Board Paper of Class 10 2017 Maths (SET 2) - Solutions

• Question 5
  Prove that tangents drawn at the ends of a diameter of a circle are parallel to each other. VIEW SOLUTION

• Question 6
  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.
  VIEW SOLUTION

• Question 7
  Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$. VIEW SOLUTION

• Question 8
  Find how many integers between 200 and 500 are divisible by 8. VIEW SOLUTION

• Question 9
  Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots. VIEW SOLUTION

• Question 10
  Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3. VIEW SOLUTION

• Question 11
  The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is $\left(\frac{7}{2}, y\right),$ find the value of y. VIEW SOLUTION

• Question 12
  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. VIEW SOLUTION

• Question 13
  Two different 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. VIEW SOLUTION

• Question 14
  Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ. VIEW SOLUTION

• Question 15
  Find the sum of n terms of the series $\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+..........$ VIEW SOLUTION

• Question 16
  If the equation (1 + m²) x² + 2mcx + c² – a² = 0 has equal roots then show that c² = a² (1 + m²). VIEW SOLUTION

• Question 17
  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.
  
  VIEW SOLUTION

• Question 18
  If the m^th term of an A. P. is $\frac{1}{n}$ and n^th term is $\frac{1}{m}$ then show that its (mn)^th term is 1. VIEW SOLUTION

• Question 19
  A metallic solid sphere of radius 10.5 cm is melted and recasted into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made? VIEW SOLUTION

• Question 20
  From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower. VIEW SOLUTION

• Question 21
  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. VIEW SOLUTION

• Question 22
  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.
  
  VIEW SOLUTION

• Question 23
  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. VIEW SOLUTION

• Question 24
  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. VIEW SOLUTION

• Question 25
  Prove that the lengths of tangents drawn from an external point to a circle are equal. VIEW SOLUTION

• Question 26
  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. VIEW SOLUTION

• Question 27
  If $a\ne b\ne 0$, prove that the points (a, a²), (b, b²) (0, 0) will not be collinear. VIEW SOLUTION

• Question 28
  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 $\frac{3}{5}$ times the corresponding sides of the given triangle. VIEW SOLUTION

• Question 29
  If 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. VIEW SOLUTION

• Question 30
  Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height of the tower is 15 m, then find the distance between the points. VIEW SOLUTION

• Question 31
  The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is $\frac{1}{27}$ of the given cone, then at what height it is cut from its base? VIEW SOLUTION