Mathematics Test

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Mathematics Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to start with A?

A
6

B
12

C
24

D
Neither 1 nor 2

Solution

As 'A' must be first letter of each word.

Total number of words = 4! = 24
Question 2
1 / -0

If $\sin A+\sin ^{2} A=1$, then find the value of $\cos ^{2} A+\cos ^{4} A$.

A
1

B
2

C
3

D
4

Solution
Question 3
1 / -0

Consider the following points:

1. (0, 5)

2. (2, –1)

3. (3, –4)

Which of the above lie on the line 3x+ y = 5 and at a distance √10 from (1, 2)?

A
1 only

B
2 only

C
1 and 2 only

D
1, 2 and 3

Solution

$3 x + y = 5$

$\sqrt{(0 - 1)^{2} + (5 - 2)^{2}} = \sqrt{10}$

$\sqrt{(2 - 1)^{2} + (- 1 - 2)^{2}} = \sqrt{10}$

$\sqrt{(3 - 1)^{2} + (- 4 - 2)^{2}} = \sqrt{40} = 2 \sqrt{10}$
Question 4
1 / -0

What is the number of arbitrary constants in the particular solution of differential equation of third order?

A
0

B
1

C
2

D
3

Solution

Particular solution do not have any constant
Question 5
1 / -0

The cumulative frequency of the largest observed value must always be:

A
Less than the total number of observations

B
Greater than the total number of observations

C
Equal to total number of observations

D
Equal to mid point of the last class interval

Solution

The cumulative frequency of the largest observed value must always be less then the total number of observations.
Question 6
1 / -0

If x and y are positive and xy > 1, then what is tan^-1x + tan^-1y equal to?

A
$\tan^{- 1} (\frac{x + y}{1 - x y})$

B
$- π + \tan^{- 1} (\frac{x + y}{1 - x y})$

C
$π - \tan^{- 1} (\frac{x + y}{1 - x y})$

D
$\tan^{- 1} (\frac{x - y}{1 + x y})$

Solution

$\tan^{- 1} x + \tan^{1} y = π + \tan^{- 1} [\frac{x + y}{1 + x y}]$

$x < 0, y < 0$ and

$x y > 1,$

$\tan^{- 1} x + \tan^{- 1} y = - π + \tan^{- 1} (\frac{x + y}{1 - x y})$
Question 7
1 / -0

A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

A
$\frac{2}{5}$

B
$\frac{1}{5}$

C
$\frac{1}{10}$

D
None of these

Solution

Total number of balls = 5

Number of black balls = 2

Required probability $= \frac{n (E)}{n (S)} = \frac{{}^{3}C_{0} \times {}^{2}C_{2}}{{}^{5}C_{2}} = \frac{2}{5} \times \frac{1}{4} = \frac{1}{10}$
Question 8
1 / -0

p, q, r, s, t, are five numbers such that the average of p, q and r is 5 and that of s and t is 10. What is the average of all the five numbers ?

A
7.75

B
7.5

C
7

D
5

Solution

According to question p + q + r = 5 x 3 = 15 ....(i)

s + t = 10 x 2 = 20 ........(ii)

From equations (i) and (ii), p + q + r + s + t = 15+ 20 = 35

Average p, q, r, s and t = $\frac{35}{5}$ = 7
Question 9
1 / -0

The mean and standard deviation of 100 items are 50, 5 and that of 150 items are 40, 6 respectively.

What is the variance of all 250 items?

A
50.6

B
53.3

C
55.6

D
59.6

Solution

Means of 100 itmes $= {\bar{x}}_{100} = 50$

Means of 150 itmes $= {\bar{x}}_{150} = 40$

Standard deviation of 100 itmes $= σ_{100} = 5$

Standard deviation of 150 itmes $= σ_{150} = 6$

variation of all of 250 itmes $= {(σ_{250})}^{2} = (7.456)^{2} = 55.6$
Question 10
1 / -0

The complete solution 3 tan² x = 1 is given by :

A
$x = n π \pm \frac{π}{3}$

B
$x = n π \pm \frac{π}{3} o n l y$

C
$x = n π \pm \frac{π}{6}$

D
$x = n π \pm \frac{π}{6} o n l y$

Solution

$\Rightarrow$
$3 \tan^{2} x = 1$

$\tan x = \pm \frac{1}{\sqrt{3}}$

$\tan x = \tan (\pm \frac{π}{6})$

$x = n π \pm \frac{π}{6}$

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Re-Attempt Weekly Quiz Competition

Mathematics Test - 8

Result

Mathematics Test - 8

Score

-

Rank

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SHARING IS CARING

Question 1

6

12

24

Neither 1 nor 2

Solution

Question 2

1

2

3

4

Solution

Question 3

1 only

2 only

1 and 2 only

1, 2 and 3

Solution

Question 4

0

1

2

3

Solution

Question 5

Less than the total number of observations

Greater than the total number of observations

Equal to total number of observations

Equal to mid point of the last class interval

Solution

Question 6

tan−1(x+y1−xy)

−π+tan−1(x+y1−xy)

π-tan−1(x+y1−xy)

tan−1(x-y1+xy)

Solution

Question 7

25

15

110

None of these

Solution

Question 8

7.75

7.5

7

5

Solution

Question 9

50.6

53.3

55.6

59.6

Solution

Question 10

x=nπ±π3

x=nπ±π3only

x=nπ±π6

x=nπ±π6only

Solution

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$\tan^{- 1} (\frac{x + y}{1 - x y})$

$- π + \tan^{- 1} (\frac{x + y}{1 - x y})$

$π - \tan^{- 1} (\frac{x + y}{1 - x y})$

$\tan^{- 1} (\frac{x - y}{1 + x y})$

$\frac{2}{5}$

$\frac{1}{5}$

$\frac{1}{10}$

$x = n π \pm \frac{π}{3}$

$x = n π \pm \frac{π}{3} o n l y$

$x = n π \pm \frac{π}{6}$

$x = n π \pm \frac{π}{6} o n l y$