# KC Sinha

## KC Sinha Solution Class 12 Chapter 4 Inverse Trigonometric Function Exercise 4.1

Exercise 4.1 TYPE 1 Question 1 Find the value of  (i) Sol : Let ..(i) ⇒ ∵ ⇒ ⇒..(ii) On comparing (i) and (ii) equations ⇒ (ii) Sol : ⇒Let ..(i) ⇒ ∵ ⇒ ⇒ ⇒..(ii) From (i) and (ii) , we get ⇒ (iii) Sol : Note: cot-1 (-θ)=π-cot-1 θ ⇒cot-1 (-√3)=π-cot-1 (√3) ⇒ ⇒ …

## KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.4

Page 15.83 EXERCISE 15.4 Type 1 QUESTION 1 Fill in the Blanks : (i) Volume of a sphere V is __ , where the radius of the sphere is r (ii) Volume of a sphere V is __ , where the diameter of the sphere is r (iii) If a and b the external and …

## KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.3

Page 15.62 EXERCISE 15.3 Type 1   QUESTION 1 Fill in the blanks : In a right circular cone : (i) h=4 m and r=3 m , l= __ (ii) l=10 cm and r=7 cm , curved surface area A = _ (iii) r=7 m and h=9m , volume V=__ (iv) l=25 cm and r=7 …

## KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.2

Page 15.43 EXERCISE 15.2 Type 1   QUESTION 1 Fill in the blanks : (i) A right circular cylinder has radius 7 cm and height 5 cm, then area of its curved surface will be __ (ii) Height of a right circular cylinder is 7 m and diameter of its base is 10 m  , …

## KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.1

Page 15.21 EXERCISE 15.1 Type 1   QUESTION 1 Fill in the blanks  (i) If each side of a cube be made m times, then ratio of original and new surface ares will be __ (ii) Volume of 10m,  5m and 6m cuboid will be __ m3. (iii) The edge and diagonal of a cube …

## KC Sinha Mathematics Solution Class 9 Chapter 14 Areas (Herons formula) exercise 14.2

Page 14.29 EXERCISE 14.2 Type 1   QUESTION 1 The base and height of a parallelogram are in the ratio of 3:2 and area is 600 sq. metres . Find its base and height Sol :   QUESTION 2 The area of a parallelogram is 72cm2 . If its one perpendicular (altitude) is double of …

## KC Sinha Mathematics Solution Class 9 Chapter 14 Areas (Herons formula) exercise 14.1

Page 14.17 EXERCISE 14.1 Type 1   QUESTION 1 Find the area of the triangle whose two sides are 8cm and 11cm and perimeter is 32cm Sol :   QUESTION 2 The base of an isosceles triangle is 12 cm, and each of the equal sides is 10 cm. Find the area of the triangle …

## KC Sinha Mathematics Solution Class 9 Chapter 13 Geometrical Constructions exercise 13.1

Page 13.12 EXERCISE 13.1 Type 1   QUESTION 1 Construct a ΔABC in which ∠B=60° , BC=6.7cm and AB+AC=10cm Sol :   QUESTION 2 Construct a ΔABC in which ∠A=60° , AC=7.5cm and AB+BC=11cm Sol :   QUESTION 3 Construct a ΔABC in which BC=5.8cm , ∠C=30° b-c=2cm Sol :   QUESTION 4 Construct a …

## KC Sinha Mathematics Solution Class 9 Chapter 12 Circle exercise 12.2

Page 12.50 EXERCISE 12.2 Type 1   QUESTION 1 (i) AB is the chord of a circle. If P and Q are two points in the same segment and ∠APB=48° , then which of the following is the measure of ∠AQB ? (a) 42° (b) 48° (c) 132° (d) 30° (ii) AB is the diameter …

## KC Sinha Mathematics Solution Class 9 Chapter 12 Circle exercise 12.1

Page 12.25 EXERCISE 12.1 Type 1   QUESTION 1 (i) How many circles can be drawn through three non-collinear points ? (a) 1 (b) 2 (c) 3 (d) infinite (ii) Of the angles subtended by the equal chords at the center of the same circle ? (a) One is equal to the other (b) One …

## KC Sinha Mathematics Solution Class 9 Chapter 11 Area of parallelograms and triangles exercise 11.1

Page 11.29 EXERCISE 11.1 Type 1   QUESTION 1 Fill in the blanks: (i) Areas of congruent rectangles are __ (ii) The area of a rhombus is __the product of the lengths of its diagonals. (iii) The area of a trapezium is __ the product of the distance between parallel sides and sum of the …

