Mathematics Test

Result

Mathematics Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

How many two digit numbers are there which are divisible by 5 ?

A
25

B
23

C
27

D
18

Solution

Two digit numbers divisible by 5 are

10,15,20,25, ......95

This is an A.P. with a=10, d=5

Tn=a+(n-1)d

$\Rightarrow 95 = 10 + (n - 1) \times 5$
$\Rightarrow n = 18$
Question 2
1 / -0

The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is

A
480

B
600

C
720

D
840

Solution

(a) Fix up a male and the remaining 4 male can be seated in 4! ways. Now no two female are to sit together and as such the 2 female are to be arranged in five empty seats between two consecutive male and number of arrangement will be ⁵P² . Hence by fundamental theorem the total number of ways is =4!*⁵P² = 24 × 20 = 480 ways.
Question 3
1 / -0

Find the value of ∫(dx/1+tanx)

A

$2 \sec ^{2} \frac{x}{2}$

B

$\log |x+\sin x|$

C

$\log |\sec x+\sin x|$

D

$\frac{1}{2}[x+\log |\sin x+\cos x|]$

Solution
Question 4
1 / -0

Find out the sum of all integral multiples of 7 between 84 and 957.

A
4895

B
4896

C
49752

D
64750

Solution
Question 5
1 / -0

Which of the following lines is concurrent with the lines 3x + 4y + 6 = 0 and 6x + 5y + 9 = 0

A
2x+3y+5=0

B
3x+3y+5=0

C
7x+9y+3=0

D
None of these

Solution
Question 6
1 / -0

What is the equation of a sphere at the center (-3, 4, 4) and of radius 6 units?

A

$x^{2}+y^{2}+z^{2}+6 x+8 y+8 x=36$

B

$x^{2}+y^{2}+z^{2}-6 x+8 y-8 z=-6$

C

$x^{2}+y^{2}+z^{2}-6 x-8 y-8 z=16$

D

$x^{2}+y^{2}+z^{2}+6 x-8 y-8 z=-5$

Solution
Question 7
1 / -0

A

B

C

D

Solution
Question 8
1 / -0

If the straight line y=mx+c touches the circle x² + y²-4y=0, then the value of c will be

A
1+√1+m²

B
1+√m²+1

C
2(1+√1+m²)

D
2+√1+m²

Solution
Question 9
1 / -0

What is the logarithm of 1/9 in a system whose base is 3?

A
3

B
1/27

C
1/2

D
-2

Solution
Question 10
1 / -0

In space, the two straight lines are known as

A
Intersecting lines

B
Perpendicular lines

C
Skew lines

D
Shortest lines

Solution

The two straight lines in space are said to be skew lines. They are neither parallel nor intersecting. Angle between skew lines is the angle between two intersecting lines drawn from any point (preferably through the origin) parallel to each of the skew lines.

The shortest distance between two skew lines is the length of the line segment perpendicular to both the lines.

Formula for finding the distance between skew lines is