1
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
In a non-right-angled triangle $$\Delta $$PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. If p = $${\sqrt 3 }$$, q = 1, and the radius of the circumcircle of the $$\Delta $$PQR equals 1, then which of the following options is/are correct?
A
Length of OE = $${1 \over 6}$$
B
Length of RS = $${{\sqrt 7 } \over 2}$$
C
Area of $$\Delta $$SOE = $${{\sqrt 3 } \over {12}}$$
D
Radius of incircle of $$\Delta $$PQR = $${{\sqrt 3 } \over {2}}$$($${2 - \sqrt 3 }$$)
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Let $$\alpha $$ and $$\beta $$ be the roots of$${x^2} - x - 1 = 0$$, with $$\alpha $$ > $$\beta $$. For all positive integers n, define

$${a_n} = {{{\alpha ^n} - {\beta ^n}} \over {\alpha - \beta }},\,n \ge 1$$

$${b_1} = 1\,and\,{b_n} = {a_{n - 1}} + {a_{n + 1}},\,n \ge 2$$

Then which of the following options is/are correct?
A
$$\sum\limits_{n = 1}^\infty {{{{b_n}} \over {{{10}^n}}}} = {8 \over {89}}$$
B
bn = $$\alpha $$n + $$\beta $$n for all n $$ \ge $$ 1
C
a1 + a2 + a3 + ... + an = an+2 $$ - $$ 1 for all n $$ \ge $$ 1
D
$$\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{{10}^n}}}} = {10 \over {89}}$$
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Let L1 and L2 denote the lines

$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$, $$\lambda $$$$ \in $$ R

and $$r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R$$

respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
A
$$r = {2 \over 9}(2\widehat i - \widehat j + 2\widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
B
$$r = {1 \over 3}(2\widehat i + k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
C
$$r = {2 \over 9}(4\widehat i - \widehat j + \widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
D
r = $$t(2\widehat i + 2\widehat j - \widehat k)$$, $$t \in R$$
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities $${3 \over {10}}$$, $${3 \over {10}}$$ and $${4 \over {10}}$$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?
A
Probability that the chosen ball is green, given that the selected bag is B3, equals $${3 \over 8}$$.
B
Probability that the selected bag is B3, given that the chosen ball is green, equals $${5 \over 13}$$.
C
Probability that the chosen ball is green equals $${39 \over 80}$$.
D
Probability that the selected bag is B3 and the chosen ball is green equals $${3 \over 10}$$.
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12