## KC Sinha Mathematics Solution Class 9 Chapter 9 Triangles exercise 9.2

Page 9.38 EXERCISE 9.2 Type 1   QUESTION 1 Fill up the blanks so that the statements given below are true : (i) In a triangle, ,difference of any two sides is __ than the third side (ii) In a triangle, sum of any two sides is ___ than the third side (iii) In a …

## KC Sinha Mathematics Solution Class 9 Chapter 10 Quadrilaterals exercise 10.2

Page 10.34 EXERCISE 10.2 Type 1   QUESTION 1 Fill in the blanks : (i) In a ΔPQR , M and N are the mid-points of PQ and PR respectively , then MN=__ (ii) In a ΔABC , D and E are the mid-points of AB and AC respectively , if AB=7.4cm , BC=5.4cm and …

## KC Sinha Mathematics Solution Class 9 Chapter 10 Quadrilaterals exercise 10.1

Page 10.20 EXERCISE 10.1 Type 1   QUESTION 1 Fill in the blanks: (i) A parallelogram will be a rhombus, if and only if its ___are Perpendicular to each other. (ii) A quadrilateral will be a parallelogram, if and only if its diagonals ___ each other. (iii) Opposite angles of a parallelogram are __ Sol …

## KC Sinha Mathematics Solution Class 9 Chapter 9 Triangles exercise 9.1

Page 9.26 EXERCISE 9.1 Type 1 QUESTION 1 Fill up the blanks so that the statement becomes true: (i) If two sides of one triangle and their __ angle are equal to the corresponding two sides and their included angle of the other triangle, then the two triangles are congruent. (ii) If __ sides of …

## KC Sinha Mathematics Solution Class 9 Chapter 8 Lines and Angles exercise 8.3

Page 8.43 Exercise 8.3 Type 1 Question 1  Fill up the blanks: (i) In a triangle sum of measures of three angles is __ (ii) In a triangle , maximum number of acute angles is __ (iii) In a triangle, minimum number of acute angles is __ (iv) In figure (i) , if ∠ACD=130° , …

## KC Sinha Mathematics Solution Class 9 Chapter 8 Lines and Angles exercise 8.2

Page 8.29 Exercise 8.2 Type 1 Question 1  Answer the following questions : (i) If any transversal intersects two parallel lines in such a way that the ratio of interior angles on the same side is 2 : 7 , then f‌ind the measure of the bigger angle in degrees. (ii) If two parallel lines …

## KC Sinha Mathematics Solution Class 9 Chapter 8 Lines and Angles exercise 8.1

Page 8.12 Exercise 8.1 Question 1  Fill in the blanks in each of the following to make the statement true: (i) Two distinct points in a plane determine __ line . Sol : unique Page 8.13 (ii) A line separates a plane into __ parts namely the __ and the itself. Sol : three , …

## KC Sinha Mathematics Solution Class 9 Chapter 7 Introduction to Euclid’s Geometry exercise 7.1

Page 7.12 Exercise 7.1 Type 1 Question 1  Which of the following statements are true and which are false ? Give reasons for your answer : (i) These exists a point through which no line can pass. Sol : False : Inf‌inite number of lines cam puss through a given point.   (ii) A terminated …

## KC Sinha Mathematics Solution Class 9 Chapter 6 Coordinate Geometry exercise 6.1

Page 6.11 Exercise 6.1 Type 1 Question 1  Write the answer of each of the following Questions : (i) What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane ? Sol : x-axis and y-axis   (ii) What is the name of each part …

## KC Sinha Mathematics Solution Class 9 Chapter 5 Linear Equations in Two Variable exercise 5.1

Page 5.21 Exercise 5 Type 1 Problems based on writing a linear equation in two variables x and y in the form ax-by+c=0 and problems on writing a given statement as a linear equations in two variables WORKING RULE : Use the following information wherever is required : 1. In order to write a given …

## KC Sinha Mathematics Solution Class 9 Chapter 4 Algebraic identities exercise 4.5

Page 4.34 Exercise 4.5 Type 1 Problems based on factorization of algebraic expressions, expressible as the sum or difference of two cubes. WORKING RULE: 1. if in the given expression, any factor is common in each term , then take out the common factors. Now , use the following identities whichever is required x3+y3=(x+y)(x2-xy+y2) x3-y3=(x-y)(x2+xy+y2) …

