Mathematics Test

Result

Mathematics Test - 11

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Weekly Quiz Competition

Question 1
2.5 / -0.83

The circle with (4, –1) and touching x-axis is

A
x2+ y2- 8x + 2y + 16 = 0

B
x2+ y2+ 18x - 2y -16 = 0

C
x2+ y2- 4x + y + 4 = 0

D
x2+ y2+ 14x - y + 4 = 0

Solution

The centre of given circle = (4, -1)

The circle is touching the X-axis.

Then the equation of the circle-

(x-h)² + (y-k)² = r²

Where (h, k) = (4, -1)

r = radius of circle

Since the circle is touching the X-axis. Then

r = k

r = -1

So, (x-4)² + (y+1)² = (-1)²
(x² -8x+16) + (y² +1+2y) = 1
x² + y² - 8x + 2y + 17 = 1
x² + y² - 8x + 2y + 16 = 0
This is the required equation of circle.
Question 2
2.5 / -0.83

The y-intercept of the circle x² + y² + 4x + 8y - 5 = 0 is

A
2√21

B
2√19

C
6

D
12

Solution

Point should be on y axis so x=0
y² +8y+5 = 0
y² +8y+16 =5+16
(y+4)² = 21
y+4 = (21)^½
y = -4 +- (21)^½
A = (0, 4+(21)^½ ) B=(0, 4-(21)^½ )
AB= [(0-0)² + {(4+(21)^½ ) - (4-(21)^½ )}]
= (2(21)^½ )
= 2(21)^½
Question 3
2.5 / -0.83

The centre of the circle passing through origin and making intercepts 8 and –4 on x and y axes respectively is

A
(4, –2)

B
(–2, 4)

C
(8, –4)

D
Both (A) and (B)

Solution

Verify g² - f² = 12
Question 4
2.5 / -0.83

A pendulum 36 cm long oscillates through an angle of 10 degrees. Find the length of the path described by its extremity.

A
31.25 cm

B
62.50 cm

C
3.620 cm

D
6.280 cm

Solution

= 6.280 cm
Question 5
2.5 / -0.83

In the fourth quadrant the value of cosine function

A
Decreases from 0 to -1

B
Increases from –∞to 0.

C
Decreases from 1 to 0

D
Increases from 0 to 1

Solution

As the angle increases from 270 °to 360 °, the sine increases from -1 to 0. As the angle increases from 270 °to 360 °, and the value of cos 270 °= 0
and cos 360 °= 1
So, the cosine increases from 0 to +1.
Question 6
2.5 / -0.83

A wire of length 15 cm is bent to form an arc of a circle with radius 6 cm. Find in radians the angle subtended at the centre.

A
2.5 radians

B
3.5 radians

C
4 radians

D
3 radians

Solution

Length of arc = 15 cm
Radius: R = 6 cm
Arc length = R*θ
(θis the angle subtended by the arc)
15 = 6*θ
θ= 5/2 radians
Question 7
2.5 / -0.83

If sin A + cos A = 1, then sin 2A is equal to

A
2

B
1/2

C
0

D
1

Solution

(Sin A + Cos A)² = sin² A + cos² A + 2 sinAcosA

1 = 1 + Sin 2A

so, Sin 2A = 0

Hence A = 0
Question 8
2.5 / -0.83

Q101. If COMPANY is coded as CODPANG , then COUNTRY will be coded as ?

A
A.COUEBRG

B
B.COCNTIG

C
C.COCNBRG

D
D.CFCNBRG
Question 9
2.5 / -0.83

A
π/4

B
π

C
π/2

D
π/3

Solution
Question 10
2.5 / -0.83

A
1/2

B
0

C
1

D
none of these

Solution