1
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^2} + 5a + 3)}} + {{{y^2}} \over {f(a + 15)}} = 1$$ be an ellipse with major axis along the y-axis. The value of 'a' can lie in the interval (s)

A
$$( - \infty , - 6)$$
B
$$( - 6,2)$$
C
$$(2,\infty )$$
D
$$( - \infty ,\infty )$$
2
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

A
a circle
B
a parabola
C
an ellipse
D
a hyperbola
3
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0
Change Language

The line y = x + 5 touches

A
the parabola y2 = 20 x
B
the ellipse $$9{x^2} + 16{y^2} = 144$$
C
the hyperbola $${{{x^2}} \over {29}} - {{{y^2}} \over 4} = 1$$
D
the circle $${x^2} + {y^2} = 25$$
4
WB JEE 2020
MCQ (More than One Correct Answer)
+2
-0
Change Language
Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point of the portion intercepted between the axes is
A
$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$
B
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$
C
$${1 \over {3{x^2}}} + {1 \over {4{y^2}}} = 1$$
D
$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12