1
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

A
m(m + n)
B
m + n
C
n(m + n)
D
$${1 \over 2}$$(m + n)
2
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is

A
$$a(1 + {t^2})$$
B
$${(1 + t)^2}$$
C
$$a(1 - {t^2})$$
D
$$(1 - {t^2})$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The value of a for which the sum of the squares of the roots of the equation $${x^2} - (a - 2)x - a - 1 = 0$$ assumes the least value is

A
0
B
1
C
2
D
3
4
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If x satisfies the inequality $${\log _{25}}{x^2} + {({\log _5}x)^2} < 2$$, then x belongs to

A
$$\left( {{1 \over 5},5} \right)$$
B
$$\left( {{1 \over {25}},5} \right)$$
C
$$\left( {{1 \over 5},25} \right)$$
D
$$\left( {{1 \over {25}},25} \right)$$
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