CBSE Class 9 - Maths - Very Short Answer Based Questions (Solved Worksheet-1) (#eduvictors)(#cbseClass9Maths)

CBSE Class 9 - Maths - Very Short Answer Based Questions 

(Solved Worksheet-1)

Q1: .Find any two irrational numbers between 0.1 and 0.12


Q2:  Simplify : √72 + √800 - √18.


Q3: What is the degree of a zero polynomial?


Q4: What is the degree of polynomial √3 ?


Q5: Factorise x² - 3x


Q6: Factorise x³ - 8


Q7:  Is 0x + 0y + c = 0, a linear equation?




Q8: In a one day cricket match, Raina and Dhoni scored 198 runs. Express this as a linear equation in two variables.


Q9: Total number of legs in a herd of goats and hens is 40. Represent this in the form of linear equation of two variables.


Q10:  What is the equation of a line parallel to x-axis?


Q11: x=4 is a line parallel to line ___________


Q12: What does the point at which the co-ordinate axes meet is called?


Q13: In which quadrant the points P(2, -3) and Q (-3, 2) lie?


Q14: What is the difference between axioms and theorems?


Q15: How many planes can be made to pass through three collinear points?


Q16: What is the measure of an angle which is complement of itself?


Q17: Two angles measure (30° - a) and (125° + 2a). If each one is the supplement of the other, then find the value of a.


Q18: A transversal l intersects two lines m and n such that a pair of alternate interior angles is equal. Then, what can you say about the lines m and n ?


Q19: If a transversal intersects two parallel lines, then which of the pairs of angles is equal.


Q20: In △ABC, ∠A = ∠B/2 = ∠C/6, then what will be the measure of ∠A?


Q21: If angles of a △ are in the ratio of 5:3:7, verify if is an acute angle △.


Q22:  Is it possible to construct a triangle, when its sides are 5.4 cm, 2.3 cm, 3.1cm?


Q23: Two opposite angles of a parallelogram are (3x — 2)° and (63 - 2x)°. Find all the angles of a parallelogram.


Q24: If a triangle and a parallelogram are on same base and between same parallels, then the ratio of the area of the triangle to the area of a parallelogram is __________.


Q25: _________ is a collection (set) of all those points in a plane, each one of which is at a constant distance from a fixed point in the plane.


Q26: Perpendicular bisectors of two chords of a circle intersect each other at the ________ of the circle.


Q27: An angle in a semi-circle is a _____________.


Q28: The sum of opposite angles of a cyclic quadrilateral is ________.


Q29: Can a angle of 7½° be using a compass?


Q30: The perimeter of an equilateral triangle is 60 m. What will be its area?


Q31: The line drawn through the mid-point of one side of a triangle parallel to the another side, __________ the third side.


Q32: What will be the area of a triangle whose sides are 13 cm, 14 cm and 15 cm?


Q33: Compute the curved surface area of a hemisphere whose diameter is 14 cm.


Q34: How many faces does a right circular cylinder have?


Q35: Find the mean of first six odd numbers.


Q36: Median of first 8 prime numbers is ____.


Q37:  Find the mode of the numbers :
14, 14, 15, 27, 26, 27, 27, 22, 13


Q38: Find the range of the data:
22, 25, 20, 32, 36, 28, 40, 45, 35, 38


Q39: A coin is tossed 500 times with the following observations :
Head : 245 times, Tail : 255 times
The coin is tossed again. The probability of getting a head is _____.


Q40: A and B are the only two outcomes of an event. Probability of (A) = 0.72, then what will be the probability of (B) and why ?

Answers

Answer 1:
Required two irrational number are :
(i) 1010010001000...
(ii) 1020020002000...


