Category: CBSE

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 3

                                                                      Section A

1.Determine the value of k for which the indicated value of x is a solution: x² + kx – 4 = 0; x = -4.

2.Find the sum of the following AP: 2, 7, 12, …………. ……… upto 10 terms.

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3.Find the ratio in which the joining of points (- 3, 10) and (6, – 8) is divided     by point    (- 1, 6).

4.Find the area of a quadrant of a circle whose circumference is 22 cm.

                                                                   Section B

5.Find discriminant of the following quadratic equation and examine the nature of real roots (if they exist): 7y²  + 4y + 5 = 0.

6.Find the sum of the first 17 terms of the AP whose nth term is given by t_n = 7 -4n.

7.In figure, O is the centre of the circle, radius of the circle is 3 cm and PA is a tangent drawn to the circle from point P. If OP = x cm and AP = 6 cm, then find the value of x.

8.2000 tickets of a lottery were sold and there are 8 prizes on these tickets. Your friend has purchased one lottery ticket. What is the probability that your friend wins a prize?

9.The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

10.The diameter of a solid metallic sphere is 16 cm. The sphere is melted and recast into 8 equal solid spherical balls. Determine the radius of the balls.

                                                                Section C

11.The sum of an integer and its reciprocal is 145/12 find the integer.

12.Find the 12th term from the end in the AP 56, 63, 70, …………….. ,329.

13.Solve for x : x – 1/x = 3, x not equal to zero

14.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it, whose sides are — of the corresponding sides of the first triangle.

15.A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. Find the probability that the marble taken out will be (i) red (ii) white (iii)not green.

16.A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the piggy bank is turned upside down, find the probability that the coin (i)will be a 50 p coin (ii)will not be a Rs 5 coin.

17.The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordi­nates of the fourth vertex.

18.Using distance formula, show that the points A, B and C are collinear: A(2, 3), B(3, 4), C(6, 7)

19.Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60°.

20.A drinking glass is in the shape of a frustum of a cone of height 14 cm. The radii of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. (Take pi = 22/7)

                                                                Section D

21.A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

22.Three positive integers a1 a₂, a₃ are in AP such that a₁ + a₂ + a₃ = 33 and a1 x a₂x a₃ = 1155. Find the integers a1, a₂ and a₃.                                                                                  .

23. A village Panchayat constructed a circular tank to serve as a bird bath. A fencing was made in the shape of quadrilateral ABCD to circumscribe the circle. Prove that AB + CD = AD + BC.
What values does the village Panchayat depict through this action?

24.In figure, PA and PB are tangents to circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 7 cm and CQ = 2.5 cm, find the length of CP.

25.The lengths of tangents drawn from an external point (point outside the circle) to a circle are equal. Prove it.

26.A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°.

27.Two men standing on either side of a cliff 80 m high, observe the angles of elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

28.Find the area of the quadrilateral formed by joining the points: A(-4, -2), B(-3, -5), C(3, -2) and D(2, 3).

29.In figure, OACB is quadrant of a circle with centre O and radius 8 cm. If OD = 5 cm, find
(i) the area of the quadrant OACB.
(ii) the area of the shaded region. (Take pi = 22/7)

30.A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.(Take pi = 22/7)

31.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. (Take pi = 22/7)

Answers

                                                             Section A

1.Determine the value of k for which the indicated value of x is a solution: x² + kx – 4 = 0;
x = -4.
Ans.

2.Find the sum of the following AP: 2, 7, 12, …………. ……… upto 10 terms.
Ans.

3.Find the ratio in which the joining of points (- 3,10) and (6, – 8) is divided by point (- 1, 6).
Ans.

4.Find the area of a quadrant of a circle whose circumference is 22 cm.
Ans.

                                                                   Section B

5.Find discriminant of the following quadratic equation and examine the nature of real roots (if they exist): 7y²  + 4y + 5 = 0.
Ans.

6.Find the sum of the first 17 terms of the AP whose nth term is given by t_n = 7 -4n.
Ans.

7.In figure, O is the centre of the circle, radius of the circle is 3 cm and PA is a tangent drawn to the circle from point P. If OP = x cm and AP = 6 cm, then find the value of x.

Ans.

8.2000 tickets of a lottery were sold and there are 8 prizes on these tickets. Your friend has purchased one lottery ticket. What is the probability that your friend wins a prize?
Ans.

9.The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Ans.

10.The diameter of a solid metallic sphere is 16 cm. The sphere is melted and recast into 8 equal solid spherical balls. Determine the radius of the balls.
Ans.

                                                                Section C

11.The sum of an integer and its reciprocal is 145/12 find the integer.
Ans.

