# UP Board 2021 Model Paper for Class 10th Maths

UP Board Exam 2021

For many students, **maths** has always been a challenging subject. While many students achieved perfect scores on their **math exams**, others have failed miserably.

**Maths** is one of those subjects where a student can score good marks if the concept is clear and the concepts can be cleared if one is doing practice.

We are providing Sample Question Papers. Solving these papers can help them revise and will improve their time management skills.

Solving these math sample papers is the best way to gain confidence.

Class 10 is a major turning point in anyone’s life and excelling in this subject would result in a huge improvement in overall grades. This question paper will improve students’ basic understanding of the topics and how they will be presented in the test.

The format of the question paper is similar to that of the UP Board examination. If the student answers this question paper before the test, they will have practical exam experience. All The Best.

**Class 10 Mathematics Sample Paper **

**UP Board 2020-2021**

T**ime Allowed: 3 Hours
General Instructions: Maximum Marks: 80**

**CLASS X
MATHEMATICS**

**SAMPLE QUESTION PAPER 2020-21**

a) The question paper is divided into four sections – Section A, Section B, Section C, and Section D.

b) The question paper has 26 questions in all.

c) All questions are compulsory.

d) Marks are indicated against each question.

e) Questions from serial numbers 1 to 7 are multiple-choice type questions. Each question carries one mark.

f) Questions from serial numbers 8 to 18 are very short answer questions.

g) Questions from serial numbers 19 to 25 are short answer questions.

h) Question number 26 is a long answer type question of 5 marks.

SECTION A (1 X 7=7)

**1. **If the angle of the sector is 60°, the radius is 3.5 cm then the length of the arc is

(a) 3 cm

(b) 3.5 cm

(c) 3.66 cm

(d) 3.8 cm

**2.** While computing the mean of grouped data, we assume that the frequencies are

(a) centered at the upper limits of the classes

(b) centered at the lower limits of the classes

(c) centered at the classmarks of the classes

(d) evenly distributed over all the classes

**3.** When the length of the shadow of a vertical pole is equal to √3 times its height, the angle of elevation of the Sun’s altitude is

(a) 30°

(b) 45°

(c) 60°

(d) 15°

**4.** A solid formed on revolving a right-angled triangle about its height is

(a) cylinder

(b) sphere

(c) right circular cone

(d) two cones

**5.** If b = 3, then any integer can be expressed as a =

(a) 3q, 3q+ 1, 3q + 2 (b) 3q

(c) none of the above (d) 3q+ 1

**6.** Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4

(a) 262

(b) 272

(c) 282

(d) 292

**7.** The number of multiples lie between n and n² which are divisible by n is

(a) n + 1

(b) n

(c) n – 1

(d) n – 2

**SECTION B **(3 X 11=33)

**
8.** If two tangents are inclined at 60 ̊ are drawn to a circle of radius 3cm then find the length of each tangent.

**9.**In the ∆ABC, D, and E are points on side AB and AC respectively such that DE II BC. If AE=2cm, AD=3cm, and BD=4.5cm, then find CE.

**10.** If tanA=3/4 , find the value of 1 /sinA+1/ cosA

**11. **The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find

the other number.

**12. **The radii of the two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of AP.

**13.** A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of

diameter 0.6cm. Find the number of balls.

**14.**Prove that in a right-angled triangle square of the hypotenuse is equal to the sum of the squares of the other two sides.

**15. **Find the sum of all natural numbers that are less than 100 and divisible by 4.

**16. **A train covers a distance of 90 km at a uniform speed. It would have taken 30 minutes less if the speed had been 15 km/hr more. Calculate the original duration of the journey

**17. **The points A ( 1 , -2 ) , B ( 2 , 3 ), C ( k , 2 )and D ( – 4 , – 3 ) are the vertices of a parallelogram. Find the value of k and the altitude of the parallelogram corresponding to the base AB.

**18. **Find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2.

**SECTION C **(5 X 7 = 35)

**19.** Prove that √3 – √2 and √3 + √5 are irrational.

**20. **Find the discriminant of the equation 3×2– 2x +1/3= 0 and hence find the nature of its roots. Find them, if they are real.

**21. ** Find the coordinates of the points of trisection ( points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).

**22. **A chord subtends an angle of 90°at at the center of a circle whose radius is 20 cm. Compute the area of the corresponding major segment of the circle.

**23. **Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

**24. **Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . .

**25.** If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

**SECTION D **(1 X 5 = 5)

**26. **Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour?

**OR**

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

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