Answer 2:
= √72 + √800 - √18
= √(36×2) + √(400 × 2) - √(9 × 2)
= 6√2 + 20√2 - 3√2
= 23√2


Answer 3: Not defined

Answer 4: Zero

Answer 5: x² - 3x = x(x - 3)

Answer6: x³ - 8 = x³ - 2³ = (x - 3)(x² + 2x + 4)

Answer 7: No. (∵ a ≠ and b ≠ 0 for a linear equation)

Answer 8: Let the runs scored by Raina and Dhoni are x & y respectively then, x + y =198

Answer 9: Let the number of goats and hens in herd are x and y respectively then, 4x + 2y = 40

Answer 10:  y=kx

Answer 11: y-axis

Answer 12: Origin (0, 0)

Answer 13: P(2, -3) lies in IV quadrant. Q(-3, 2) lies in II quadrant.

Answer 14: Axioms are are self evident truths, thus require no proof. While theorems need proof.

Answer 15: Infinite.

Answer 16:  Let the angle be x, then Angle x = Complement of x,
x= 90 - x
x= 45


Answer 17:  Angles (30° - a) and (125° + 2a) are supplementary of each other, then
     30°—a + 125° + 2a = 180"
 ⇒ a = 180° - 155° = 25°


Answer 18: m and n lines are parallel

Answer 19:  Pair of alternate interior angles Or a pair of corresponding angles.


Answer: 20:
In ABC,

∠A + ∠B + ∠C = 180° By given conditions)

⇒ ∠A +2∠A + 6∠A = 180°

⇒ 9∠A = 180°

⇒  ∠A = 20°


Answer 21:
Let the angles of triangle are 5x, 3x and 7x, then
5x + 3x + 7x = 180°
⇒ 15x = 180°

Thus, x=12

Angles are 60°, 36°, 84°
∵ Each angle is less than 90°
∴  The triangle is an acute angled triangle.


Answer 22:  No, Because, 2.3 + 3.1 = 5.4cm (third side). It is not possible to construct a triangle.


Answer 23:
Since opposite angles of a parallelogram are equal
∴ 3x-2 = 63-2x
⇒ x= 13°

Angles of a parallelogram : (39—2)°, (180 - 37)°, (63 - 26)°, (180 - 37)°
ie, 37°, 143°, 377, 143°


Answer 24:  If a triangle and a parallelogram are on same base and between same parallels, then the ratio of the area of the triangle to the area of a parallelogram is 1: 2.


Answer 25: A circle is a collection (set) of all those points in a plane, each one of which is at a constant distance from a fixed point in the plane.


Answer 26: Perpendicular bisectors of two chords of a circle intersect each other at the centre of the circle.


Answer 27:  An angle in a semi-circie is a right angle.


Answer 28: The sum of opposite angles of a cyclic quadrilateral is 180°.


Answer 29: Yes. Bisector of 60° ÷ 2 = 30° ÷ 2 = 15° ÷ 2 = 7½°


Answer 30:
Perimeter of an equilateral triangle = 3a = 60m
⇒ a=20m
area = a²√3/4   = (√3/4) × 20 × 20 = 100√3 m².


Answer 31: The line drawn through the mid-point of one side of a triangle parallel to the another side, bisects the third side.


Answer 32: a = 13cm, b = 14cm, c = 15cm
s = (a + b + c)/2 = (13 + 14 + 15)/2 = 21 cm

∴ Area = √(21)(21-13)(21-14)(21-15) = √(21 × 8 × 7 × 6)
= 21 × 4 = 84 cm²


Answer 33:  Given diameter of hemisphere = 14 cm
∴  radius (r) = 7 cm
 Curved surface area =2πr²
= (22/7) x 7 x 7 = 308 cm²


Answer 34: 3


Answer 35:
Mean = (1 + 3+5+7+9+11)/6 = 36 / 6 = 6


Answer 36:
 2,3,5,7, 11,13, 17,19
 Median = (7 + 11)/2 = 18 /2 = 9


Answer 37:  Mode = 27


Answer 38:
Range = highest value — lowest value
= 45-20
=25


Answer 39:
Probability of getting ahead = (245/500) = 0.49


Answer 40: Since, P(A) + P(B) =1

∴ P(B) =1-0.72

= 0.28

∵ Sum of probabilities is 1.


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