1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

A
$$(2,3)$$ or $$( - 2, - 3)$$
B
$$( - 2,3)$$ or $$(2,3)$$
C
$$(3,2)$$ or $$( - 3,2)$$
D
$$( - 3,2)$$ or $$(2,3)$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x - 22y + 1 = 0$$ passes through the point

A
$$( - a, - b)$$
B
$$(a, - b)$$
C
$$( - a,b)$$
D
$$(a,b)$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC = 10, then OP equals

A
$${{\sqrt 5 } \over {\sqrt 2 }}$$ unit
B
$${5 \over {\sqrt 2 }}$$ unit
C
$$2\sqrt 5 $$ unit
D
$$5\sqrt 2 $$ unit
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

A
$${x^2} = y$$
B
$${y^2} = x$$
C
$${y^2} = 2x$$
D
$${x^2} = 2y$$
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