EXERCISE 15.4 Page No 293: Question 1: The following distribution gives the daily income of 50 workers of a factory. Daily income (in Rs) 100 − 120 120 − 140 140 − 160 160 − 180 180 − 200 Number of workers 12 14 8 6 10 Convert the distribution above to a less than …
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EXERCISE 15.3 Page No 287: Question 1: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Monthly consumption (in units) Number of consumers 65 − 85 4 85 − 105 5 105 − 125 13 125 …
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EXERCISE 15.2 Page No 275: Question 1: The following table shows the ages of the patients admitted in a hospital during a year: age (in years) 5 − 15 15 − 25 25 − 35 35 − 45 45 − 55 55 − 65 Number of patients 6 11 21 23 14 5 Find the …
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EXERCISE 15.1 Page No 270: Question 1: A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Number of plants 0 − …
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EXERCISE 14.2 Question 1: Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) …
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EXERCISE 14.1 Page No 308: Question 1: Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = _______. (ii) The probability of an event that cannot happen is _________. Such as event is called _________. (iii) The probability of an event that is certain to happen is …
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EXERCISE 13.5 Page No 258: Question 1: A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g …
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EXERCISE 13.4 Page No 257: Question 1: A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. Answer: Radius (r1) of Radius (r2) of Capacity of glass = Volume …
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EXERCISE 13.3 Page No 251: Question 1: A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder. Answer: Radius (r1) of hemisphere = 4.2 cm Radius (r2) of cylinder = 6 cm Let the height of the cylinder …
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EXERCISE 13.2 Page No 247: Question 1: A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π. Answer: Given that, Height (h) …
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EXERCISE 13.1 Page No 244: Question 1: 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboids. Answer: Given that, Volume of cubes = 64 cm3 (Edge) 3 = 64 Edge = 4 cm If cubes are joined end to end, the dimensions of the resulting cuboid will …
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EXERCISE 12.3 Page No 234: Question 1: Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Answer: It can be observed that RQ is the diameter of the circle. Therefore, ∠RPQ will be 90º. By applying …
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EXERCISE 12.2 Page No 230: Question 1: Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. Answer: Let OACB be a sector of the circle making 60° angle at centre O of the circle. Area of sector of angle θ = Area of sector …
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EXERCISE 12.1 Page No 225: Question 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Answer: Radius (r1) of 1st circle = 19 cm Radius (r2) or 2nd circle = 9 cm Let …
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EXERCISE 11.2 Page No 221: Question 1: Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction. Answer: A pair of tangents to the given circle can be constructed as follows. …
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EXERCISE 11.1 Page No 219: Question 1: Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Give the justification of the construction. Answer: A line segment of length 7.6 cm can be divided in the ratio of 5:8 as follows. Step 1 Draw line segment AB …
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EXERCISE 10.2 Page No 213: Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm Answer: Let O be …
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EXERCISE 10.1 Page No 209: Question 1: How many tangents can a circle have? Answer: A circle can have infinite tangents. Question 2: Fill in the blanks: (i) A tangent to a circle intersects it in _______ point (s). (ii) A line intersecting a circle in two points is called a __________. (iii) A circle …
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EXERCISE 9.1 Page No 203: Question 1: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °. Answer: It …
EXERCISE 8.4 Page No 193: Question 1: Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. Answer: We know that, will always be positive as we are adding two positive quantities. Therefore, We know that, However, Therefore, Also, Question 2: Write all the other trigonometric ratios of ∠A …
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EXERCISE 8.3 Page No 189: Question 1: Evaluate (I) (II) (III) cos 48° − sin 42° (IV)cosec 31° − sec 59° Answer: (I) (II) (III)cos 48° − sin 42° = cos (90°− 42°) − sin 42° = sin 42° − sin 42° = 0 (IV) cosec 31° − sec 59° = cosec (90° − 59°) …
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EXERCISE 8.2 Page No 187: Question 1: Evaluate the following (i) sin60° cos30° + sin30° cos 60° (ii) 2tan245° + cos230° − sin260° (iii) (iv) (v) Answer: (i) sin60° cos30° + sin30° cos 60° (ii) 2tan245° + cos230° − sin260° (iii) (iv) (v) Question 2: Choose the correct option and justify your choice. (i) (A). …
