1
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let S be the set of all column matrices $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]$$ such that $${b_1},{b_2},{b_3} \in R$$ and the system of equations (in real variables)

$$\eqalign{ & - x + 2y + 5z = {b_1} \cr & 2x - 4y + 3z = {b_2} \cr & x - 2y + 2z = {b_3} \cr} $$

has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]$$$$ \in $$S?
A
$$x + 2y + 3z = {b_1}$$, $$\,4y + 5z = {b_2}$$ and $$x + 2y + 6z = {b_3}$$
B
$$x + y + 3z = {b_1}$$, $$5x + 2y + 6z = {b_2}$$ and $$ - 2x - y - 3z = {b_3}$$
C
$$ - x + 2y - 5z = {b_1}$$, $$\,2x - 4y + 10z = {b_2}$$ and $$x - 2y + 5z = {b_3}$$
D
$$x + 2y + 5z = {b_1}$$, $$2x + 3z = {b_2}$$ and $$x + 4y - 5z = {b_3}$$
2
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is $$\sqrt 2 $$, then which of the following statement(s) is (are) TRUE?
A
For the ellipse, the eccentricity is 1$$\sqrt 2 $$ and the length of the latus rectum is 1
B
For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2
C
The area of the region bounded by the ellipse between the lines $$x = {1 \over {\sqrt 2 }}$$ and x = 1 is $${1 \over {4\sqrt 2 }}(\pi - 2)$$
D
The area of the region bounded by the ellipse between the lines $$x = {1 \over {\sqrt 2 }}$$ and x = 1 is $${1 \over {16}}(\pi - 2)$$
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let s, t, r be non-zero complex numbers and L be the set of solutions $$z = x + iy(x,y \in R,\,i = \sqrt { - 1} )$$ of the equation $$sz + t\overline z + r = 0$$ where $$\overline z $$ = x $$-$$ iy. Then, which of the following statement(s) is(are) TRUE?
A
If L has exactly one element, then |s|$$ \ne $$|t|
B
If |s| = |t|, then L has infinitely many elements
C
The number of elements in $$L \cap \{ z:|z - 1 + i| = 5\} $$ is at most 2
D
If L has more than one element, then L has infinitely many elements
4
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : (0, $$\pi $$) $$ \to $$ R be a twice differentiable function such that $$\mathop {\lim }\limits_{t \to x} {{f(x)\sin t - f(t)\sin x} \over {t - x}} = {\sin ^2}x$$ for all x$$ \in $$ (0, $$\pi $$).

If $$f\left( {{\pi \over 6}} \right) = - {\pi \over {12}}$$, then which of the following statement(s) is (are) TRUE?
A
$$f\left( {{\pi \over 4}} \right) = {\pi \over {4\sqrt 2 }}$$
B
$$f(x) < {{{x^4}} \over 6} - {x^2}$$ for all x$$ \in $$(0, $$\pi $$)
C
There exists $$\alpha $$$$ \in $$(0, $$\pi $$) such that f'($$\alpha $$) = 0
D
$$f''\left( {{\pi \over 2}} \right) + f\left( {{\pi \over 2}} \right) = 0$$
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12