RBSE Class 10 Maths Board Paper 2018 English Medium

RBSE Class 10 Maths Board Paper 2018 English Medium are part of RBSE Class 10 Maths Board Model Papers. Here we have given Rajasthan RBSE Class 10 Maths Board Paper 2018 English Medium.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 10
Subject	Maths
Paper Set	Board Paper 2018
Category	RBSE Model Papers

Rajasthan RBSE Class 10 Maths Board Paper 2018 English Medium

Time: 3.15 Hours
Maxim Marks: 80

General Instructions to the Examinees

1. Candidate must write first his/her Roll on the question paper compulsory.
2. All the questions are compulsory.
3. Write the answer to each question in the given answer sheet only.
4. For question having more than one part, the answers to those parts are to be written together in continuity.
5. If there is any error/difference/contradiction in Hindi & English versions of the question paper, the question of Hindi versions should be treated valid.

6. Part	No.of Question	Marks per Question
   A	1 – 10	1
   B	11 – 15	2
   C	16 – 25	3
   D	26 – 30	6

7. There are internal choices in Q. No. 27 and Q.No 29
8. Write on both sides of the pages of your answer-book. If any rough work is to be done, do it on last pages of the answer-book and cross with slant lines and write ‘Rough Work’ on them.
9. Draw the graph of Question No. 26 on graph paper.

Section – A

Question 1.
Find the value of 31\(\frac { 1 }{ 6 } \)  x 3\(\frac { 5 }{ 6 }\) by using Ekaadhiken Purven Sutra. [1]

Question 2.
Solve :\(\frac { 1 }{ x-3 } +\frac { 1 }{ x-7 } = \frac { 1 }{ x-1 } +\frac { 1 }{ x-9 }\) [1]

Question 3.
Write the sum of powers of prime factors of 196. [1]

Question 4.
Write the value of cos50°.cosec40°. [1]

Question 5.
If the ratio of the length of a vertical bar to its shadow is 1:\(\sqrt { 3 }\), then find the elevation angle of the sun. [1]

Question 6.
Write the locus of the points equidistant from the two given points. [1]

Question 7.
Find the ratio between the chords which are equidistant from the center of a circle. [1]

Question 8.
A dice is thrown once. Find the probability of getting an odd number. [1]

Question 9.
In a city, the fare of a taxi for first kilometer is ₹5 and after that, it is ₹3. If distance covered is x km and fare is ₹y, then express it in the form of equation. [1]

Question 10.
If the elevation angle of a camera situated at the top of a pole from a point 20 meter away from the base of the pole is 60°, Find the height of the pole. [1]

Section – B

Question 11.
Find the square root of 6889 by using Dwandwa Yoga Method. [2]

Question 12.
If the product of two numbers is 525 and their H.C.F. is 5, then find their L.C.M. [2]

Question 13.
The total surface area of a cube is 216 square meter. Find the side of the cube. [2]

Question 14.
The radius of a semi-sphere is 7cm, find the total surface area of it. [2]

Question 15.
A CCTV camera is placed on the top of a 24 m high pole in such a way that traffic can be seen beyond 25 meters of line of sight of it. Find the area of the Green patch around the pole. [2]

Section -C

Question 16.
By using division algorithm method find quotient and remainder when polynomial P(x) = x⁴ – 3x² + 4x – 3 is divided by g(x) = x² + 1 – x. [3]

Question 17.
If second and third terms of an Arithmetic Progression are 3 and 5 respectively, then find the sum of first 20 terms of it. [3]

Question 18.
The angles of elevation of the top of a tower from two points at a distance of 9 m and 25 m from the base of the tower in the same straight line are complementary. Find the height of the tower. [3]

Question 19.
In the given figure if OP.OQ = OR.OS then show that ∠OPS = ∠ORQ and ∠OQR = ∠OSP. [3]

Question 20.
In a trinagle ABC, the medians AD, BE and CF pass through the point G. If AD=9cm, GE = 4.2 cm, and GC = 6cm, then find the values of the lengths of AG, BE and FG. [3]

Question 21.
In the given figure some angles are represented by x, y, and z. Find the values of these angles. [3]

Question 22.
Draw two tangents PA and PB from an external point P to a circle of radius 4cm, where angle between PA and PB is 65°. [3]

Question 23.
The radius of a circular park is 4.2 m. A path of 1.4 m width is made around the circular park. Find the area of the path. [3]

Question 24.
The length and diameter of a roller are 2.5 m and 1.4 m respectively. How much are will be planned by roller in 10 revolutions? [3]

Question 25.
In a bag, one white ball, two black balls and three red balls of same size are placed. A ball is drawn at random from this bag. Find the probability. [3]

1. ball is white
2. ball is not black
3. ball is red

Section – D

Question 26.
Solve the following pair of linear equations by graphical method : [6]
2x + y = 6, 2x – y = 2
Thus find the value of p in the relation 6x + 7y = p.

Question 27.
Prove that : [6]

1. \(\sqrt { \frac { 1+cos\theta }{ 1-cos\theta } } =cosec\theta+cot\theta\)
2. \(\frac { tan\theta }{ 1-cot\theta } +\frac {cot\theta}{1-tan\theta} = 1+ tan\theta +cot\theta\)

OR

Prove that :

1. If sinθ + cosθ = p and secθ + cosecθ = 4, then prove that q(p² – 1) = 2p.
2. \(\frac { cosA }{ 1-tanA } + \frac { sinA }{ 1-cotA } = sinA+cosA\)

Question 28.

1. If distance between points (x, 3) and (5, 7) is 5, then find the value of x. [6]
2. Find the ratio in which the line 3x + y=9 divides the line segment joining the points (1, 3) and (2, 7).

Question 29.
ABC is a right angled triangle whose ∠B is right angle. If points D and E are situated on the side AB and BC respectively, then prove that AE² + CD² = AC² + DE² [6]

OR

If two sides of a cyclic quadrilateral are parallel, then prove that other sides are equal and its diagonals are also equal to each other.

Question 30.
Find the mean and mode of the following frequency distribution : [6]

Score	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Number of Students	4	28	42	20	6

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