Mathematics Test

Result

Mathematics Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

The angle between lines y²sin²θ-xysin²θ+x²(cos²θ-1) = 1 is

A
π/3

B
π/4

C
2π/3

D
π/2
Question 2
1 / -0

Three identical dice are rolled. The probability that the same number will appear on each of them is

A
1/36

B
1/18

C
1/6

D
3/18
Question 3
1 / -0

If the sides of a triangle are proportional to the cosines of the opposite angles then the triangle is

A
right angled

B
equilateral

C
obtuse angled

D
none of these
Question 4
1 / -0

If the difference between the corresponding roots of x² + ax + b = 0 and x² + bx + a = 0 is same and a ≠ b, then

A
a + b + 4 = 0

B
a + b - 4 = 0

C
a - b - 4 = 0

D
a - b + 4 = 0
Question 5
1 / -0

If A.M. between two numbers is 5 and their G.M. is 4, then their H.M. is

A
16/5

B
14/5

C
11/5

D
none of these

Solution

If x, y and z respectively represent AM, GM and HM between two numbers a and b, then

y² = xz

Here x = 5, y = 4

then 16 = 5 x z

z = 16/5
Question 6
1 / -0

A condition for a function y = f (x) to have an inverse is that it should be

A
defined for all x

B
continuous every where

C
an even function

D
strictly monotone and continuous in the domain
Question 7
1 / -0

The number of 4-digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is

A
120

B
300

C
420

D
20

Solution

Each even number must have 0, 2, 4 or 6 in is units place

Here total number of digits = 7

When 0 occurs at units place there is no restriction on other places and when 2 or 4 occurs at units place there is restriction on thousands' place as 0 can not be put at thousands' place

Case I When 0 occurs at units place:

∴ The number of numbers formed in this case

The units' place can be filled up by any one of the three digits 2, 4 and 6 in 3 ways
∴ The number of numbers formed in this case

∴ The required number = 120 + 300 = 420
Question 8
1 / -0

A

B

C

D
Question 9
1 / -0

A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If (15/AB )² + (10/AC)² = (6/AD)2, then the equation of line is

A
2x+3y+22=0

B
5x-4y+7=0

C
3x-2y+3=0

D
3x+2y+3=0

Solution
Question 10
1 / -0

X follows a binomial distribution with parameters n = 6 and p. If 4 P (X = 4) = P (X = 2), then p =

A
1/2

B
1/4

C
1/6

D
1/3