12.Find the 12th term from the end in the AP 56, 63, 70, …………….. ,329.
Ans.

13.Solve for x : x – 1/x = 3, x not equal to zero
Ans.

14.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it, whose sides are — of the corresponding sides of the first triangle.
Ans.

15.A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. Find the probability that the marble taken out will be (i)red (ii) white (iii)not green.
Ans.

16.A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the piggy bank is turned upside down, find the probability that the coin (i)will be a 50 p coin (ii)will not be a Rs 5 coin.
Ans.

17.The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordi­nates of the fourth vertex.
Ans.

18.Using distance formula, show that the points A, B and C are collinear: A(2, 3), B(3, 4), C(6, 7)
Ans.

19.Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60°.
Ans.

20.A drinking glass is in the shape of a frustum of a cone of height 14 cm. The radii of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. (Take pi = 22/7)
Ans.

                                                                Section D

21.A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Ans.

22.Three positive integers a1 a₂, a₃ are in AP such that a₁ + a₂ + a₃ = 33 and a1 x a₂x a₃ = 1155. Find the integers a1, a₂ and a₃. 
Ans.

                                                                                .

23. A village Panchayat constructed a circular tank to serve as a bird bath. A fencing was made in the shape of quadrilateral ABCD to circumscribe the circle. Prove that AB + CD = AD + BC.
What values does the village Panchayat depict through this action?

Ans.

24.In figure, PA and PB are tangents to circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 7 cm and CQ = 2.5 cm, find the length of CP.

Ans.

25.The lengths of tangents drawn from an external point (point outside the circle) to a circle are equal. Prove it.
Ans.

26.A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°.
Ans.

27.Two men standing on either side of a cliff 80 m high, observe the angles of elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.
Ans.

28.Find the area of the quadrilateral formed by joining the points: A(-4, -2), B(-3, -5), C(3, -2) and D(2, 3).
Ans.

29.In figure, OACB is quadrant of a circle with centre O and radius 8 cm. If OD = 5 cm, find
(i) the area of the quadrant OACB.
(ii) the area of the shaded region. (Take pi = 22/7)

Ans.

30.A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.(Take pi = 22/7)
Ans.

31.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. (Take pi = 22/7)

Ans.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

• All questions are compulsory.
• This question paper consists of 30 questions divided into four sections- A, B, C and D.
• Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
• There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
• Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I

Section – A

Question 1.
What is the common difference of an A.P. in which a₂₁ – a₇ = 84 ? [1]
Solution:
Given, a₂₁ – a₇ = 84
⇒ (a + 20d) – (a + 6d) = 84
⇒ a + 20d – a – 6d = 84
⇒ 20d – 6d = 84
⇒ 14d = 84
Hence common difference = 6

Question 2.
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. [1]
Solution:
Given, ∠APB = 60°
∠APO = 30°

In right angle ΔOAP,
\(\frac { OP }{ OA }\) = cosec 30°
⇒ \(\frac { OP }{ a }\) = 2
⇒ OP = 2a

Question 3.
If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun? [1]
Solution:
In ΔABC,
tan θ = \(\frac { AB }{ BC }\)

⇒ tan θ = \(\frac { 30 }{ 10\surd 3 }\) = √3
⇒ tan θ = tan 60°
⇒ θ = 60°
Hence angle of elevation is 60°.

Question 4.
The probability of selecting a rotten apple randomly from a heap of 900 apples is 0-18. What is the number of rotten apples in the heap? [1]
Solution:
Total apples = 900
P(E) = 0.18

No. of rotten apples = 900 × 0.18 = 162

Section – B

Question 5.
Find the value of p, for which one root of the quadratic equation px² – 14x + 8 = 0 is 6 times the other. [2]
Solution:
Given equation is px² – 14x + 8 = 0
Let one root = α
then other root = 6α

Question 6.
Which term of the progression 20, 19\(\frac { 1 }{ 4 }\), 18\(\frac { 1 }{ 2 }\), 17\(\frac { 3 }{ 4 }\), … is the first negative term ? [2]
Solution:
Given, A.P. is 20, 19\(\frac { 1 }{ 4 }\), 18\(\frac { 1 }{ 2 }\), 17\(\frac { 3 }{ 4 }\), …..

Question 7.
Prove that the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord. [2]
Solution:
Given, a circle of radius OA and centred at O with chord AB and tangents PQ & RS are drawn from point A and B respectively.