## KC Sinha Mathematics Solution Class 9 Algebraic identities exercise 4.4

[lateapage] Page 4.26 Exercise 4.4 Type 6 Question 1 Factorize the following if : (i) (x+1) is a factor of 2×3 – 3×2 – 8x – 3 Sol : Step-1⇒2×3-3×2-8x-3 Step-2⇒2×3+2×2-5×2-5x-3x-3 Step-3⇒2×2(x+1)-5x(x+1)-3(x+1) [After writing step 1 , jumped to 3 and written 3 times (x+1) and multiply it with suitable algebric expression or number so …

## KC Sinha Mathematics Solution Class 9 Chapter 4 Algebraic identities exercise 4.3

Page 4.21 Exercise 4.3 Type 4 Problem based on f‌inding factors of trinomial polynomial of the form ax2+bx+c Working Rule: 1. Take out any variable or constant which is common factor in the given trinomial and write the remaining expression in the bracket. 2. Find a×c and let this be k . Now , f‌ind …

## KC Sinha Mathematics Solution Class 9 Chapter 4 Algebraic identities exercise 4.2

Page 4.7 Exercise 4.2 Type 1 Question 1 Factorize the following : (i) x2+4x+4 Sol: Using identity: a2+b2+2ab=(a+b)2=(a+b)(a+b) ⇒x2+22+2(x)(2) ⇒(x+2)2 ⇒(x+2)(x+2) (ii) x2-18x+81 Sol: Using identity: a2+b2-2ab=(a-b)2=(a-b)(a-b) ⇒x2+92-2(x)(9) ⇒(x-9)2 ⇒(x-9)(x-9) (iii) 4×2+4x+1 Sol: Using identity: a2+b2+2ab=(a+b)2=(a+b)(a+b) ⇒(2x)2+12+2(2x)(1) ⇒(2x+1)2 ⇒(2x+1)(2x+1) (iv) Sol: Using identity: a2+b2+2ab=(a+b)2=(a+b)(a+b) ⇒ ⇒ ⇒ (v) 25a2-60ab+36b2 Sol: Using identity: a2+b2-2ab=(a-b)2=(a-b)(a-b) ⇒(5a)2+(6b)2-2(5a)(6b) ⇒(5a-6b)2 …

## KC Sinha Mathematics Solution Class 9 Chapter 4 Algebraic identities exercise 4.1

Page 4.7 Exercise 4.1 Type 1 Question 1 Using suitable identities, f‌ind the following products : (i) (x+3)(x+3) Sol : Here we use identity a=3 , b=3 (x+a)(x+a)=x2+(a+b)x+ab ⇒x2+(3+3)x+3×3 ⇒x2+6x+9   (ii) (x-3)(x+5) Sol : Using identity: (x+a)(x+b)=x2+(a+b)x+ab a=-3 , b=5 ⇒x2+(-3+5)x+(-3)(5) ⇒x2+2x-15   (iii) (5x+2)(5x-3) Sol: Using identity: (x+a)(x+b)=x2+(a+b)x+ab replace x=5x , a=2 , …

## KC Sinha Mathematics Solution Class 9 Chapter 3 Polynomials exercise 3.2

Page 3.19 Exercise 3.2 Question 1 Fill up the blanks : (i) When x2+2x-3 is divided by (x-1) , remainder = __ Sol : Divisor=x-1 Zero of x-1 is 1 ∴ By remainder theorem , Remainder=p(1)=(1)2+2(1)-3 =1+2-3 =0   (ii) If (x-2) is a factor of the polynomial p(x)  , then p(2)= __ Sol : …

## KC Sinha Mathematics Solution Class 9 Chapter 3 Polynomials exercise 3.1

Page 3.10 Exercise 3.1 Type 1 Problems based on definition of terms related to polynomial and identifying polynomials WORKING RULE: 1. Write down the given polynomial in such a way that the variable is in the numerator in each term 2. If each term of an algebraic expression contains only non-negative integrals powers of x …

## KC Sinha Mathematics Solution Class 9 Chapter 2 Operations on Real Numbers and Laws of Exponents for Real Numbers exercise 2.1

Page 2.20 Exercise 2.1 Type 1 Question 1 Classif‌y the following numbers as rational or irrational, (i) 3+√5 Sol :Irrational   (ii) 7√5 Sol :Irrational   (iii) Sol :Irrational   (iv) 5+√5-√5 Sol : Rational   (v) √2+21 Sol : Irrational   (vi) π-2 Sol :Irrational   (vii) √2 + √3 Sol : Irrational   …

