# RBSE Class 10 Maths Model Paper 4 English Medium

RBSE Class 10 Maths Model Paper 4 English Medium are part of RBSE Class 10 Maths Board Model Papers. Here we have given RBSE Class 10 Maths Sample Paper 4 English Medium.

 Board RBSE Textbook SIERT, Rajasthan Class Class 10 Subject Maths Paper Set Model Paper 4 Category RBSE Model Papers

## RBSE Class 10 Maths Sample Paper 4 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.
Solve $$\frac {3x + 6}{6x + 3} = \frac {5x + 4}{2x + 7}$$ by Vedic method. [1]

Question 2.
Find 2252 using Yavadunam sutra. [1]

Question 3.
Whether $$\frac {64}{455}$$ has terminating decimal representation? [1]

Question 4.
The shadow of a vertical pillar is same the height of the pillar. Find the angle of elevation of the sun. [1]

Question 5.
Find the value of sin250° + sin240°. [1]

Question 6.
In the given figure, PQ is tangent to the circle at C. Find ∠PCB. [1]

Question 7.
In the given figure, ∠ABC = 45°, then prove that OA ⊥ OC. [1]

Question 8.
The A.M. of four numbers x1, x2, x3, x4, is 5. If each number is decreased by 1, what will be the new A.M? [1]

Question 9.
To minimise the pollution, which certificate, the government should make mandatory for all Vehicles? [1]

Question 10.
The angle of depression of a car standing on the road from a CCTV Camera installed at the top of a building is 30°. If the distance between the Camera and the car is 24 m, find the height of the building. [1]

Part – B

Question 11.
Using division method find $$\sqrt{6889}$$. [2]

Question 12.
A circular path around a sports field. Raman takes 18 minutes to complete one round of the circular path, while Anupriya takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point? [2]

Question 13.
Find the circumference of the incircle of a square with side 14 cm. [2]

Question 14.
The radius of a circular grassland is 35 m. There is a footpath of width 7 m around it. Find the area of the footpath. [2]

Question 15.
Two cars moving with velocities 120 km/hour and 40 km/hour respectively are brought to rest with an equal retardation 5 meter/sec2 by applying sudden brakes on both of them. Find the ratio of distances travelled by them after applying the brakes.  [2]

Part – C

Question 16.
Divide 16 into two parts such that 2 times the square of the larger part is 164 more than the square of the smaller part. [3]

Question 17.
If pair of equations 2x + 3y = 7, (a + b)x + (2a – b)y = 21 have infinite many solutions then find a and b. [3]

Question 18.
A bridge above the river makes an angle of 45° with the bank of the river. If the length of the bridge above the river is 150m then find the breadth of the river. [3]

Question 19.
In the given figure, in ΔABC, DE || BC, if AD = 4x – 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x – 3, then find the value of x. [3]

Question 20.
ΔABC ~ ΔPQR area ΔABC = 16 cm2 and area ΔPQR = 9 cm2. If AB = 2.1 cm then find the length of side PQ. [3]

Question 21.
In a cyclic quadrilateral ABCD if AD || BC then prove that ∠A = ∠D. [3]

Question 22.
Given an equilateral traingle of side length 20 cm. From each vertex of the triangle an arc of radius 10 cm is drawn as shown in the figure. Find the area if the shaded region [3]

($$\sqrt {3}$$ = 1.73, π = 3.14)

Question 23.
A candle of diameter 2.8 cm is formed from a cuboid of diameter 11 cm x 3.5 cm x 2.5. Find the length of the candle. [3]

Question 24.
In ΔABC, DE || BC and $$\frac {AD}{DB} = \frac {3}{5}$$. If AC = 5.6cm, then find the measure of AE. [3]

Question 25.
Following are the marks obtained by some students find the mode of their marks [3]

 Marks obtained 10 20 30 40 50 60 70 80 No of students 2 8 16 26 20 16 7 4

Part – D

Question 26.
Find all zeroes of the polynomial f(x) = 3x4 + 6X3 – 2x2 – 10x – 5, if its two roots are $$\sqrt {\frac{5}{3}}$$ and – $$\sqrt {\frac{5}{3}}$$ [6]

Question 27.
Prove that if secθ + tanθ = P, then prove that $$\frac{P^{2}-1}{P^{2}+1}=\sin \theta$$ [6]

OR

A 1.5 m high observer is at 28.5 m distance from a port. Elevation angle of top of the port from his eyes is 45°. Find hight of port.

Question 28.
If (0, 0) and (3,$$\sqrt {3}$$ ) are two vertices of an equilateral triangle, then find the third vertex. [6]

Question 29.
In ΔABC prove that the sum of two medians is greater then third one. [6]

OR

A circle touches all sides of a quadrilateral. Prove that at the centre internal angles made by the opposite sides are supplementary.

Question 30.
Compare mean obtained by deviation method with step-deviation method for this following distribution. [6]

 Height 200 600 1000 1400 1800 2200 No.of villages 142 265 560 271 89 16

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