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EXERCISE 8.1 Page No 181: Question 1: In ΔABC right angled at B, AB = 24 cm, BC = 7 cm. Determine (i) sin A, cos A (ii) sin C, cos C Answer: Applying Pythagoras theorem for ΔABC, we obtain AC2 = AB2 + BC2 = (24 cm)2 + (7 cm)2 = (576 + 49) cm2 = 625 …
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EXERCISE 7.4 Page No 171: Question 1: Determine the ratio in which the line 2x + y − 4 = 0 divides the line segment joining the points A(2, − 2) and B(3, 7) Answer: Let the given line divide the line segment joining the points A(2, −2) and B(3, 7) in a ratio k : 1. Coordinates of the …
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EXERCISE 7.3 Page No 170: Question 1: Find the area of the triangle whose vertices are: (i) (2, 3), (− 1, 0), (2, − 4) (ii) (− 5, − 1), (3, − 5), (5, 2) Answer: (i) Area of a triangle is given by (ii) Question 2: In each of the following find the value …
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EXERCISE 7.2 Page No 167: Question 1: Find the coordinates of the point which divides the join of (− 1, 7) and (4, − 3) in the ratio 2:3. Answer: Let P(x, y) be the required point. Using the section formula, we obtain Therefore, the point is (1, 3). Question 2: Find the coordinates of the …
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EXERCISE 7.1 Page No 161: Question 1: Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b) Answer: (i) Distance between the two points is given by (ii) Distance between is given by (iii) Distance between is given by Question 2: Find the distance …
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EXERCISE 6.6 Page No 152: Question 1: In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that . Answer: Let us draw a line segment RT parallel to SP which intersects extended line segment QP at point T. Given that, PS is the angle bisector of ∠QPR. ∠QPS = ∠SPR … (1) …
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EXERCISE 6.5 Page No 150: Question 1: Sides of triangles are given below. Determine which of them are right triangles? In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 …
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EXERCISE 6.4 Page No 143: Question 1: Let and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC. Answer: Video Solution Question 2: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of …
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EXERCISE 6.3 Page No 138: Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) (iv) (v) (vi) Answer: (i) ∠A = ∠P = 60° ∠B …
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EXERCISE 6.2 Page No 128: Question 1: In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii). (i) (ii) Answer: (i) Let EC = x cm It is given that DE || BC. By using basic proportionality theorem, we obtain (ii) Let AD = x cm It is given that DE || BC. …
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EXERCISE 6.1 Page No 122: Question 1: Fill in the blanks using correct word given in the brackets:− (i) All circles are __________. (congruent, similar) (ii) All squares are __________. (similar, congruent) (iii) All __________ triangles are similar. (isosceles, equilateral) (iv) Two polygons of the same number of sides are similar, if (a) their corresponding …
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EXERCISE 5.4 Page No 115: Question 1: Which term of the A.P. 121, 117, 113 … is its first negative term? [Hint: Find n for an < 0] Answer: Given A.P. is 121, 117, 113 … a = 121 d = 117 − 121 = −4 an = a + (n − 1) d = 121 + (n − 1) (−4) = 121 − 4n + 4 = …
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EXERCISE 5.3 Page No 112: Question 1: Find the sum of the following APs. (i) 2, 7, 12 ,…., to 10 terms. (ii) − 37, − 33, − 29 ,…, to 12 terms (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms (iv) ,………, to 11 terms Answer: (i)2, 7, 12 ,…, to 10 terms For this …
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EXERCISE 5.2 Page No 105: Question 1: Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. a d n an I 7 3 8 …… II − 18 ….. 10 0 III ….. − 3 18 − 5 IV − 18.9 2.5 ….. 3.6 V …
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EXERCISE 5.1 Page No 99: Question 1: In which of the following situations, does the list of numbers involved make as arithmetic progression and why? (i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. (ii) The amount of air present …
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EXERCISE 4.4 Question 1: Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (I) 2×2 −3x + 5 = 0 (II) (III) 2×2 − 6x + 3 = 0 Answer: We know that for a quadratic equation ax2 + bx + c = 0, discriminant is b2 − 4ac. (A) If b2 − 4ac > 0 → two distinct real roots …
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EXERCISE 4.3 Page No 87: Question 1: Find the roots of the following quadratic equations, if they exist, by the method of completing the square: Answer: Question 2: Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula. Answer: Page No 88: Question 3: Find the roots of the …
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EXERCISE 4.2 Page No 76: Question 1: Find the roots of the following quadratic equations by factorisation: Answer: Roots of this equation are the values for which= 0 ∴ = 0 or = 0 i.e., x = 5 or x = −2 Roots of this equation are the values for which= 0 ∴ = 0 or = 0 i.e., x = −2 or x = Roots of …