## KC Sinha Mathematics Solution Class 9 Chapter 1 Real numbers exercise 1.3

Page 1.41 Exercise 1.3 Type 1 Question 1 Visualise the number 2.662 on the number line by successive magnif‌ication. Sol :   Question 2 Visualise the number 2.437 on the number line by successive magnif‌ication. Sol :   Type 2 Question 3 Represent on the number line   Question 4 Represent on the number line …

## KC Sinha Mathematics Solution Class 9 Chapter 1 Real numbers exercise 1.2

Page 1.35 Exercise 1.2 Type 1 Question 1  Are the square roots of all positive integers irrational ? If not, then give an example of the square root of a positive integer which is a rational number. Sol : No; Example: √9=3, which is a rational number Question 2 Identify two Statements in the following …

## KC Sinha Mathematics Solution Class 9 Chapter 1 Real numbers exercise 1.1

Page 1.24 Exercise 1.1 Type 1 Question 1  State whether the following statements are true or false ? Also give reasons for your answer. (i) Every whole number is a natural number Sol :  False, since 0 (zero) is a whole number but not a natural number. (ii) Every integer is a rational number Sol …

## KC Sinha Mathematics Solution Class 10 Chapter 15 Probability Exercise 15.1

Exercise 15.1 Exercise 15.1 Question 1 A Which of the following have ‘equally likely’ outcomes? Explain. (i) A player calls for a head in a toss of a coin. The coin shows up either heads or tails. (ii) Mr Sharma has one child. The child is either a boy or a girl. (iii) An attempt …

## KC Sinha Mathematics Solution Class 10 Chapter 14 Surface Area and Volumes Exercise 14.4

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.4 Question 1 The radii of the ends of a frustum of a cone 45 cm high are 28cm and 7cm. Find its volume, the curved surface area. [Take π=22/7] Sol : Frustum = difference of two right circular cones OAB and OCD Let the height …

## KC Sinha Mathematics Solution Class 10 Chapter 14 Surface Area and Volumes Exercise 14.3

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.3 Question 1 Two cylindrical vessels are filled with oil. The radius of one vessel is 15 cm and its height is 25 cm. The radius and height of the other vessel are 10cm and 18 cm respectively. Find the radius of a cylindrical vessel 30 …

## KC Sinha Mathematics Solution Class 10 Chapter 14 Surface Area and Volumes Exercise 14.2

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.2 Question 1 A toy is in the form a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. Find the volume of the toy.  Sol : Given: Diameter of a hemisphere = 7cm So,  Height of …

## KC Sinha Mathematics Solution Class 10 Chapter 14 Surface Area and Volumes Exercise 14.1

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.1 Question 1 Three cubes each of side 5 cm are joined end to end to form a cuboid. Find the surface area of the resulting cuboid. Sol :     Length of each side of cube = 5cm According to question, Three cubes are joined …

## KC Sinha Mathematics Solution Class 10 Chapter 13 Area related to Circles Exercise 13.1

Exercise 13.1 Exercise 13.1 Question 1 The circumference of a circle exceeds its diameter by 16.8 cm. Find the circumference of the circle. Sol : We know that, circumference of a circle, C = 2πr and diameter, D = 2r According to the question, C = D + 16.8 ⇒ 2πr = 2r + 16.8 ⇒ 2πr …

## KC Sinha Mathematics Solution Class 10 Chapter 12 Constructions Exercise 12.1

Exercise 12.1 Exercise 12.1 Question 1 Divide a line segment 4.2 cm long internally in the ratio 5:3 Also, write the steps of construction. Sol : Step1: Draw a line segment AB of length 4.2 cm Step2: Draw a line AC at any angle below AB Step3: take any distance in compass and keep the …

## KC Sinha Mathematics Solution Class 10 Chapter 11 Circles Exercise 11.2

Exercise 11.1 Exercise 11.2 Exercise 11.2 Question 1 From a point P, the length of the tangent to a circle is 15 cm, and the distance of P from the centre of the circle is 17cm. Then what is the radius of the circle? Sol : Let the centre of circle be O so that …

## KC Sinha Mathematics Solution Class 10 Chapter 11 Circles Exercise 11.1

Exercise 11.1 Exercise 11.2 Exercise 11.1 Question 1 The length of a tangent from a point A at a distance 5cm from the centre of a circle is 4cm. Find the radius of the circle. Sol : Let the centre of circle be O so that AO = 5 cm Tangent is AB whose length …

