1
WB JEE 2022
+1
-0.25

A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k are positive constants. The maximum velocity attained by the particle is

A
$${2 \over 3}\sqrt {{{{a^3}} \over k}}$$
B
$${1 \over 3}\sqrt {{{{a^3}} \over k}}$$
C
$$\sqrt {{{{a^3}} \over k}}$$
D
$$2\sqrt {{{{a^3}} \over k}}$$
2
WB JEE 2021
+1
-0.25
Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B and describes n units more than that of B in acquiring the same velocity, then
A
$$(f + f'){m^2} = ff'n$$
B
$$(f - ff'){m^2} = ff'n$$
C
$$(f' - f)n = {1 \over 2}ff'{m^2}$$
D
$${1 \over 2}(f + f')m = ff'{n^2}$$
3
WB JEE 2021
+2
-0.5
If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = 3y, then
A
(h, k) = (0, 0) only
B
(h, k) = $$\left( {{1 \over 8}, - {1 \over {16}}} \right)$$ only
C
(h, k) = (0, 0) or $$\left( {{1 \over 8},{1 \over {16}}} \right)$$
D
no such point P exists
4
WB JEE 2020
+1
-0.25
If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is
A
$$- {1 \over 9}$$
B
$$- {2 \over 9}$$
C
$$- {1 \over 3}$$
D
$$- {4 \over 9}$$
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