1
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Three lines $${L_1}:r = \lambda \widehat i$$, $$\lambda $$ $$ \in $$ R,

$${L_2}:r = \widehat k + \mu \widehat j$$, $$\mu $$ $$ \in $$ R and

$${L_3}:r = \widehat i + \widehat j + v\widehat k$$, v $$ \in $$ R are given.

For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are collinear?
A
$$\widehat k$$
B
$$\widehat k$$ + $$\widehat j$$
C
$$\widehat k$$ + $${1 \over 2}$$$$\widehat j$$
D
$$\widehat k$$ $$-$$ $${1 \over 2}$$$$\widehat j$$
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
For $$a \in R,\,|a|\, > 1$$, let

$$\mathop {\lim }\limits_{n \to \infty } \left( {{{1 + \root 3 \of 2 + ...\root 3 \of n } \over {{n^{7/3}}\left( {{1 \over {{{(an + 1)}^2}}} + {1 \over {{{(an + 2)}^2}}} + ... + {1 \over {{{(an + n)}^2}}}} \right)}}} \right) = 54$$
A
$$-$$6
B
$$-$$7
C
8
D
$$-$$9
3
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Let f : R be a function. We say that f has

PROPERTY 1 if $$\mathop {\lim }\limits_{h \to 0} {{f(h) - f(0)} \over {\sqrt {|h|} }}$$ exists and is finite, and

PROPERTY 2 if $$\mathop {\lim }\limits_{h \to 0} {{f(h) - f(0)} \over {{h^2}}}$$ exists and is finite. Then which of the following options is/are correct?
A
f(x) = sin x has PROPERTY 2
B
f(x) = x2/3 has PROPERTY 1
C
f(x) = |x| has PROPERTY 1
D
f(x) = x|x| has PROPERTY 2
4
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Let x $$ \in $$ R and let $$P = \left[ {\matrix{ 1 & 1 & 1 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$, $$Q = \left[ {\matrix{ 2 & x & x \cr 0 & 4 & 0 \cr x & x & 6 \cr } } \right]$$ and R = PQP$$-$$1, which of the following options is/are correct?
A
There exists a real, number x such that PQ = QP
B
For $$x = 0$$, if $$R \left[ {\matrix{ 1 \cr a \cr b \cr } } \right] = 6\left[ {\matrix{ 1 \cr a \cr b \cr } } \right]$$, then a + b =5
C
For x = 1, there exists a unit vector $$\alpha \widehat i + \beta \widehat j + \gamma \widehat k$$ for which $$R\left[ {\matrix{ \alpha \cr \beta \cr \gamma \cr } } \right] = \left[ {\matrix{ 0 \cr 0 \cr 0 \cr } } \right]$$
D
$$\det R = \det \left[ {\matrix{ 2 & x & x \cr 0 & 4 & 0 \cr x & x & 5 \cr } } \right] + 8$$, for all x $$ \in $$ R
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12