Vardaan Learning Institute

Solution:
Let the total number of people surveyed be $x$.
Given, 10% of $x = 20$
$\Rightarrow \frac{10}{100} \times x = 20$
$\Rightarrow x = 20 \times 10 = 200$.
Total 200 young people were surveyed.

Solution:
Looking at the graph (assuming peak is at 4-5 hours), the maximum number of students watched TV for 4 to 5 hours.

Solution:
Total balls = $4 + 2 = 6$.
Probability of Red Ball = $\frac{\text{No. of Red Balls}}{\text{Total Balls}} = \frac{4}{6} = \frac{2}{3}$.
Probability of Yellow Ball = $\frac{2}{6} = \frac{1}{3}$.
Since $\frac{2}{3} > \frac{1}{3}$, getting a Red ball is more likely than getting a Yellow ball.

Solution:
Outcomes of a die: {1, 2, 3, 4, 5, 6}
(a) Prime numbers: 2, 3, 5
(b) Not a prime number: 1, 4, 6

Solution:
W (Women): |||| |||| |||| |||| |||| |||| (28)
M (Men): |||| |||| |||| | (15)
B (Boys): |||| | (5)
G (Girls): |||| |||| || (12)
(Note: Exact count depends on precise tally of the provided string).

Solution:
Frequency Table:
800-810: ||| (3)
810-820: || (2)
820-830: | (1)
830-840: |||| |||| (9)
840-850: |||| | (5)
850-860: | (1)
860-870: ||| (3)
870-880: | (1)
880-890: | (1)
890-900: |||| (4)
Total: 30

Solution:
(i) The group 830-840 has the maximum number of workers (9).
(ii) Workers earning ₹850 or more = $1 + 3 + 1 + 1 + 4 = 10$.
(iii) Workers earning less than ₹850 = $3 + 2 + 1 + 9 + 5 = 20$.

Solution:
Total = 720. Central Angles:
Ordinary Bread: $\frac{320}{720} \times 360^\circ = 160^\circ$
Fruit Bread: $\frac{80}{720} \times 360^\circ = 40^\circ$
Cakes: $\frac{160}{720} \times 360^\circ = 80^\circ$
Biscuits: $\frac{120}{720} \times 360^\circ = 60^\circ$
Others: $\frac{40}{720} \times 360^\circ = 20^\circ$
Total = $360^\circ$.

Solution:
Total = 72. Central Angles:
Hindi: $\frac{40}{72} \times 360^\circ = 200^\circ$
English: $\frac{12}{72} \times 360^\circ = 60^\circ$
Marathi: $\frac{9}{72} \times 360^\circ = 45^\circ$
Tamil: $\frac{7}{72} \times 360^\circ = 35^\circ$
Bengali: $\frac{4}{72} \times 360^\circ = 20^\circ$

Solution:
Total outcomes = 10.
(i) Getting 6: One outcome (6). P = $1/10$.
(ii) Less than 6: {1,2,3,4,5}. 5 outcomes. P = $5/10 = 1/2$.
(iii) Greater than 6: {7,8,9,10}. 4 outcomes. P = $4/10 = 2/5$.
(iv) 1-digit number: {1..9}. 9 outcomes. P = $9/10$.

Solution:
A rectangle is convex because all its diagonals lie in its interior and all angles are less than $180^\circ$. A concave polygon has at least one angle greater than $180^\circ$ and some diagonals lie outside.
Histogram would clearly show bars of height 10, 25, 15, 5.

Solution:
(i) P(Ace) = $4/52 = 1/13$.
(ii) P(Red Card) = $26/52 = 1/2$.
(iii) P(Face Card) = $12/52 = 3/13$.
(iv) P(10 of Spades) = $1/52$.

Solution:
Total = 120.
South Indian fraction = $40/120 = 1/3$.
Central Angle = $\frac{1}{3} \times 360^\circ = 120^\circ$.

Solution:
Mean = $\frac{\sum x}{N} = \frac{74}{25} = 2.96$.

Solution:
Highest frequency is 15 in interval 20-30.
Class size = $10 - 0 = 10$.