General Test - 40

Let the length of train \(x=4 a\), time \(=2 b\)

Speed \(=\frac{4 a}{2 b}\)

Let the length of train \(Y=7 a\), time \(=3 b\)

Speed \(=\frac{7 a}{3 b}\)

Ratio of the speed \(=\frac{\frac{4 a} { 2 b}}{\frac{7 a }{ 3 b}}=6: 7\)

Speed of train \(Y=\frac{36}{6} \times 7=42\)

In m/s \(=42 \times \frac{5}{18}\)

\(=\frac{35}{3}\) m/s

\(\frac{2}{3}, \frac{3}{5}, \frac{8}{11}, \frac{7}{9}, \frac{11}{17} \)

\(\frac{2}{3}=0.67 \),\(\frac{3}{5}=0.6 \),\(\frac{8}{11}=0.727 \),\(\frac{7}{9}=0.778 \),\(\frac{11}{17}=0.647\)

Clearly, \(0.778\) is largest.Thus, \(\frac{7}{9}\) is largest.

Sum of first12 results = 12 × 14

Sum of last 12 results = 12 × 17

13th result = x (let)

Now,12 × 14 + 12 × 17 + x = 25 × 18

x = 78

An integer isa numerical value in a number system that is not fractional. They are positive and negative counting numbers including zero.

Option A={\(\frac {17} {3} \) - \(\frac {5} {3} \)}=\(\frac {12} {3} \)=4

Option B={\(\frac {22} {3} \) - \(\frac {11} {3} \)}=\(\frac {11} {3} \)

Option C={\(\frac {13} {5} \) - \(\frac {2} {5} \)}=\(\frac {11} {5} \)

Option D={\(\frac {11} {5} \) - \(\frac {3} {5} \)}=\(\frac {8} {5} \)

Since fractional numbers are not integers

So,

{\(\frac {17} {3} \) - \(\frac {5} {3} \)}=\(\frac {12} {3} \)=4 is an integer.

Volume of alcohol in mixture \(=\frac{1}{5} \times 15=3\) litres

Volume of water in the mixture \(=\frac{4}{5} \times 15=12\) litres

Total volume of mixture \(=3+15=18\) litres

\(\%\) alcohol in the mixture \(=\frac{3}{18} \times 100 \%=\frac{50}{3} \%=16 \frac{2}{3} \%\)

We know that in a single throw of two dice, the total number of possible outcomes is 6 × 6 = 36

Let S be the sample space. Then, n(S) = 36

Let E = event of getting a total of 8. Then,

E = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}∴ n(E) = 5

So, the probability of obtaining a total of '8’\(= P ( E )\)\(\Rightarrow \frac{ n ( E )}{ n ( S )}\)\(\Rightarrow\frac{5}{36}\)

Given:

The ratio between the largest angle and the smallest angle of a triangle is 2 ∶ 1.

The second-largest angle of a triangle is 33°.

According to the question,

The second-largest angle of a triangle is 33°.

The sum of the remaining angle of a triangle = 180° - 33° = 147°

Let the largest angle and the smallest angle of a triangle be 2x and x respectively.

Again,

2x + x = 147°

⇒ 3x = 147°

\(⇒ x = \frac{147°}{3}\)

⇒ x = 49°

⇒ 2x = 2 × 49° = 98°

The value of 50 percent of the largest angle of the triangle \(= \frac{98°}{2}\) = 49°

∴ The value of 50 percent of the largest angle of the triangle is 49°.