1
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k$$ be three vectors. A vector in the plane of $${\overrightarrow b }$$ and $${\overrightarrow c }$$, whose projection on $${\overrightarrow a }$$ is of magnitude $$\sqrt {2/3,} $$ is :
A
$$2\widehat i + 3\widehat j - 3\widehat k$$
B
$$2\widehat i + 3\widehat j + 3\widehat k$$
C
$$-2\widehat i - \widehat j + 5\widehat k$$
D
$$2\widehat i + \widehat j + 5\widehat k$$
2
IIT-JEE 1993
Subjective
+5
-0
In a triangle $$ABC, D$$ and $$E$$ are points on $$BC$$ and $$AC$$ respectively, such that $$BD=2DC$$ and $$AE=3EC.$$ Let $$P$$ be the point of intersection of $$AD$$ and $$BE.$$ Find $$BP/PE$$ using vector methods.
3
IIT-JEE 1993
Subjective
+5
-0
Numbers are selected at random, one at a time, from the two- digit numbers $$00, 01, 02 ......, 99$$ with replacement. An event $$E$$ occurs if only if the product of the two digits of a selected number is $$18$$. If four numbers are selected, find probability that the event $$E$$ occurs at least $$3$$ times.
4
IIT-JEE 1993
Subjective
+5
-0
Find the coordinates of the point at which the circles $${x^2}\, + \,{y^2} - \,4x - \,2y = - 4\,\,and\,\,{x^2}\, + \,{y^2} - \,12x - \,8y = - 36$$ touch each other. Also find equations common tangests touching the circles in the distinct points.
JEE Advanced Papers
EXAM MAP