Draw OM ⊥ AB, and join OA and OB.
In ∆OAM and ∆OMB,
OA = OB (Radii)
OM = OM (Common)
∠OMA = ∠OMB (Each 90°)
∆OAM = ∆OMB (By R.H.S. Congurency)
∠OAM = ∠OBM (C.PC.T.)
Also, ∠OAP = ∠OBR = 90° (Line joining point of contact of tangent to centre is perpendicular on it)
On addition,
∠OAM + ∠OAP = ∠OBM + ∠OBR
⇒ ∠PAB = ∠RBA
⇒ ∠PAQ – ∠PAB = ∠RBS – ∠RBA
⇒ ∠QAB = ∠SBA
Hence Proved

Question 8.
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA [2]
Solution:
Given, a quad. ABCD and a circle touch its all four sides at P, Q, R, and S respectively.

To prove: AB + CD = BC + DA
Now, L.H.S. = AB + CD
= AP + PB + CR + RD
= AS + BQ + CQ + DS (Tangents from same external point are always equal)
= (AS + SD) + (BQ + QC)
= AD + BC
= R.H.S.
Hence Proved.

Question 9.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q. [2]
Solution:
Let co-ordinate of P (0, y)
Co-ordinate of Q (x, 0)

Question 10.
If the distances of P(x, y), from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y. [2]
Solution:
Given, PA = PB

⇒ x² + 25 – 10x + y² + 1 – 2y = x² + 1 + 2x + y² + 25 – 10y
⇒ -10x – 2y = 2x – 10y
⇒ -10x – 2x = -10y + 2y
⇒ 12x = 8y
⇒ 3x = 2y
Hence Proved.

Section – C

Question 11.
If ad ≠ bc, then prove that the equation (a² + b²) x² + 2 (ac + bd) x + (c² + d²) = 0 has no real roots. [3]
Solution:
Given, ad ≠ bc
(a² + b²) x² + 2(ac + bd)x + (c² + d²) = 0
D = b² – 4ac
= [2(ac + bd)]² – 4 (a² + b²) (c² + d²)]
= 4[a²c² + b²d² + 2abcd] – 4(a²c² + a²d² + b²c² + b²d²)
= 4[a²c² + b²d² + 2abcd – a²c² – a²d² – b²c² – b²d²]
= 4[-a²d² – b²c² + 2abcd]
= -4[a²d² + b²c² – 2abcd]
= -4[ad – bc]²
D is negative
Hence given equation has no real roots.
Hence Proved.

Question 12.
The first term of an A.E is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P. [3]
Solution:
Given, a = 5, a_n = 45, S_n = 400
We have, S_n = \(\frac { n }{ 2 }\) [a + a_n]
⇒ 400 = \(\frac { n }{ 2 }\) [5 + 45]
⇒ 400 = \(\frac { n }{ 2 }\) [50]
⇒ 25n = 400
⇒ n = 16
Now, a_n = a + (n – 1) d
⇒ 45 = 5 + (16 – 1)d
⇒ 45 – 5 = 15d
⇒ 15d = 40
⇒ d = \(\frac { 8 }{ 3 }\)
So n = 16 and d = \(\frac { 8 }{ 3 }\)

Question 13.
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. [3]
Solution:
Let height AB of tower = h m.

Question 14.
A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. [3]
Solution:
Given, no. of white balls = 15
Let no. of black balls = x
Total balls = (15 + x)
According to the question,
P(Blackball) = 3 × P(White ball)
⇒ \(\frac { x }{ 15+x }\) = 3 × \(\frac { 15 }{ 15+x }\)
⇒ x = 45
No. of black balls in bag = 45

Question 15.
In what ratio does the point (\(\frac { 24 }{ 11 }\), y) the line segment joining the points P(2, -2) and Q(3, 7) ? Also, find the value of y. [3]

Solution:
Let point R divides PQ in the ratio k : 1

Question 16.
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semi-circle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. [3]

Solution:
Given, radius of large semi-circle = 4.5 cm

Question 17.
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. [Use π = \(\frac { 22 }{ 7 }\)]

Solution:
Angle for shaded region = 360° – 60° = 300°
Area of shaded region

Question 18.
Water in a canal, 5-4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ? [3]
Solution:
Width of canal = 5.4 m
Depth of canal = 1.8 m
Length of water in canal for 1 hr = 25 km = 25000 m
Volume of water flown out from canal in 1 hr = l × b × h = 5.4 × 1.8 × 25000 = 243000 m³
Volume of water for 40 min = 243000 × \(\frac { 40 }{ 60 }\) = 162000 m³
Area to be irrigated with 10 cm standing water in field = \(\frac { Volume }{ Height }\)
= \(\frac { 162000\times 100 }{ 10 }\) m²
= 1620000 m²
= 162 hectare

Question 19.
The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. [3]
Solution:
Slant height of frustum ‘l’ = 4 cm
Perimeter of upper top = 18 cm

