RBSE Class 10 Maths Model Paper 3 English Medium

RBSE Class 10 Maths Model Paper 3 English Medium are part of RBSE Class 10 Maths Board Model Papers. Here we have given RBSE Class 10 Maths Sample Paper 3 English Medium.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 10
Subject	Maths
Paper Set	Model Paper 3
Category	RBSE Model Papers

RBSE Class 10 Maths Sample Paper 3 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.

Part – A

Question 1.
Add 7534, 2459,1932 by vedic method. [1]

Question 2.
Solve using Sutra Shunyam Samyas achhay the equation [latex]\frac {1}{x+2} + \frac{1}{x+6} = \frac{1}{x+1} + \frac{1}{x+7}[/latex] [1]

Question 3.
Whether the decimal expansion of the number [latex]\frac{441}{2^{2} \times 5^{7} \times 7^{2}}[/latex] is terminating or non-terminating ? [1]

Question 4.
Evaluate 2sin45°. cos45°. [1]

Question 5.
Evaluate 3sin60° – 4sin³60° [1]

Question 6.
What is the locus of a point equidistant from the given points? [1]

Question 7.
What is the name of the point common to the tangent line and circle? [1]

Question 8.
In a college, the marks obtained by 10 students of class X are 7, 8, 5, 6, 7, 8, 9, 4, 5 and 6 respectively find the average mark of class. [1]

Question 9.
If a CCTV Camera mounted on a pillar can see the objects up to a distance of 14 meters from the base of the pole, find the area of the green patch around the pole. (π = [latex]\frac {22}{7}[/latex] ) [1]

Question 10.
If the total sound pollution of a city is 60 decibels and the amount of pollution due to different factors are given in pie chart, then find out the amount of sound pollution due to band party. All the pie chart should drawn in the question also. [1]

Part – B

Question 11.
Solve 842 x 858 using Urdhva tiryagbhyam and viloknam Sutra. [2]

Question 12.
What can you say about the prime factors of the rational number 43.[latex]\overline{123456789}[/latex]? [2]

Question 13.
The circumference of a circle is 176 cm find its radius. [2]

Question 14.
The height of a cylinder is 11 cm and its curved surface area is 968 cm². Find the radius of the cylinder. [2]

Question 15.
A CCTV Camera has been installed at the top of a 8 meter high straight vertical pole for smooth ground surface traffic controlling. The Camera can watch the traffic up to 10 meter slant distance on the ground. Determine the ground surface area around the pole that it can smoothly watch. (Take π = 3.14 ) [2]

Part-C

Question 16.
Find the zeroes of the polynomial x² – ( [latex]\sqrt {3}[/latex] + 1)x + [latex]\sqrt {3}[/latex]. Find their sum. [3]

Question 17.
Comment on the nature of solution of the pair of linear equations 2x + 3y + 13, 5x – 2y = 4. [3]

Question 18.
Evaluate [latex]\left(\frac{\sin 35^{\circ}}{\cos 55^{\circ}}\right)^{2}+\left(\frac{\cos 55^{\circ}}{\sin 35^{\circ}}\right)^{2}-2 \cos 60^{\circ}[/latex] [3]

Question 19.
Prove that the locus of centers of the circles passing through the points A and B is the bisector of the line segment AB. [3]

Question 20.
A ladder 10 meter long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall. [3]

Question 21.
In the given figure, AB is diameter and ∠DAB = 40°, then find the value of ∠DCA. [3]

Question 22.
A wheel of a bicycle makes 5000 rotation to complete a distance of 11 km. Find the diameter of the wheel. [3]

Question 23.
5 m, 30 m, and 3 m are length, breadth, and height of a wall respectively. Find how many bricks of dimenson 20 cm x 10 cm x 7.5 cm will be required to make the wall. [3]

Question 24.
In a triangle medians AD, BE and CF intersect each other at G Prove that AD + BE > [latex]\frac{3}{2}[/latex]AB. [3]

Question 25.
One card is drawn from a well shuffled pack of 52 cards. Find the probability of getting jack of red colour. [3]

Part – D

Question 26.
Solve the following linear equation with help of graphical method 2x+3y = 13 and 5x – 2y = 4 find out value of a with help of these while 5x – 3y = a. [6]

Question 27.
Prove that [latex]\sqrt { \frac { sec\theta +1 }{ sec\theta -1 } } =cot\theta +cosec\theta [/latex] [6]

OR

The angle of elevation of the top of a pillar from a point on the ground is 15°. On walking 100 m towards the tower, the angle of elevation is found to be 30°. Calculate the height of the tower(where tan15° = 2 – [latex]\sqrt {3}[/latex] )

Question 28.
If 2a is a side of an equilateral triangle, then find the possible coordinates of its vertices. [6]

Question 29.
Prove that perpendicular bisectors of sides of a triangle are concurrent. [6]

OR

A circle touches all sides of a parallelogram. Prove that the internal angles made by the sides at the center are 90°.

Question 30.
Find the arithmatic mean of the following frequency distribution using basic method. [6]

Class	0-10	10-20	20-30	30-40	40-50
Frequency	9	12	15	10	14

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