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JEE Main || Algebra || Super Quiz 12

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Question 1

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4. Then the sum of all possible values of |a-d| is

Question 2

The question has FOUR options. ONLY ONE of these four options is the correct answer.

Let a, b

and a²+ b²

0. Suppose

where

i=. If z = x + iy and z S, then (x, y) lies on

I) the circle with radius and centre for a > 0, b 0

II) the circle with radius -and centre for a < 0, b 0

III) the x-axis for a 0, b = 0

IV) the y-axis for a = 0, b 0

Question 3

Suppose

is a given line segment in the plane and

is a scalene triangle. The number of points

in the plane such that the triangle with vertices

(in some order) is similar to triangle

Question 4

The mean of the series

is 51. If 6 is replaced with 11, then find the new mean.

Question 5

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is:

Question 6

For all positive integral values of n,

is equal to