Question 20.
The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe. [3]
Solution:
Inner radius of pipe ‘r’ = 30 cm
The thickness of pipe = 5 cm
Outer radius ‘R’ = 30 + 5 = 35 cm
Now, Volume of hollow pipe = Volume of Cuboid

Section – D

Question 21.
Solve for x:

Solution:

Question 22.
Two taps running together can fill a tank in 3\(\frac { 1 }{ 13 }\) hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank ? [4]
Solution:
Let tank fill by one tap = x hrs
other tap = (x + 3) hrs
Together they fill by 3\(\frac { 1 }{ 13 }\) = \(\frac { 40 }{ 13 }\) hrs

Either x – 5 = 0 or 13x + 24 = 0
x = 5, x = -24/13 (Rejected)
One tap fill the tank in 5 hrs
So other tap fill the tank in 5 + 3 = 8 hrs

Question 23.
If the ratio of the sum of the first n terms of two A.P.S is (7n + 1) : (4n + 27), then find the ratio of their 9th terms. [4]
Solution:
Ratio of the sum of first n terms of two A.P.s are

Hence ratio of 9th terms of two A.P.s is 24 : 19

Question 24.
Prove that the lengths of two tangents drawn from an external point to a circle are equal. [4]
Solution:
Given, a circle with centre O and external point P. |
Two tangents PA and PB are drawn.

To Prove: PA = PB
Construction: Join radius OA and OB also join O to P.
Proof: In ∆OAP and ∆OBP,
OA = OB (Radii)
∠A = ∠B (Each 90°)
OP = OP (Common)
∆AOP = ∆BOP (RHS cong.)
PA = PB [By C.PC.T.]
Hence Proved.

Question 25.
In the given figure, XY and XY are two parallel tangents to a circle with centre O and another tangent AB with a point of contact C, is intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°. [4]

Solution:
Given, XX’ & YY’ are parallel.
Tangent AB is another tangent which touches the circle at C.

To prove: ∠AOB = 90°
Construction: Join OC.
Proof: In ∆OPA and ∆OCA,
OP = OC (Radii)
∠OPA = ∠OCA (Radius ⊥ Tangent)
OA = OA (Common)
∆OPA = ∆OCA (CPCT)
∠1 = ∠2 …(i)
Similarly, ∆OQB = ∆OCB
∠3 = ∠4 …(ii)
Also, POQ is a diameter of circle
∠POQ = 180° (Straight angle)
∠1 + ∠2 + ∠3 + ∠4 = 180°
From eq. (i) and (ii),
∠2 + ∠2 + ∠3 + ∠3 = 180°
⇒ 2(∠2 + ∠3) = 180°
⇒ ∠2 + ∠3 = 90°
Hence, ∠AOB = 90°
Hence Proved.

Question 26.
Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are \(\frac { 3 }{ 4 }\) times the corresponding sides of the ∆ABC. [4]
Solution:
BC = 7 cm, ∠B = 45°, ∠A = 105°
∠C = 180 ° – (∠B + ∠A) = 180° – (45° + 105°) = 180° – 150° = 30°

Steps of construction:

1. Draw a line segment BC = 7 cm.
2. Draw an angle 45° at B and 30° at C. They intersect at A.
3. Draw an acute angle at B.
4. Divide angle ray in 4 equal parts as B₁, B₂, B₃ and B₄.
5. Join B₄ to C.
6. From By draw a line parallel to B₄C intersecting BC at C’.
7. Draw another line parallel to CA from C’ intersecting AB ray at A.
   Hence, ∆A’BC’ is required triangle such that ∆A’BC’ ~ ∆ABC with A’B = \(\frac { 3 }{ 4 }\) AB.

Question 27.
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3 = 1.732] [4]
Solution:
Let aeroplane is at A, 300 m high from a river. C and D are opposite banks of river.

Question 28.
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear, then find the value of k. [4]
Solution:
Since A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear points, so area of triangle = 0.

Question 29.
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product. [4]
Solution:
When two different dice are thrown together
Total outcomes = 6 × 6 = 36
(i) For even sum: Favourable outcomes are
(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6),
(3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6),
(5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)
No. of favourable outcomes = 18

(ii) For even product: Favourable outcomes are
(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
No. of favourable outcomes = 27

Question 30.
In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [4]

Solution:
Area of Shaded region = Area of a rectangle – Area of a semi-circle

Question 31.
In a rain-water harvesting system, the rainwater from a roof of 22 m × 20 m drains into a cylindrical tank having a diameter of base 2 m and height 35 m. If the tank is full, find the rainfall in cm. Write your views on water conservation. [4]
Solution:
Volume of water collected in system = Volume of a cylindrical tank

