1
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Which one of the following statements is not a tautology?
A
(p $$ \wedge $$ q) $$ \to $$ (~ p) $$ \vee $$ q
B
(p $$ \wedge $$ q) $$ \to $$ p
C
( p $$ \vee $$ q) $$ \to $$ ( p $$ \vee $$ (~q))
D
p $$ \to $$ ( p $$ \vee $$ q)
2
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S($$\alpha $$) = {(x, y) : y2 $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ $$\alpha $$} and A($$\alpha $$) is area of the region S($$\alpha $$). If for a $$\lambda $$, 0 < $$\lambda $$ < 4, A($$\lambda $$) : A(4) = 2 : 5, then $$\lambda $$ equals
A
$$2{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$
B
$$2{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$
C
$$4{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$
D
$$4{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$
3
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is $$2y \over x^2$$. If the curve passes through the centre of the circle x2 + y2 – 2x – 2y = 0, then its equation is :
A
x loge|y| = 2(x – 1)
B
x2 loge|y| = –2(x – 1)
C
x loge|y| = x – 1
D
x loge|y| = –2(x – 1)
4
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\mathop a\limits^ \to = 3\mathop i\limits^ \wedge + 2\mathop j\limits^ \wedge + x\mathop k\limits^ \wedge $$ and $$\mathop b\limits^ \to = \mathop i\limits^ \wedge - \mathop j\limits^ \wedge + \mathop k\limits^ \wedge $$ , for some real x. Then $$\left| {\mathop a\limits^ \to \times \mathop b\limits^ \to } \right|$$ = r is possible if :
A
0 < r < $$\sqrt {{3 \over 2}} $$
B
$$3\sqrt {{3 \over 2}} < r < 5\sqrt {{3 \over 2}} $$
C
$$ r \ge 5\sqrt {{3 \over 2}} $$
D
$$\sqrt {{3 \over 2}} < r \le 3\sqrt {{3 \over 2}} $$
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