The ratio of the height of a tower and the length of its shadow on the ground is `sqrt3 : 1`. What is the angle of elevation of the sun?

Concept: Heights and Distances

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Concept: Surface Areas and Volumes Examples and Solutions

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

Concept: Simple Problems on Single Events

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

Concept: Distance Formula

Find the roots of the following quadratic equations by factorisation

`sqrt2 x^2 + 7x + 5sqrt2 = 0`

Concept: Solutions of Quadratic Equations by Factorization

Find how many integers between 200 and 500 are divisible by 8.

Concept: Sum of First n Terms of an AP

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

Concept: Number of Tangents from a Point on a Circle

Find the value of k for which the equation x^{2} + k(2x + k − 1) + 2 = 0 has real and equal roots.

Concept: Nature of Roots

Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5

Concept: Division of a Line Segment

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD

Concept: Tangent to a Circle

If the m^{th} term of an A.P. be `1/n` and n^{th} term be `1/m`, then show that its (mn)^{th} term is 1.

Concept: Arithmetic Progression

Find the sum of *n* terms of the series `(4 - 1/n) + (4 - 2/n) + (4 - 3/n)+ ......`

Concept: nth Term of an AP

If the equation (1 + m^{2}) x^{2} + 2mcx + c^{2} – a^{2} = 0 has equal roots then show that c^{2} = a^{2} (1 + m^{2})

Concept: Quadratic Equations

The `3/4` th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Concept: Surface Areas and Volumes Examples and Solutions

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

Concept: Areas of Sector and Segment of a Circle

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

Concept: Circles Examples and Solutions

Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles

Concept: Similarity of Triangles

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (`7/2`, y). Find the value of y

Concept: Area of a Triangle

Two different dice are thrown together. Find the probability that the numbers obtained have a sum less than 7

Concept: Simple Problems on Single Events

Two different dice are thrown together. Find the probability that the numbers obtained have a product less than 16

Concept: Simple Problems on Single Events

In a simultaneous throw of a pair of dice, find the probability of getting a doublet of odd numbers

Concept: Probability - A Theoretical Approach

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/h.

Concept: Heights and Distances

Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are `2/3` times the corresponding sides of the isosceles triangle.

Concept: Division of a Line Segment

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Concept: Number of Tangents from a Point on a Circle

The ratio of the sums of m and n terms of an A.P. is m^{2} : n^{2}. Show that the ratio of the m^{th} and n^{th} terms is (2m – 1) : (2n – 1)

Concept: Sum of First n Terms of an AP

Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Concept: Pair of Linear Equations in Two Variables

If a≠b≠0, prove that the points (a, a^{2}), (b, b^{2}) (0, 0) will not be collinear.

Concept: Distance Formula

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

Concept: Volume of a Combination of Solids

Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25

Concept: Concept Or Properties of Probability

A chord PQ of a circle of radius 10 cm substends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle.

Concept: Circles Examples and Solutions

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of water

Concept: Heights and Distances

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.

Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle

In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water.

Concept: Surface Areas and Volumes Examples and Solutions

## CBSE previous year question papers Class 10 Mathematics with solutions 2016 - 2017

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