JEE Main Test 44

Result

JEE Main Test 44

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

Number of ways to choose an ordered pair (a,b) of numbers from the set {1, 2, 3, ......,10} such that |a - b| ≤ 5 is

A
80

B
90

C
70

D
60

Solution

|a - b| ≤ 5 means |a - b| = 0 or 1 ≤ |a - b| ≤ 5

|a - b| = 0 ⇒ a = b which is possible in 10 ways

Let x, y, z represent, numbers before, in between and after a and b. then

x + y + z = 8, 0 ≤ y ≤ 4 and x, z ≥ 0

= coefficient of x⁸ in (1 + x + x² + ......+ x⁸)² (1 + x + x² + x³ + x⁴) = 35

Number of ways in which a ≠ b and |a - b| ≤ 5 is

= 2 × 35 = 70 (a and b can be in any order)

So, total number of ways = 10 + 70 = 80.

The correct answer is: 80
Question 2
4 / -1

The integers x, y and z each are perfect squares and x > y > z > 0, if x, y, z from A. P., then find the smallest possible value of x

A
36

B
49

C
25

D
16

Solution

Let x =a²,y=b², z=c²

Then, 2b²=a²+c²,

Since b is at least 2, consider the values of b from 2 onwards.

The first such value occurs when b = 5, (and then a = 7,c = 1),

So the least possible value of x =a²=49

The correct answer is: 49