1
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows :

$${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$

R1 : rectangle of largest area, with sides parallel to the axes, inscribed in E1;

En : ellipse $${{{x^2}} \over {a_n^2}} + {{{y^2}} \over {b_n^2}} = 1$$ of the largest area inscribed in $${R_{n - 1}},n > 1$$;

Rn : rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.

Then which of the following options is/are correct?
A
The eccentricities of E18 and E19 are not equal.
B
The distance of a focus from the centre in E9 is $${{\sqrt 5 } \over {32}}$$.
C
$$\sum\limits_{n = 1}^N {(area\,of\,{R_n})} $$ < 24, for each positive integer N.
D
The length of latusrectum of E9 is $${1 \over 6}$$
2
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 = $${{\sqrt 3 } \over {2}}$$($${2 - \sqrt 3 }$$)
3
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
$$\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{{10}^n}}}} = {10 \over {89}}$$
4
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 = $$t(2\widehat i + 2\widehat j - \widehat k)$$, $$t \in R$$
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12