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Question 10.
Which term of the A.P. 8, 14, 20, 26,… will be 72 more than its 41st term? [2]
Solution:
A.P. is 8, 14, 20, 26,….
a = 8, d = 14 – 8 = 6
Let a_n = a₄₁ + 72
a + (n – 1)d = a + 40d + 72
⇒ (n – 1) 6 = 40 × 6 + 72 = 240 + 72 = 312
⇒ n – 1 = 52
⇒ n = 52 + 1 = 53rd term

Section – C

Question 18.
From a solid right circular cylinder of height 24 cm and radius 0.7 cm, a right circular cone of the same height and same radius is cut out. Find the total surface area of the remaining solid. [3]
Solution:
Given,
Height of cylinder ‘h’ = 2.4 cm,
Radius of base ‘r’ = 0.7 cm

Question 19.
If the 10th term of an A.E is 52 and the 17th term is 20 more than the 13th term, find the A.P. [3]
Solution:
Given, a₁₀ = 52;
a₁₇ = a₁₃ + 20
⇒ a + 16d = a + 12d + 20
⇒ 16d = 12d + 20
⇒ 4d = 20
⇒ d = 5
Also, a + 9d = 52
⇒ a + 9 × 5 = 52
⇒ a + 45 = 52
⇒ a = 7
Therefore A.E = 7, 12, 17, 22, 27,….

Question 20.
If the roots of the equation (c² – ab) x² – 2(a² – bc) x + b² – ac = 0 in x are equal, then show that either a = 0 or a³ + b³ + c³ = 3abc. [3]
Solution:

Section – D

Question 28.
Solve for x:

Solution:

Question 29.
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less on the journey. Find the original speed of the train. [4]
Solution:
Let original speed of train = x km/hr
Increased speed of train = (x + 5) km/hr
Distance = 300 km
According to the question,

Question 30.
A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower. [4]
Solution:
Let AB is a tower, the car is at point D at 30° and goes to C at 45° in 12 minutes.

Question 31.
In the given figure, ΔABC is a right-angled triangle in which ∠A is 90°. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region. [4]

Solution:
In right ΔBAC, by Pythagoras theorem,

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Question 10.
For what value of n, are the terms of two A.Ps 63, 65, 67,…. and 3, 10, 17,…. equal ? [2]
Solution:
1st A.P. is 63, 65, 67,…
a = 63, d = 65 – 63 = 2
a_n = a + (n – 1 )d = 63 + (n – 1) 2 = 63 + 2n – 2 = 61 + 2n
2nd A.E is 3, 10, 17,…
a = 3, d = 10 – 3 = 7
a_n = a + (n – 1 )d = 3 + (n – 1) 7 = 3 + 7n – 7 = 7n – 4
According to question,
61 + 2n = 7n – 4
⇒ 61 + 4 = 7n – 2n
⇒ 65 = 5n
⇒ n = 13
Hence, 13th term of both A.P. is equal.

Section – C

Question 18.
A toy is in the form of a cone of radius 3-5 cm mounted on a hemisphere of the same radius on its circular face. The total height of the toy is 15*5 cm. Find the total surface area of the toy. [3]
Solution:
Given, radius of base ‘r’ = 3.5 cm
Total height of toy = 15.5 cm
Height of cone ‘h’ = 15.5 – 3.5 = 12 cm

Question 19.
How many terms of an A.E 9, 17, 25,… must be taken to give a sum of 636? [3]
Solution: A.P. is 9, 17, 25,….,
S_n = 636
a = 9, d = 17 – 9 = 8

Question 20.
If the roots of the equation (a² + b²) x² – 2 (ac + bd) x + (c² + d²) = 0 are equal, prove that \(\frac { a }{ b }\) = \(\frac { c }{ d }\) [3]
Solution:

Section – D

Question 28.
Solve for x:

Solution:

Question 29.
A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it? [4]
Solution:
Let B can finish a work in x days
so, A can finish work in (x – 6) days
Together they finish work in 4 days
Now,

⇒ 4 (2x – 6) = x² – 6x
⇒ 8x – 24 = x² – 6x
⇒ x² – 14x + 24 = 0
⇒ x² – 12x – 2x + 24 = 0
⇒ x(x – 12) – 2(x – 12) = 0
⇒ (x – 12) (x – 2) = 0
Either x – 12 = 0 or x – 2 = 0
x = 12 or x = 2 (Rejected)
B can finish work in 12 days
A can finish work in 6 days.

