Express 98 as a product of its primes. *
2 points
2² × 7
2² × 7²
2 × 7²
23 × 7
Other:
2. The probability of getting less than 3 in a single throw of a die is : *
2 points
1/3
1/2
1
2/5
Other:
3. Mode is the : *
2 points
middle most frequent value
least frequent value
maximum frequent value
none of these
Other:
4. A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is : *
2 points
2 : 1
2 : 3
3 : 2
3 : 1
Other:
5. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is: *
2 points
6
5
4
7
Other:
6. When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is : *
2 points
30°
45°
60°
15°
Other:
7. The points (-5, 1), (1, p) and (4, -2) are co-linear if the value of p is *
2 points
-1
2
3
1
Other:
8. If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is : *
2 points
18
0
19
77
Other:
Answers
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Solution :-
1) 98 = 2 * 7 * 7 = 2 * 7²
2)
→ Total outcomes = 6
→ Less than 3 = 1 and 2 = total 2 .
so,
→ Probability = (2/6) = (1/3)
3) Mode is the = maximum frequent value .
4) Volume of cylinder : Volume of cone = πr²h : (1/3)πr²h = 1 : (1/3) = 3 : 1 .
5)
→ Radius = √(Distance from centre)² - (length of tangent)²
→ Radius = √(10² - 8²) = √(100 - 64) = √36 = 6 cm .
6)
→ Let height of pole = h
→ shadow = √3h .
so,
→ tan θ = height of pole / shadow
→ tan θ = h / √3 h
→ tan θ = 1/√3
→ tan θ = tan 30°
→ θ = 30°
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