1
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if\,x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if\, - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x} & {if\,x \ge {\pi \over 2}} \cr } } \right.$$. Then,
A
f is discontinuous for all A and B
B
f is continuous for all A = $$-$$ 1 and B = 1
C
f is continuous for all A = 1 and B = $$-$$ 1
D
f is continuous for all real values of A, B
2
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and $${x_3} = {5 \over 2}$$
A
are parallel to each other
B
are pairwise perpendicular
C
are concurrent
D
are not concurrent
3
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The equation x log x = 3 $$-$$ x
A
has no root in (1, 3)
B
has exactly one root in (1, 3)
C
x log x $$-$$ (3 $$-$$ x) > 0 in [1, 3]
D
x log x $$-$$ (3 $$-$$ x) < 0 in [1, 3]
4
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, $$-$$ 4) and Q(9, 6). Let R be a point on the arc of the parabola between P and Q. Then, the area of $$\Delta$$PQR is largest when
A
$$\angle$$PQR = 90$$^\circ$$
B
R(4, 4)
C
R$$\left( {{1 \over 4},1} \right)$$
D
R$$\left( {1,{1 \over 4}} \right)$$
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