General Test

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General Test - 19

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Weekly Quiz Competition

Question 1
4 / -1

Two horses P and Q are running at a certain point at the speed of 15 km/hr and 17 km/hr respectively. What is the distance between them after 5 hrs if they running in the opposite directions?

A
10 km

B
160 km

C
170 km

D
18 km

Solution

Given:

Two horses P and Q are running at a certain point at the speed of 15 km/hr and 17 km/hr respectively.

If the speed of the two trains is x km/hr and y km/hr respectively if x > y.

Relative speed, if opposite directions = (x + y) km / hr

Speed = $\frac{Distance}{Time}$

Relative speed of both horses = 17 + 15 = 32 km/hr

Distance between them after 5 hrs = 32 × 5 = 160 km
Question 2
4 / -1

If a boat walks smoothly along the streamline, the distance of $36$ km is completed in $3$ hours. While returning, it completes the same distance in $9$ hours. So what is the speed of the boat?

A
$8$ km $/$ hr

B
$12$ km $/$ hr

C
$14$ km $/$ hr

D
$10$ km $/$ hr

Solution

Let the speed of the boat be $c$ and the speed of the current is $v$ .

So we have,

Speed of the boat with the stream $= c + v = \frac{36}{3} = 12$ km/hr

Speed of the boat against the stream $= c - v = \frac{36}{9} = 4$ km $/$ hr

By adding the above result obtained and removing $v$ , we get,

$\Rightarrow 2 c = 16$ km $/$ hr

$\Rightarrow c = 8$ km $/$ hr
Question 3
4 / -1

A train 'B' speeding with 100 km/hr crosses another train C, running in the same direction, in 2 minutes. If the length of train B and C be 150 m and 250 m respectively, what is the speed of train C (in km/hr)?

A
75

B
88

C
95

D
110

Solution

Given:

Speed of train B = 100 km/hr

Let speed of train C be x km/hr,

Length of train B and C are 150 m and 250 m respectively.

As we know,

Speed $= \frac{Distance}{Time}$

⇒ (100 - x) × $\frac{5}{18}$ = $\frac{150 + 250}{2 \times 60}$

⇒ (100 - x) $= \frac{400}{120} \times \frac{18}{5}$

⇒ 100 - x = 12

⇒ x = 100 - 12

⇒ x = 88

Speed of the train C is 88 km/hr.
Question 4
4 / -1

If (x – 4) and (x + 6) are the factors of equation x² + ax + b = 0 then find the value of (a – b)?

A
22

B
-34

C
17

D
26

Solution

Given:

(x – 4) and (x + 6) are the factors of equation x² + ax + b = 0

If (x – p) is the factors equation x² + ax + b = 0 then ‘p’ will be the root of the equation.

Roots of equation x² + ax + b = 0 will be: 4 and -6.

Putting the values of the roots we will get two equations as follows:

16 + 4a + b = 0

⇒ 4a + b = -16 ---- (1)

And

36 – 6a + b = 0

⇒ -6a + b = - 36 ---- (2)

Solving these two equations we get

⇒ a = 2 and b = -24

So,

(a – b) = 2 – (-24) = 26
Question 5
4 / -1

Simplify:

$1.45 \div 2.9 \times 4.11+1.002-.005+.98$

A
$2.032$

B
$3.032$

C
$4.032$

D
$5.032$

Solution

Solving, using BODMAS rule,

$=\left(\frac{1.45}{2.9}\right) \times(4.11)+1.002-.005+.98$

$=(0.5) \times(4.11)+1.002-.005+.98$$=2.055+1.002-.005+.98$$=4.032$
Question 6
4 / -1

The average price of 20 books is Rs. 14, while the average price of 18 of these books is Rs. 13. Out of the remaining two books, if the value of one book is 21.05% of the other, what will be the value of each of these two books?

