of the height of the arch m from the centre of the base is:
1
2
3
4
11
PYQ 2015
medium
mathematics ID: bitsat-2
The eccentricity of an ellipse, with its centre at origin, is . If one of the directrices is , then the equation of the ellipse is
1
2
3
4
12
PYQ 2016
medium
mathematics ID: bitsat-2
The parabola having its focus at (3,2) and directrix along the y-axis has its vertex at
1
2
3
4
(\dfrac23,2)
13
PYQ 2016
medium
mathematics ID: bitsat-2
The locus of the point of intersection of two tangents to the parabola
y²=4ax, which are at right angle to one another is
1
2
3
4
x+y+a=0
14
PYQ 2017
medium
mathematics ID: bitsat-2
The length of the semi-latus rectum of an ellipse is one third of its major axis. Its eccentricity would be
1
2
3
4
(1)/(\sqrt2)
15
PYQ 2018
medium
mathematics ID: bitsat-2
Consider the equation of parabola y²+4ax=0 where a>0. Which of the following is correct?
1
Tangent at the vertex is x=0
2
Directrix of the parabola is x=0
3
Vertex of the parabola is not at the origin
4
Focus of the parabola is at (a,0)
16
PYQ 2020
medium
mathematics ID: bitsat-2
The locus of the point of intersection of two tangents to the parabola
y²=4ax
which are at right angle to one another is
1
2
3
4
x+y+a=0
17
PYQ 2020
easy
mathematics ID: bitsat-2
The parabola having its focus at (3,2) and directrix along the y-axis has its vertex at
18
PYQ 2021
medium
mathematics ID: bitsat-2
The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be
1
(2)/(3)
2
√((2)/(3))
3
\dfrac1√(3)
4
\dfrac1√(2)
19
PYQ 2026
medium
mathematics ID: bitsat-2
Let P be a point on the parabola, . If the distance of P from the centre of the circle, is minimum, then the equation of the tangent to the parabola at P, is :
1
2
3
4