NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers Exercise 1.1 : Solutions of Questions on Page Number : 7 Q1 : Use Euclid’s division algorithm to find the HCF of: Answer : (i) 135 and 225 Since 225 > 135, we apply the division lemma to 225 and 135 to obtain 225 = 135 x 1 + 90 Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to obtain 135 = 90 x 1 + 45 We consider the new divisor 90 and new remainder 45, and apply the division lemma to…
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Exercise 15.1 : Solutions of Questions on Page Number : 283 Q1 : In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Answer : Number of times the batswoman hits a boundary = 6 Total number of balls played = 30 ∴ Number of times that the batswoman does not hit a boundary = 30 – 6 = 24 Q2 : 1500 families with 2 children were selected randomly, and the following data were recorded: Number of girls in a family 2…
Exercise 14.1 : Solutions of Questions on Page Number : 239 Q1 : Give five examples of data that you can collect from day to day life. Answer : In our day to day life, we can collect the following data. 1. Number of females per 1000 males in various states of our country 2. Weights of students of our class 3. Production of wheat in the last 10 years in our country 4. Number of plants in our locality 5. Rainfall in our city in the last 10 years Q2 : Classify the data in Q1 above as primary…
Exercise 13.1 : Solutions of Questions on Page Number : 213 Q1 : A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of sheet for it, if a sheet measuring 1 m² costs Rs 20. Answer : It is given that, length (l) of box = 1.5 m Breadth (b) of box = 1.25 m Depth (h) of box = 0.65 m…
Exercise 12.1 : Solutions of Questions on Page Number : 202 Q1 : A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board? Answer : Side of traffic signal board = a Perimeter of traffic signal board = 3 × a By Heron’s formula, Perimeter of traffic signal board = 180 cm Side of traffic signal board Using equation (1), area of traffic signal board Q2 : The triangular side walls…
Exercise 11.1 : Solutions of Questions on Page Number : 191 Q1 : Construct an angle of 90° at the initial point of a given ray and justify the construction. Answer : The below given steps will be followed to construct an angle of 90°. (i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R. (ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S. (iii) Taking S as centre and with the same radius…
Exercise 10.1 : Solutions of Questions on Page Number : 171 Q1 : Fill in the blanks (i) The centre of a circle lies in __________ of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior) (iii) The longest chord of a circle is a __________ of the circle. (iv) An arc is a __________ when its ends are the ends of a diameter. (v) Segment of a circle is the region between an arc and __________ of the circle. (vi)…
Exercise 9.1 : Solutions of Questions on Page Number : 155 Q1 : Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels. (i) (ii) (iii) (iv) (v) (vi) Answer : (i) Yes. It can be observed that trapezium ABCD and triangle PCD have a common base CD and these are lying between the same parallel lines AB and CD. (ii) No. It can be observed that parallelogram PQRS and trapezium MNRS have a common base RS. However, their vertices, (i.e., opposite to…
Exercise 8.1 : Solutions of Questions on Page Number : 146 Q1 : The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer : Let the common ratio between the angles be x. Therefore, the angles will be 3x, 5x, 9x, and 13x respectively. As the sum of all interior angles of a quadrilateral is 360º, ∴ 3x + 5x + 9x + 13x = 360º 30x = 360º x = 12º Hence, the angles are 3x = 3 x 12 = 36º 5x = 5 x 12 = 60º…
Triangles Class 9 Exercise 7.1 : Solutions of Questions on Page Number : 118 Q1 : In quadrilateral ACBD, AC = AD and AB bisects ∠ A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD? Answer : In ΔABC and ΔABD, AC = AD (Given) ∠ CAB = ∠ DAB (AB bisects ∠ A) AB = AB (Common) ∴ ΔABC ≅ ΔABD (By SAS congruence rule) ∴ BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Q2 :ABCD is a quadrilateral in which AD = BC and…