English Medium

Academic Year: 2018-2019

Date: March 2019

Duration: 3h

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(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: [0.024] Arithmetic Progressions

Evaluate:`(tan 65°)/(cot 25°)`

Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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

Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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

Chapter: [0.023] Quadratic Equations

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

Chapter: [0.011000000000000001] 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: [0.023] Quadratic Equations

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

Chapter: [0.031] 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: [0.040999999999999995] Triangles [0.040999999999999995] Triangles [0.040999999999999995] Triangles

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

Chapter: [0.022000000000000002] 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: [0.023] Quadratic Equations

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

Chapter: [0.011000000000000001] 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: [0.031] Lines (In Two-dimensions) [0.031] Lines (In Two-dimensions)

How many multiples of 4 lie between 10 and 205?

Chapter: [0.024] Arithmetic Progressions

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

Chapter: [0.024] Arithmetic Progressions

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

Chapter: [0.07200000000000001] Probability [0.07200000000000001] Probability

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

(a) a prime number.

(b) an odd number

Chapter: [0.07200000000000001] Probability [0.07200000000000001] 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: [0.040999999999999995] Triangles

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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: [0.040999999999999995] 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: [0.061] 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: [0.062] 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: [0.062] 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: [0.071] Statistics

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

Chapter: [0.011000000000000001] 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: [0.021] Polynomials

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

Chapter: [0.023] Quadratic Equations

Prove that:

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

Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

Prove that:

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

Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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: [0.031] Lines (In Two-dimensions)

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

Chapter: [0.031] 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: [0.040999999999999995] 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: [0.024] 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: [0.033] Constructions

Prove that :

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

Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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

Chapter: [0.023] 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: [0.023] Quadratic Equations

In ∆ ABC, AD ⊥ BC.

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

Chapter: [0.040999999999999995] 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: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities

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: [0.071] 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: [0.031] 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: [0.062] Surface Areas and Volumes

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