1
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let S1 : x2 + y2 = 9 and S2 : (x $$-$$ 2)2 + y2 = 1. Then the locus of center of a variable circle S which touches S1 internally and S2 externally always passes through the points :
A
$$\left( {{1 \over 2}, \pm {{\sqrt 5 } \over 2}} \right)$$
B
(1, $$\pm$$ 2)
C
$$\left( {2, \pm {3 \over 2}} \right)$$
D
(0, $$\pm$$ $$\sqrt 3 $$)
2
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let g(x) = $$\int_0^x {f(t)dt} $$, where f is continuous function in [ 0, 3 ] such that $${1 \over 3}$$ $$ \le $$ f(t) $$ \le $$ 1 for all t$$\in$$ [0, 1] and 0 $$ \le $$ f(t) $$ \le $$ $${1 \over 2}$$ for all t$$\in$$ (1, 3]. The largest possible interval in which g(3) lies is :
A
$$\left[ { - 1, - {1 \over 2}} \right]$$
B
$$\left[ { - {3 \over 2}, - 1} \right]$$
C
[1, 3]
D
$$\left[ {{1 \over 3},2} \right]$$
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $$-$$a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2 + b2 is equal to :
A
425
B
250
C
925
D
650
4
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
In a triangle ABC, if $$|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$$, then the projection of the vector $$\overrightarrow {AB} $$ on $$\overrightarrow {AC} $$ is equal to :
A
$${{25} \over 4}$$
B
$${{127} \over 20}$$
C
$${{85} \over 14}$$
D
$${{115} \over 16}$$
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