CBSE 10 Maths Question Paper-2017

What is the angle of elevation of the sun if the ratio of the height of a tower and the length of its shadow on the ground is 3:1?

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

If the volume and surface area of a solid hemisphere are numerically equal, what is the diameter of the hemisphere?

What is the probability that the square of a number chosen at random from the set {3, 2, 1, 0, 1, 2, 3} is less than or equal to 1?

Find the roots of the quadratic equation 2x^2 + 7x + 5 = 0.

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

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

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

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

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.

If the sum of the first m and first n terms of an A.P. is 2:2, show that the ratio of its m-th and n-th terms is (2-1) : (2-1).

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), find the value of y.

Show that ∆ ABC, where A(-2, 0), B(2, 0), C(0, 2) and ∆ PQR where P(-4, 0), Q(4, 0), R(0, 4) are similar triangles.

Two dice are thrown together. Find the probability that the numbers obtained (i) have a sum less than 7, (ii) have a product less than 16, (iii) is a doublet of odd numbers.

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

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

If the equation 2x² + 7x + 5 = 0 has equal roots, show that 2x² + 7x + 5 = 0 has equal roots.

The sum of the first m terms of an A.P. is the same as the sum of its first n terms. Show that the sum of its first (m + n) terms is zero.

A solid metallic sphere of diameter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.

From the top of a 7 m high building, the angle of elevation of the top of a hill is 60° and the angle of depression of its foot is 45°. Find the height of the tower.

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?

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

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?

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

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

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.

If 0 ≠ a, b, prove that the points (a, b), (0, 0), and (b, a) will not be collinear.

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are 3/5 times the corresponding sides of the given triangle.

The sum of first m terms of an A.P. is the same as the sum of its first n terms. Show that the sum of its first (m + n) terms is zero.

A solid metallic sphere of diameter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.