A
Rs. 36, Rs. 10

B
Rs. 38, Rs. 8

C
Rs. 40, Rs. 6

D
Rs. 25, Rs. 21

Solution

Let the price of remaining 2 books be x and y.x = 21.05%y⇒ x = 0.2105y

⇒ Total price of 20 books = Rs. 14 × 20 = Rs. 280

⇒ Total price of 18 books = Rs. 13 × 18 = Rs. 234

Total price = Price of 18 books + Price of 2 books⇒ 280 = 234 + x + y⇒ 46=(1+0.2105)y⇒y = 38

⇒ x = 0.2105y ⇒ x = 8
Question 7
4 / -1

Which of the following is not the additive inverse of a?

A
a

B
a$\times$( -1)

C
-a

D
None of these

Solution

The additive inverse of a is ( -a).

The additive inverse of an integer is the same integer value with opposite sign.
Question 8
4 / -1

A 460 litre of the mixture contains milk and water in the ratio 11 ∶ 12. How much milk must be added to the mixture so that it contains milk and water in the proportion of 3 ∶ 2. (In liters)

A
160

B
150

C
130

D
140

Solution

Milk content in mixture$=\frac{11}{23} \times 460=220$litres

Water content$=460-220=240$litres

Now, Milk content after addition= $240 \times \frac{3}{2}=360$litres

Milk added$=360-220=140$litres
Question 9
4 / -1

The probability of getting a number on a roll of one die having total of 6 outcomes is p. A pair of die is rolled. The mean is equal to 0.5. Find the probability of not getting number 5 on at most one die on roll of the pair of dice.

A
$\frac{1}{12}$

B
$\frac{11}{12}$

C
$\frac{143}{144}$

D
$\frac{1}{144}$

Solution

$\Rightarrow \mathrm{n} \times \mathrm{p}=0.5$ {Mean = n × probability of each outcome}

$\Rightarrow 6 \mathrm{p}=0.5$

$\Rightarrow \mathrm{p}=\frac{1}{12}$

Probability of not getting number 5 on at most one die $=1-\mathrm{p}$ (Getting number 5 on both dice) $=1-(\frac{1}{12} \times \frac{1}{12})$ $=\frac{143}{144}$
Question 10
4 / -1

Which of the following condition is TRUE about the similarity of triangle ABC and DEF given below?

A
$\angle A =\angle D , \angle B =\angle E , \angle C =\angle F$

B
$\angle A =\angle E , \angle B =\angle D , \angle C =\angle F$

C
$\angle A =\angle F , \angle B =\angle D , \angle C =\angle E$

D
None of these

Solution

If $\angle A=\angle D$, then
$\Rightarrow \frac{A B}{A C}=\frac{D E}{D F}$
$\Rightarrow \frac{14}{10}=\frac{7}{5} $
$\Rightarrow \frac{7}{5}=\frac{7}{5}$

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Re-Attempt Weekly Quiz Competition

General Test - 19

Result

General Test - 19

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SHARING IS CARING

Question 1

10 km

160 km

170 km

18 km

Solution

Question 2

8 km/hr

12 km/hr

14 km/hr

10 km/hr

Solution

Question 3

75

88

95

110

Solution

Question 4

22

-34

17

26

Solution

Question 5

\(2.032\)

\(3.032\)

\(4.032\)

\(5.032\)

Solution

Question 6

Rs. 36, Rs. 10

Rs. 38, Rs. 8

Rs. 40, Rs. 6

Rs. 25, Rs. 21

Solution

Question 7

a

a\(\times\)( -1)

-a

None of these

Solution

Question 8

160

150

130

140

Solution

Question 9

\(\frac{1}{12}\)

\(\frac{11}{12}\)

\(\frac{143}{144}\)

\(\frac{1}{144}\)

Solution

Question 10

\(\angle A =\angle D , \angle B =\angle E , \angle C =\angle F\)

\(\angle A =\angle E , \angle B =\angle D , \angle C =\angle F\)

\(\angle A =\angle F , \angle B =\angle D , \angle C =\angle E\)

None of these

Solution

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$8$ km $/$ hr

$12$ km $/$ hr

$14$ km $/$ hr

$10$ km $/$ hr