Question 30.
From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in a same straight line with its base, with angles of depression 30° and 45°. Find the distance between cars.
[Take √3 = 1.732] [4]
Solution:
Let AB is a tower.
Cars are at point C and D respectively

Distance between two cars = x + y = 173.2 + 100 = 273.2 m

Question 31.
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. [4]

Solution:
Given, C (O, OB) with AC = 24 cm AB = 7 cm and ∠BOD = 90°

∠CAB = 90° (Angle in semi-circle)
Using pythagoras theorem in ∆CAB,
BC² = AC² + AB² = (24)² + (7)² = 576 + 49 = 625
⇒ BC = 25 cm
Radius of circle = OB = OD = OC = \(\frac { 25 }{ 2 }\) cm
Area of shaded region = Area of semi-circle with diamieter BC – Area of ∆CAB + Area of sector BOD

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2013

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
4.  Use of calculators is not permitted.

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question.l In Fig. 1, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is I Q cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD, then calculate the length of CD.

Solution.

CBSE Sample Papers Class 10 Maths

Question.2 A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then calculate the height of the wall.
Solution.

Question.3 A box contains cards numbered 6 to 50. A card is drawn at random from the box. Calculate the probability, that the drawn card has a number which is a perfect square.
Solution.

Question.4 If n is taken as 22/7 calculate the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution.
Solution.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 Solve the following for x:

Solution.

Question.6 Find the number of all three-digit natural numbers which are divisible by 9.
Solution.

Question.7 In Fig. 2, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

Solution.

Question.8 In Fig. 3, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Solution.

Question.9 Two coins are tossed simultaneously. Find the probability of getting at least one head.
Solution.

Question.10 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Solution.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 For what values of k, are the roots of the quadratic equation:
(k + 4) x²+ (k + l) x + 1 = 0 equal?
Solution.

Question.12 The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the A.P.
Solution.

Question.13 Draw a pair of tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.
Solution.

Question.14 As observed from the top of a 60m high light-house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light-house, find the distance between the two ships. [Use √3 = 1.732]
Solution.

Question.15 Prove that the points A(2, 3), B(-2, 2), C(-l, -2) and D(3, -1) are the vertices of a square ABCD
Solution.

Question.16 Find the ratio in which point P(-l, y) lying on the line segment joining points A(-3,10) and B(6, -8) divides it. Also find the value of y.
Solution.

Question.17 In Fig. 4, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region. [Use π = 22/7 ]

Solution.

Question.18 A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm. If the total
height of the toy is 31 cm, find its total surface area. [Use π = 22/7 ]
Solution.

Question.19 A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by; a plane parallel to its base. Find the ratio in the volumes of the two parts of the cone.
Solution.

Question.20 A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.
Solution.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 Solve for x:

Solution.

Question.22 A box contains cards numbered 3, 5, 7, 9,…,35, 37. A card is drawn at random from the
box. Find the probability that the number on the drawn card is a prime number.
Solution.

Question.23 The sum of first n terms of an A.P. is 5n² + 3n. If its m^th term is 168, find the value of m. Also find the 20^th term of this A.P.
Solution.

Question.24 Prove that the lengths of tangents drawn from an external point to a circle are equal.
Solution.

Question.25 In Fig. 5, the sides AB, BC and CA of triangle ABC touch a circle with centre O’and radius r at P, Q and R respectively.
Prove that:
(i) AB + CQ = AC + BQ
(ii) Area (ΔABC) = 1/2 (Perimeter of ΔABC ) x r

Solution.

Question.26 The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
Solution.

Question.27 If the points A(l, -2), B(2,3), C(-3,2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.
Solution.

Question.28 Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute. Find the rate of flow of water in the pipe in km/h. [Use π = 22/7 ]
Solution.

Question.29 While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed/hour of the plane.
Do you appreciate the values shown by the pilot, namely, promptness in providing help to the injured and his efforts to reach in time?
Solution.

Question.30 A container, open at the top and made up of metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs 10 per 100 cm2. [Take π = 3.14]
Solution.

Question.31 Find the probability that a leap year selected at random, will contain 53 Mondays.
Solution.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-I.
Question.1 Calculate the common difference of the A.P.

Solution.

Question.10 Three coins are tossed simultaneously. Find the probability of getting exactly two heads.
Solution.

Question.17 For what value of k, are the roots of the quadratic equation (k – 12)x² + 2(k – 12)x + 2 = 0 equal?
Solution.

Question.18 The 8th term of an A.P. is equal to three times its third term. If its 6th term is 22, find the A.P.
Solution.

Question.19 Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Solution.

Question.20 Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus ABCD. Is ABCD a square?
Solution.

Question.28 Solve for x:

Solution.

Question.29 For the triangle ABC formed by the points A(4, -6), B(3, -2) and C(5, 2), verify that median divides the triangle into two triangles of equal area.
Solution.

