Mathematics Test

Result

Mathematics Test - 2

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

A
4

B
5

C
3

D
1

Solution
Question 2
4 / -1

A block of mass 5 kg slides down from rest along a frictionless inclined plane that makes an angle of 30^∘ with horizontal. What will be the speed of the block after it covers a distance of 3.6 m along the plane? [g = 10 m/s²]

A
5 m/s

B
6 m/s

C
7 m/s

D
8 m/s

Solution
Question 3
4 / -1

The equation 6x²- 5xy - 6y² + 14x + 5y + 4 = 0 represents:

A
A circle

B
A hyperbola

C
An ellipse

D
A pair of perpendicular straight lines

Solution
Question 4
4 / -1

A

B

C

D

Solution
Question 5
4 / -1

A
0

B
1

C
2

D
3

Solution
Question 6
4 / -1

A

B

C

D

Solution
Question 7
4 / -1

"If three forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two."

The above statement is known as ____________.

A
Pythagoras

B
Lami's theorem

C
Kummer's theorem

D
Hamilton's theorem

Solution
Question 8
4 / -1

The conic x² + xy + y² + x + y = 1 is:

A
a circle

B
a hyperbola

C
a parabola

D
a pair of straight lines

Solution

Given:

Second degree equation, x² + xy + y² + x + y = 1

Compare with second-degree equation ax² + 2hxy + by² + 2gx + 2fy + c = 0

So, a = 1, b = 1, h = 0.5, g = 0.5, f = 0.5 and c = -1

Now, Δ = abc + 2fgh - af²- bg² - ch²

Δ = 1 × 1 × (-1) + 2 x 0.5 x 0.5 x 0.5 – 1 × (0.5)²– 1 × (0.5)² - (-1) x (0.5)²

= -1 – 0.25 - 0.25 - 0.25 + 0.25

So, Δ = -1.5

Now, h² – ab = (0.5)² – 1 × 1 = -0.75

So, h² – ab < 0 and a = b

It represents a circle.
Question 9
4 / -1

Three particles A, B and C are projected from the same point with the same initial speed making angles 30^∘, 45^∘and 60^∘ respectively with the horizontal. Which of the following statements is correct?

A
A, B and C have unequal ranges

B
Ranges of A and C are equal and less than that of B

C
Ranges of A and C are equal and greater than that of B

D
A, B and C have equal ranges

Solution

All of the particles A, B and C are projected from the same point with the same initial speed making angles 30^∘, 45^∘and 60^∘respectively with the horizontal. According to the law of projectile motion, if two bodies thrown at same speed at angles such that their sum is equal to π/2 then both of them will have the same range, so A and C will have same range. Also the range is maximum when angle of projection is 45^∘. So the ranges of A and C are equal and less than that of B.
Question 10
4 / -1

A

B

C

D

Solution