Date: March 2019

Duration: 3h

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections – A, B, C, and D.

(iii) Section A comprises 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.

(iv) There is no overall choice. However, an internal choice has been provided in two questions of 1 mark, two questions of 2 marks, 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.

(v) The use of calculators is not permitted.

Which term of the A.P. −4, −1, 2, ... is 101?

Chapter: [2.02] Arithmetic Progressions

Evaluate:`(tan 65°)/(cot 25°)`

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°**.**

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.

Chapter: [2.03] Quadratic Equations

Find a rational number between `sqrt(2) "and" sqrt(7)`.

Chapter: [1.01] Real Numbers

Write the number of zeroes in the end of a number whose prime factorization is 2^{2 }× 5^{3} × 3^{2} × 17.

Chapter: [2.03] Quadratic Equations

Find the distance between the points (a, b) and (−a, −b).

Chapter: [6.01] Lines (In Two-dimensions)

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm^{2} and 121 cm^{2}. If EF = 15⋅4 cm, find BC.

Chapter: [3.02] Triangles

Find the solution of the pair of the equation :`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0

Chapter: [2.01] Pair of Linear Equations in Two Variables

Find the value(s) of k for which the pair of equations

kx + 2y = 3

3x + 6y = 10 has a unique solution.

Chapter: [2.03] Quadratic Equations

Use Euclid's division algorithm to find the HCF of 255 and 867.

Chapter: [1.01] Real Numbers

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

Chapter: [6.01] Lines (In Two-dimensions) [6.01] Lines (In Two-dimensions)

How many multiples of 4 lie between 10 and 205?

Chapter: [2.02] Arithmetic Progressions

Determine the A.P. whose third term is 16 and 7^{th} term exceeds the 5^{th} by 12.

Chapter: [2.02] Arithmetic Progressions

Three different coins are tossed simultaneously. Find the probability of getting exactly one head.

Chapter: [5.01] Probability [5.01] Probability

A die is thrown once. Find the probability of getting.

(a) a prime number.

(b) an odd number

Chapter: [5.01] Probability [5.01] Probability

In the given figure, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL^{2} + CM^{2}) = 5 BC^{2}.

Chapter: [3.02] Triangles

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

Chapter: [3.02] Triangles

In Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]

Chapter: [7.01] Areas Related to Circles [7.01] Areas Related to Circles

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.

Chapter: [7.02] Surface Areas and Volumes

A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Chapter: [7.02] Surface Areas and Volumes

Calculate the mode of the following distribution:

Class |
10 − 15 | 15 − 20 | 20 − 25 | 25 − 30 | 30 − 35 |

Frequency |
4 | 7 | 20 | 8 | 1 |

Chapter: [5.02] Statistics

Show that `(2+3√2)/7` is not a rational number, given that √2 is an irrational number.

Chapter: [1.01] Real Numbers

Obtain all the zeroes of the polynomial 2x^{4} − 5x^{3} − 11x^{2 }+ 20x + 12 when 2 and − 2 are two zeroes of the above polynomial.

Chapter: [2.04] Polynomials [2.04] Polynomials

A motorboat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Chapter: [2.04] Polynomials [2.04] Polynomials

Prove that:

(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

Prove that:

`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2cosecθ`

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.

Chapter: [6.01] Lines (In Two-dimensions)

Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear.

Chapter: [6.01] Lines (In Two-dimensions)

ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.

Chapter: [3.02] Triangles

In an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Chapter: [2.02] Arithmetic Progressions

Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Chapter: [3.03] Constructions

Prove that :

2(sin^{6} θ + cos^{6} θ) − 3 (sin^{4} θ + cos^{4 }θ) + 1 = 0

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

Solve for x : `1/(2a + b + 2x) =1/(2a) + 1/b + 1/(2x); x ≠ 0, x ≠ (−2a −b)/2`, a, b ≠ 0

Chapter: [2.03] Quadratic Equations

The sum of the areas of two squares is `640m^2` . If the difference in their perimeter be 64m, find the sides of the two square

Chapter: [2.03] Quadratic Equations

In ∆ ABC, AD ⊥ BC.

Prove that AC^{2} = AB^{2} +BC^{2} − 2BC x BD

Chapter: [3.02] Triangles

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.

Chapter: [4.02] Trigonometric Identities [4.03] Introduction to Trigonometry

Find the mean of each of the following frequency distributions

Class interval | 10 - 30 | 30 - 50 | 50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 |

Frequency | 5 | 8 | 12 | 20 | 3 | 2 |

Chapter: [5.02] Statistics

The following table gives production yield in kg per hectare of wheat of 100 farms of a village :

Production yield(kg/hectare) : |
40−45 | 45−50 | 50−55 | 55−60 | 60−65 | 65−70 |

Number of farms |
4 | 6 | 16 | 20 | 30 | 24 |

Change the distribution to a 'more than type' distribution, and draw its ogive.

Chapter: [6.01] Lines (In Two-dimensions)

A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm^{2}. (Take π = 3⋅14)

Chapter: [7.02] Surface Areas and Volumes

#### Other Solutions

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files

## CBSE previous year question papers Class 10 Mathematics with solutions 2018 - 2019

Previous year Question paper for CBSE Class 10 Maths-2019 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.

By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 10.

How CBSE Class 10 Question Paper solutions Help Students ?

• Question paper solutions for Mathematics will helps students to prepare for exam.

• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.

• For finding solution of question papers no need to refer so multiple sources like textbook or guides.