Question.30 The sum of first m terms of an AP is 4m² – m. If its n^th term is 107, find the value of n. Also find the 21^th term of this A.P.
Solution.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.
Question.1 Calculate the common difference of the A.P

Solution.

Question.10 Two dice are thrown simultaneously. Find the probability of getting a doublet.
Solution.

Question.17 For what value of k, are the roots of the quadratic equation x² + k² = 2 (k + l)y equal?
Solution.

Question.18 The 9^th term of an A.P. is equal to 6 times its second term. If its 5^th term is 22, find the A.P.
Solution.

Question.19 Draw two tangents to a circle of radius 3.5 cm, from a point P at a distance of 6.2 cm from its centre.
Solution.

Question.20 Find that value of k for which point (0, 2), is equidistant from two points (3, k) and (k, 5).
Solution.

Question.28. Solve for x:

Solution.

Question.29 The sum of first q terms of an A.P. is 63q – 3q². If its p^th term is -60, find the value of p. Also find the 11th term of this A.P.
Solution.

Question.30 Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3,5) and C(2, 6).
Solution.

Download Solved CBSE Sample Papers for Class 10 Maths Set 2 2019 PDF to understand the pattern of questions asks in the board exam. Know about the important topics and questions to be prepared for CBSE Class 10 Maths board exam and Score More marks. Here we have given Maths Sample Paper for Class 10 Solved Set 2.

Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 2

CBSE Sample Papers

We hope the Solved CBSE Sample Papers for Class 10 Maths Set 2, help you. If you have any query regarding CBSE Sample Papers for Class 10 Maths Solved Set 2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 English Honeydew Chapter 9 The Great Stone Face I

NCERT Solutions for Class 8 English Honeydew Chapter 9 The Great Stone Face I

Class 8 English Honeydew Chapter 9 The Great Stone Face I Questions From Textbook

COMPREHENSION CHECK (PAGE 129)

Write ‘True’ or ‘False’ against each of the following statements.

1. The Great Stone Face stood near where Ernest and his mother lived.
2. One would clearly distinguish the features of the Stone Face only from a distance.
3. Ernest loved his mother and helped her in her work.
4. Though not very rich, Gathergold was a skilful merchant.
5. Gathergold died in poverty and neglect.
6. The Great Stone Face seemed to suggest that Ernest should not fear the general.

Answer:

1. False
2. True
3. True
4. False
5. True
6. True

WORKING WITH THE TEXT (Page 130)

Answer the following questions.
Question 1:

1. What was the Great Stone Face?
2. What did Young Ernest wish when he gazed at it?

Answer:

1. The Great Stone Face was the work of nature. The rocks were put one over the other on the mountain side. They resembled the features of a human face.
2. Young Ernest wished that the stone face could speak. He wished to love the man dearly whoever resembled that face.

Question 2:
What was the story attributed to the Stone Face?
Answer:
The story attributed to the Stone Face was that some day a child with the likeness of that face would be born. He would become the greatest and noblest person of his age.

Question 3:
What gave the people of the valley the idea that the prophecy was about to come true for the first time?
Answer:
A youngman named Gathergold had left the valley many years ago. By the time he grew old, he had grown rich. When he returned to his native valley, a rumour spread that he resembled the Stone Face. People thought that the prophecy had come true.

Question 4:

1. Did Ernest see in Gathergold the likeness of the Stone Face?
2. Who did he confide in and how was he proved right?

Answer:

1. No, Ernest did not see any likeness of the Stone Face in Gathergold.
2. He confided in the Great Stone Face. After Gathergold’s death as his wealth and gold had already disappeared, it was generally agreed that Gathergold had no resemblance with the Great Stone Face.

Question 5:

1. What made people believe General Blood- and-Thunder was their man?
2. Ernest compared the man’s face with the Stone Face. What did he conclude?

Answer:

1. General Blood-and-thunder had risen to high position from a soldier. When he returned to the valley, his childhood friends said that the General had always looked like the Stone Face.
2. Ernest could not find any likeness between the General and the Stone Face.

WORKING WITH THE LANGUAGE (Page 130)

Question 1:
Look at the following words.
Like — likeness
punctual — punctuality
The words on the left are adjectives and those on the right are their noun forms.
Write the noun forms of the following words by adding -ness or -itv to them appropriately. Check the spelling of the new words.

1. lofty _____________
2. able _____________
3. happy _____________
4. near _____________
5. noble _____________
6. pleasant _____________
7. dense _____________
8. great _____________
9. stable _____________

Answer:

1. loftiness
2. ability
3. happiness
4. nearness
5. nobility
6. enormity
7. pleasantness
8. density
9. greatness
10. stability

Question 2:
Add-iv to each of the following adjectives, then use them to fill in the blanks.

