# Class 10 Maths - Revision Assignment - 3 (1 - Mark Questions - Answers)

Duration: 40 minutes                                                                        All Chapters

Q1: If m is the prime number then, what is the LCM of m, m² and m³.

Q2(CBSE 2019): Express 429 as product of prime factors?

Q3:  If one zero of the quadratic polynomial x² - 5x - 6 is 6 then find the other zero.

Q4: Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1.

Q5(CBSE 2013): What is the lowest value of x²+ 4x + 2 ?

Q6(CBSE 2016): Find whether the following pair of linear equation is consistent or inconsistent:

3x + 2y = 8,

6x - 4y = 9

Q7(MCQ):  The pair of equations x = a and y = b graphically represents lines which are

(A) parallel

(B) intersecting at (b, a)

(C) coincident

(D) intersecting at (a, b)

Q8(CBSE 2010): What are the values of k for which the quadratic equation 2x² - kx + k = 0 has equal roots?

Q9: The quadratic formula was first given by an ancient Indian Mathematician in 1025 AD. Name the Indian mathematician.

Q10(CBSE 2017): Find how many integers between 200 and 500 are divisible by 8.

Q11: Find the first four terms of an AP Whose first term is -2 and common difference is -2.

Q12(CBSE 2020): What is the distance of the point P(- 3,- 4) from the x -axis?

Q13(CBSE 2019):  Find the coordinates of a point A, where AB is a diameter of the circle with centre (- 2, 2) and B is the point with coordinates (3, 4).

Q14: (Fill in the blanks) If two polygons are similar then the same ratio of the corresponding sides is referred to as the ________________.

Q15:  △ABC is an equilateral triangle of side 4cm, then length of one of its altitude is __________ .

Q16: If tan(3x + 30º) = 1 then find the value of x.

Q17(CBSE 2019) : If sin x + cos y = 1; x = 30° and y is an acute angle, find the value of y.

Q18(CBSE 2015): The ________ of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object. (Fill in the blank.)

Q19(CBSE 2011): A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5m away from the wall, find the length of the ladder.

Q20: A chord of a circle of radius 10 cm, subtends a right angle at its centre. What is the length of the chord?

Q21: A parallelogram circumscribing a circle is a ______________. (Fill in the blank)

Q22: To divide a line segment AB in the ratio 2:5, a ray AX is drawn such that ∠BAX is acute. Then points are marked at equal intervals on AX . What is the minimum number of these points?

Q23: The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Q24(MCQ):  If the circumference of a circle and the perimeter of a square are equal, then

(a) Area of the circle = Area of the square

(b) Area of the circle > Area of the square

(c) Area of the circle < Area of the square

(d) Nothing definite can be said about the relation between the areas of the circle and square.

Q25: What is the name of a line which intersects a circle at two distinct points?

Q26: Find the ratio of volumes of two cylinders (of radius r and R) with equal height.

Q27(CBSE 2012): The radius of sphere is r cm. It is divided into two equal parts. Find the whole surface of two parts.

Q28(CBSE 2020): Find the class-marks of the classes 10-25 and 35-66.

Q29(CBSE 2012): For finding the popular size of readymade garments, which central tendency is used?

Q30: Find the probability of an impossible event.

A1: m³

A2: 429 = 3 × 11 × 13

A3: Let α, 6 be the zeros of given polynomial.

Then Sum of Zeros, α + 6 = 5

⇒ α = -1

A4: Let α and β be the zeroes of the required polynomial f(x).

Then (α + β) = 0 and αβ = -1

∴f(x) = x² - (α + β)x + αβ

⇒ f(x) = x² - 0x + (-1)

⇒ f(x) = x² - 1

Hence, required polynomial f(x) = x² - 1.

A5: x²+ 4x + 2

= (x²+ 4x + 4)- 2

= (x + 2)² - 2

Here (x + 2)² is always positive and its lowest value is zero.

⇒ x + 2 = 0

⇒ x = -2

Thus lowest value of x²+ 4x + 2  is -2 when x + 2 = 0.

A6: Since

3        2

--  ≠ --

6        -4

i.e.

a₁       b₁

__  ≠ ___

a₂       b₂

∴ the pair of linear equation is consistent.

A7: (D) intersecting at (a, b)

A8: Comparing with ax²+ bx + c = 0 we a = 2, b = -k and c = k .

For equal roots, D = 0

⇒     b²- 4ac = 0

⇒     (-k)²- 4(2)(k) = 0

⇒     k²- 8k = 0

⇒    k(k - 8) = 0

⇒     k = 0 or k = 8     (Answer)

A9: Sridharacharya

A10: AP formed is 208, 216, 224, ..., 496

Here,

an = 496, a = 208,  d = 8

an = a +(n -1)d

208 + (n - 1) × 8 = 496

8 (n- 1) = 288

n-1=36

A11:

a₁ = -2,

a₂ = a₁ + d = - 2 +(-2) = -4

a₃ = a₂ + d = -4 + (-2) = -6

a₄ = a₃ + d = -6 + (-2) = -8

Thus first four terms are -2, -4, -6, -8

A12: Graphically, Point P(- 3,- 4) is 4 units from the x -axis and 3 units from the y -axis.

You may use distance formula to compute it.

A13: Use mid-point formula to solve it. Co-ordinates of A are (-7, 0)

A14: Scale Factor

A15: Altitude Formula = (a√3)/2  where 'a' is the edge

Altitude = 2√3 cm

A16: tan(3x + 30º) = 1 = tan 45º

3x + 30º = 45º

x = 5º           (Ans)

A17: We have, sin x + cosy = 1

sin 30° + cos y = 1

0.5 + cos y=1

cos y =1- 0.5 =0.5 = cos 60°

y= 60°

A18: Angle of depression

A19: 5m (Use cos 60°)

A20: 10√2 cm (Hint Apply Pythagoras theorem)

A21: rhombus

A22: Minimum number of points marked on AX are 2 + 5 = 7

A23: 264 sq. cm

Angle subtended in 1 minutes = 6°

Angle subtended in 35 minutes (θ) = 6° ×35 = 210°

Use formula Area of sector = (θ/360)×πr² = 264

A24: (b) Area of the circle > Area of the square

A25: Secant

A26: πR²h : πr²h = R² : r²

A27

TSA of each hemisphere = 3πr²

Total surface of two hemispheres (separate) =  6πr²

A28: Class mark of 10 - 25 = (10 + 25)/2  = 17.5

Class mark of 35 - 55 = (35 + 55)/ 2 =  45

A29: Mode

A30: Zero