# CBSE Sample Papers Class 10 Mathematics 2019 ## myCBSEguide App

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## Sample Paper of Maths Class 10 – in PDF

Sample papers for class 10 maths 2019 – with Solution ## CBSE Sample Papers Class 10 Mathematics 2019

myCBSEguide provides CBSE Class 10 Sample Papers of Mathematics for the year 2018, 2019,2020 with solutions in PDF format for free download. The CBSE Sample Papers for all – NCERT books and based on CBSE latest syllabus must be downloaded and practiced by students. Class 10 Mathematics New Sample Papers follow the blueprint of that year only. Student must check the latest syllabus and marking scheme. Sample paper for Class 10 Mathematics and other subjects are available for download as PDF in-app too.

## Sample Papers Class 10 Mathematics 2018-19

Time allowed: 3Hours
Max. Marks: 80

General Instructions:

1. All the questions are compulsory.
2. The questions paper consists of 30 questions divided into 4 sections A, B, C, and D.
3. Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each. Section D comprises of 8 questions of 4 marks each.
4. 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 alternatives in all such questions.
5. Use of calculators is not permitted.

### Section – A

1. Find the value of a, for which point {tex}P\left( {\frac{a}{3},2} \right){/tex} is the mid-point of the line segment joining the points Q(-5, 4) and R(-1,0).
2. Find the value of k, for which one root of the quadratic equation kx2 -14x+8 = 0 is 2.

### OR

Find the value(s) of k for which the equation x2 + 5݇kx + 16 = 0 has real and equal roots.

3. Write the value of {tex}{\cot ^2}\theta – \frac{1}{{{{\sin }^2}\theta }}{/tex}.

### OR

If {tex}\sin \theta = \cos \theta {/tex}, then find the value of {tex}2\tan \theta + {\cos ^2}\theta {/tex}.

4. If nth term of an A.P. is (2n + 1), what is the sum of its first three terms?
5. In figure if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and {tex}\angle ADE = 48^\circ {/tex}. Find {tex}\angle ABC{/tex} 6. After how many decimal places will the decimal expansion of {tex}\frac{{23}}{{{2^4} \times {5^3}}}{/tex} terminate?

### Section – B

1. The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find the other number.

### OR

Show that {tex}7 – \sqrt 5 {/tex} is irrational, give that {tex}\sqrt 5 {/tex} is irrational.

2. Find the 20th term from the last term of the AP 3, 8, 13, ….., 253

### OR

If 7 times the 7th term of an A.P is equal to 11 times its 11th term, find its 18th term.

3. Find the coordinates of the point P which divides the join of A(-2, 5) and B(3, -5) in the ratio 2:3
4. A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.
5. Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.
6. For what value of p will the following pair of linear equations have infinitely many
solutions
(p – 3)x + 3y = p
px + py = 12

### Section-C

1. Use Euclid’s Division Algorithm to find the HCF of 726 and 275.
2. Find the zeroes of the following polynomial:
{tex}5\sqrt 5 {x^2} + 30x + 8\sqrt 5 {/tex}
3. Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.
4. 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.

### OR

Find the value of k for which the points (3k – 1, k – 2), (k, k – 7) and (k – 1, k – 2) are collinear.

5. Prove that {tex}\cot \theta – \tan \theta = \frac{{2{{\cos }^2}\theta – 1}}{{\sin \theta \cos \theta }}{/tex}

### OR

Prove that {tex}\sin \theta (1 + \tan \theta ) + \cos \theta (1 + \cos \theta ) = \sec \theta + \cos ec\theta {/tex}

6. The radii of two concentric circles are 13 cm and 8 cm. AB is a 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.
7. In figure {tex}\angle 1 = \angle 2{/tex} and {tex}\Delta NSQ \cong \Delta MTR{/tex}, then prove that {tex}\Delta PTS \sim \Delta PRQ{/tex} ### OR

In {tex}\Delta ABC{/tex}, if AD is the median, then show that AB2 + AC2 = 2(AD2 + BD2) 8. Find the area of the minor segment of a circle of radius 42cm, if length of the corresponding arc is 44cm.
9. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.

### OR

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.

10. The table shows the daily expenditure on grocery of 25 households in a locality. Find the modal daily expenditure on grocery by a suitable method.
 Daily Expenditure (In Rs.) 100-150 150-200 200-250￼ 250-300 300-350 No of households 4 5 12 2 2

### Section – D

1. A train takes 2 hours less for a journey of 300km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train.

### OR

Solve for {tex}x:\frac{1}{{(a + b + x)}} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x},\left[ {a \ne 0,b \ne 0,x \ne 0,x \ne – (a + b)} \right]{/tex}

2. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
3. Prove that in a right-angled triangle square of the hypotenuse is equal to sum of the squares of other two sides.
4. Draw a {tex}\Delta ABC{/tex} with sides 6cm, 8cm and 9 cm and then construct a triangle similar to {tex}\Delta ABC{/tex} whose sides are {tex}\frac{3}{5}{/tex} of the corresponding sides of {tex}\Delta ABC{/tex}.
5. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30o to 45o , how long will the car take to reach the observation tower from this point?

### OR

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 300 and the angle of depression of its shadow from the same point in water of lake is 600. Find the height of the cloud from the surface of water.

6. The median of the following data is 525. Find the values of x and y if the total frequency is 100.
Class IntervalFrequency
0-1002
100 – 2005
200 – 300x
300 – 40012
400 – 50017
500 – 60020
600 – 700Y
700 – 8009
800 – 9007
900 – 10004

### OR

The following data indicate the marks of 53 students in Mathematics.

MarksNumber of students
0 – 105
10 – 203
20 – 304
30 – 403
40 – 504
50 – 604
60 – 707
70 – 809
80 – 907
90 – 1008

Draw less than type gives for the data above and hence find the median.

7. The radii of circular ends of a bucket of height 24 cm are 15 cm and 5 cm. Find the area of its curved surface.
8. If {tex}\sec \theta + \tan \theta = p,{/tex} then find the value of cosec{tex}\theta {/tex}.

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## Sample Papers for Class 10 2019 in PDF

To download Sample Papers Class 10 Mathematics 2019, Science-Social Science, English Communicative, English Language and literature, Hindi Course A  and Hindi course B do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website. ### 17 thoughts on “CBSE Sample Papers Class 10 Mathematics 2019”

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