1. Why didn’t you turn up at the meeting? We all were ______ waiting for you.
2. ______ write your name and address in capital letters.
3. I was______ surprised to see him at the railway station. I thought he was not coming.
4. It is______ believable that I am not responsible for this mess.
5. He fell over the step and ______ broke his arm.

Answer:

1. eagerly
2. kindly
3. pleasantly
4. perfectly
5. nearly

Question 3:
Complete each sentence below using the appropriate forms of the verbs in brackets.

1. I ______ (phone) you when I (get) home from school.
2. Hurry up! Madam  ______ (be) annoyed if we ______ (be) late.
3. If it ______ (rain) today, we ______ (not) go to the play.
4. When you  ______ (see) Mandal again, you  ______ (not/recognise) him. He is growing a beard.
5. We are off today. We  ______  (write) to you after we ______ (be) back.

Answer:

1. shall phone: get
2. will be; are
3. rains, shall not go
4. see; will not recognise
5. shall write; are

SPEAKING AND WRITING (Page 131)

Question 1:
Imagine you are Ernest. Narrate the story that his mother told him.
Begin like this: My mother and I were sitting at the door of our cottage. We were looking at the Great Stone Face. I asked her if she had ever seen any one who looked like the Stone Face. Then she told me this story.
Answer:
She had heard that story from her own Mother that some day a child would be born resembling the Stone Face. In manhood he would become the greatest and noblest person of his time.

Question 2:
Imagine you are Gathergold. Write briefly the incident of your return to the valley.
Begin like this: My name is Gathergold. I left the valley of the Great Stone Face fifty years ago. I am now going back home. Will the people of the valley welcome me? Do they know that I am very rich?
Answer:
I drove to my native village in a horse drawn carriage. The people mistook me for the Great Stone Face. They welcomed me and shouted, “Sure enough, the old prophecy is true and the great man has arrived at last”.

MORE QUESTIONS SOLVED

I. SHORT ANSWER TYPE QUESTIONS

Question 1:
What is the significance of the Great Stone Face?
Answer:
The Stone Face was a work of nature. It was formed on the side of a mountain by rocks. Viewed from a distance, those rocks looked like the features of a human face. People linked stories to that face. The people living in that valley believed that some day a great and noble person with the likeness of that face would come.

Question 2:
What did the spectator see when he went near the Great Stone Face?
Answer:
When the spectator went near the Great Stone Face, he lost the outline of the enormous face and could see only a heap of gigantic rocks, piled one upon an¬other.

Question 3:
How did Ernest grow up to be a mild and quiet youth?
Answer:
Ernest never forgot of the story that his mother told him. He was dutiful to his mother and helpful to her many things, assisting her much with his little hands, and .more with his loving heart. In this manner he grew up to be a mild and quiet youth.

Question 4:
How did Gathergold become rich?
Answer:
Gathergold was a young man when he left his native valley and settled at a distant seaport. He set up there as a shopkeeper. He was very sharp in business matters and therefore became very rich in a very short span of time.

Question 5:
How did people’s opinion change about Gathergold after his death?
Answer:
Gathergold died one day. His wealth had disappeared before his death. Since the melting away of his gold, it had been generally believed that there was no like¬ness between the ruined merchant and the majestic face upon the mountain.

II. LONG ANSWER TYPE QUESTIONS

Question 1:
What was the prophecy connected with the Stone Face? Did it come true?
Answer:
The prophecy is a statement about some event in future. The people of the valley believed that the Stone Face was auspicious for them. It made the land fertile with its gaze.
The old prophecy about the Stone Face was that at some future day a child would be born there who will grow up to become great and noble. The child would look like the Stone Face. Some people thought it was just idle talk. It appears finally Ernest himself would be declared to be the great man resembling the Stone Face.

Question 2:
Who was Ernest? What personal qualities made him great?
Answer:
Ernest was a little boy who lived with his Mother in a valley. His interest grew in the Great Stone Face which smiled on him. His Mother told him the prophecy about that Face. The boy never forgot that story. He spent hours looking at that face. He regarded it as his teacher. He was inspired to be noble, kind and helpful. These qualities could make him the man with the likeness of the Face.

More CBSE Class 8 Study Material

• NCERT Maths Solutions Class 8
• NCERT Class 8 Science Solutions
• CBSE Class 8 Social Science Solutions
• NCERT Class 8 English Solutions
• NCERT Solutions for Class 8 English Honeydew
• NCERT Solutions for Class 8 English It So Happened
• NCERT Hindi Class 8 Solutions
• CBSE Class 8 Sanskrit Solutions
• NCERT Solutions

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