1
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the length of the perpendicular from the point ($$\beta $$, 0, $$\beta $$) ($$\beta $$ $$ \ne $$ 0) to the line,
$${x \over 1} = {{y - 1} \over 0} = {{z + 1} \over { - 1}}$$ is $$\sqrt {{3 \over 2}} $$, then $$\beta $$ is equal to :
A
2
B
1
C
-2
D
-1
2
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - x} & 1 \cr {\cos \theta } & 1 & x \cr } } \right|$$ and
$${\Delta _2} = \left| {\matrix{ x & {\sin 2\theta } & {\cos 2\theta } \cr { - \sin 2\theta } & { - x} & 1 \cr {\cos 2\theta } & 1 & x \cr } } \right|$$, $$x \ne 0$$ ;

then for all $$\theta \in \left( {0,{\pi \over 2}} \right)$$ :
A
$${\Delta _1} - {\Delta _2}$$ = x (cos 2$$\theta $$ – cos 4$$\theta $$)
B
$${\Delta _1} + {\Delta _2}$$ = - 2x3
C
$${\Delta _1} + {\Delta _2}$$ = – 2(x3 + x –1)
D
$${\Delta _1} - {\Delta _2}$$ = - 2x3
3
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :
A
$${1 \over {10}}$$
B
$${1 \over {17}}$$
C
$${1 \over {11}}$$
D
$${1 \over {12}}$$
4
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Which one of the following Boolean expressions is a tautology?
A
(p $$ \vee $$ q) $$ \wedge $$ (~ p $$ \vee $$ ~ q)
B
(p $$ \vee $$ q) $$ \vee $$ ( p $$ \vee $$ ~ q)
C
(p $$ \wedge $$ q) $$ \vee $$ ( p $$ \wedge $$ ~ q)
D
(p $$ \vee $$ q) $$ \wedge $$ ( p $$ \vee $$ ~ q)
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