1
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The equation of the plane containing the straight line $${x \over 2} = {y \over 3} = {z \over 4}$$ and perpendicular to the plane containing the straight lines $${x \over 3} = {y \over 4} = {z \over 2}$$ and $${x \over 4} = {y \over 2} = {z \over 3}$$ is :
A
x $$-$$ 2y + z = 0
B
3x + 2y $$-$$ 3z = 0
C
x + 2y $$-$$ 2z = 0
D
5x + 2y $$-$$ 4z = 0
2
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If   $$A = \left[ {\matrix{ {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr {{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \cr {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \cr } } \right]$$

then A is :
A
invertible for all t$$ \in $$R.
B
invertible only if t $$=$$ $$\pi $$
C
not invertible for any t$$ \in $$R
D
invertible only if t $$=$$ $${\pi \over 2}$$.
3
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If   $$f\left( x \right) = \int {{{5{x^8} + 7{x^6}} \over {{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} \,dx,\,\left( {x \ge 0} \right),$$

$$f\left( 0 \right) = 0,$$    then the value of $$f(1)$$ is :
A
$$ - $$ $${1 \over 2}$$
B
$$ - $$ $${1 \over 4}$$
C
$${1 \over 2}$$
D
$${1 \over 4}$$
4
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A data consists of n observations : x1, x2, . . . . . . ., xn.    

If     $$\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n$$    and

$$\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,$$

then the standard deviation of this data is :
A
2
B
$$\sqrt 5 $$
C
5
D
$$\sqrt 7 $$
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