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EXERCISE 4.1 Page No 73: Question 1: Check whether the following are quadratic equations: Answer: It is of the form . Hence, the given equation is a quadratic equation. It is of the form . Hence, the given equation is a quadratic equation. It is not of the form . Hence, the given equation is not a quadratic …
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EXERCISE 3.7 Page No 68: Question 1: The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju. …
EXERCISE 3.6 Page No 67: Question 1: Solve the following pairs of equations by reducing them to a pair of linear equations: Answer: Let and, then the equations change as follows. Using cross-multiplication method, we obtain Putting and in the given equations, we obtain Multiplying equation (1) by 3, we obtain 6p + 9q = 6 (3) Adding equation …
EXERCISE 3.5 Page No 62: Question 1: Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. Answer: Therefore, the given sets of lines are parallel to each other. Therefore, they will not intersect …
EXERCISE 3.4 Page No 56: Question 1: Solve the following pair of linear equations by the elimination method and the substitution method: Answer: (i) By elimination method Multiplying equation (1) by 2, we obtain Subtracting equation (2) from equation (3), we obtain Substituting the value in equation (1), we obtain By substitution method From equation …
EXERCISE 3.3 Page No 53: Question 1: Solve the following pair of linear equations by the substitution method. Answer: (i) x + y = 14 (1) x − y = 4 (2) From (1), we obtain x = 14 − y (3) Substituting this value in equation (2), we obtain Substituting this in equation (3), we obtain (ii) From (1), we obtain Substituting this value …
EXERCISE 3.2 Page No 49: Question 1: Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who …
EXERCISE 3.1 Page No 44: Question 1: Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. Answer: Let the present age of …
EXERCISE 2.4 Question 1: Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: Answer: (i) Therefore, , 1, and −2 are the zeroes of the given polynomial. Comparing the given polynomial with , we obtain a = 2, b = 1, c = −5, d = 2 …
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EXERCISE 2.3 Page No 36: Question 1: Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) (ii) (iii) Answer: Quotient = x − 3 Remainder = 7x − 9 Quotient = x2 + x − 3 Remainder = 8 Quotient = −x2 − 2 Remainder = −5x +10 Question 2: Check whether the first polynomial …
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EXERCISE 20.3 QUESTION 1 Find the sum of the following geometric progressions: (i) to 7 terms; Sol : Here, a=2 and r=3 = 2787 – 1 = 2186 (ii) to 8 terms Sol : Here, a=1 and r=3 = 3280 (iii) to 9 terms; Sol : Here, a=1 and (iv) to n …
EXERCISE 19.1 QUESTION 1 If the term of a sequence is given by write down its first five terms. Sol : Given : For = 1 For = 2 For = 3 For = 13 For = 21 Thus, the first five terms of the sequence are QUESTION 2 A sequence is defined by …
Exercise 2.2 Question 1 Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) Sol : or or Therefore , the zeroes of are 4 and -2 . Sum of zeroes Product of zeroes (ii) Sol : Therefore , the zeroes of are and Sum …
Exercise 2.1 Question 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) Sol : (i) The number of zeroes is 0 as the graph does not cut the x-axis at any point. (ii) Sol …
Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.4 Question 1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (i) Sol : The denominator is in the form of Hence, the decimal expansion of is terminating. …
Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.3 Question 1 Prove that is irrational . Sol : Let is a rational number. Therefore, we can find two integers a , b such that Let a and b have a common factor other than 1 . Then we can divide them by the …
Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.2 Question 1 Express each number as product of its prime factors: (i) 140 Sol : (ii) 156 Sol : (iii) 3825 Sol : (iv) 5005 Sol : (v) 7429 Sol : Question 2 Find the LCM and HCF of …
Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.1 Question 1 Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 Sol : (i) 135 and 225 Since 225 > 135, we apply the division lemma to 225 and 135 to obtain 225 = 135 × 1 + 90 …
Light : is a form of energy which enables us to see objects from which it comes (or from which it reflects.) Luminous objects : Those objects which gives out their own light are called luminous objects. examples are sun , candle, Lamp etc Non-Luminous objects : Those objects which are unable to gives out …
PERIODIC CLASSIFICATION OF ELEMENTS Firstly what is element , an element is a substance containing atoms of only one type e.g Na , Au , Ca , etc . Up till now there are around 118 elements are found . Which is such a large amount and is not possible to learn about each and every …
COAL AND PETROLEUM Firstly what is fuel ,fuel is a material that consist of energy stored in it. Most of the fuel are free carbons (coal , coke ,charcoal) or just carbon compounds (kerosene , LPG , petrol). When carbon in any form is burned in oxygen (of air) and forms carbon-di-oxide also releases heat …