## KC Sinha Mathematics Solution Class 10 Chapter 10 Coordinates Geometry Exercise 10.4

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.4 Question 1 A Find the area of the triangle whose vertices are (3, -4), (7, 5), (-1, 10) Sol : Given: (3, -4), (7, 5), (-1, 10)   Let us Assume A(x1, y1) = (3, -4)   Let us Assume B(x2, y2) = (7, 5) …

## KC Sinha Mathematics Solution Class 10 Chapter 10 Coordinates Geometry Exercise 10.3

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.3 Question 1 A Find the coordinates of the point which divides the line segment joining (2,4) and (6,8) in the ratio 1:3 internally and externally. Sol :   Let P(x,y) be the point which divides the line segment internally.   Using the section formula for the internal …

## KC Sinha Mathematics Solution Class 10 Chapter 10 Coordinates Geometry Exercise 10.2

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.2 Question 1 A Find the distance between the following pair of points: (0, 0), (- 5, 12) Sol : Given points are (0, 0) and (- 5, 12)     We need to find the distance between these two points. We know that distance(S) between …

## KC Sinha Mathematics Solution Class 10 Chapter 10 Coordinates Geometry Exercise 10.1

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.1 Question 1 A In which quadrants do the following points lie: (10, -3) Sol :   Given coordinate (10,-3) lies in Quadrant IV because as shown in the figure that those coordinate who have (+, -) sign lies in IV quadrants, or can say whose …

## KC Sinha Mathematics Solution Class 10 Chapter 9 Some Applications of Trigonometry: Height and Distances Exercise 9.1

Exercise 9.1 Exercise 9.1 Question 1 In ΔABC, ∠ A = 90°, AB = 12 cm and  cm, then find ∠B. Sol : Let us draw a diagram according to the question specification so that it gives us a better understanding of the problem. We know that  According to the question, it is asked that we find the angle …

## KC Sinha Mathematics Solution Class 10 Chapter 8 Arithmetic Progressions Exercise 8.4

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.4 Question 1 The sum of n terms of an A.P. is . Find its 20th term. Sol : Taking n = 1, we get ⇒ S1 = 4 ⇒ a1 = 4 Taking n = 2, we get ⇒ S2 = 13 ∴ a2 = S2 – S1 = 13 – 4 = 9 Taking n …

## KC Sinha Mathematics Solution Class 10 Chapter 8 Arithmetic Progressions Exercise 8.3

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.3 Question 1 Three numbers are in A.P. Their sum is 27 and the sum of their squares is 275. Find the numbers. Sol : Let the three numbers are in AP = a, a + d, a + 2d According to the question, The sum …

## KC Sinha Mathematics Solution Class 10 Chapter 8 Arithmetic Progressions Exercise 8.2

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.2 Question 1 A Find the indicated terms in each of the following arithmetic progression: 1, 6, 11, 16, …, t16, Sol : Given: 1, 6, 11, 16, …   Here, a = 1   d = a2 – a1 = 6 – 1 = 5   and …

## KC Sinha Mathematics Solution Class 10 Chapter 8 Arithmetic Progressions Exercise 8.1

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.1 Question 1 A Write the first three terms of the following sequences defined by: tn = 3n + 1 Sol : Given: tn = 3n + 1 Taking n = 1, we get t1 = 3(1) + 1 = 3 + 1 = 4 Taking n = 2, …

## KC Sinha Mathematics Solution Class 10 Chapter 7 Quadratic Equations Exercise 7.5

Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.5 Question 1 Divide 12 into two parts such that their product is 32. Sol : Let the first number be ‘X’, so the other number will be ’(12–X)’. ∵ X (12 – X) = 32 12X – X2 = 32 X2 – 12X + 32 = …

## KC Sinha Mathematics Solution Class 10 Chapter 7 Quadratic Equations Exercise 7.4

Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.4 Question 1 A Write the discriminate of each of the following quadratic equation: x2 + 4x + 3 =0 Sol : d = b2 – 4ac d = (4)2 – 4 (1) (3) d = 16 – 12 d = 4 Question 1 B  Write the …

## KC Sinha Mathematics Solution Class 10 Chapter 7 Quadratic Equations Exercise 7.3

Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.3 Question 1 Determine whether  and  are the solutions of the equation 6×2 — x — 12 = 0 or not. Sol : Put both the values of x in the equation. When  = 0 When  = 0 R.H.S = L.H.S Therefore,  and  are the solutions of the given …

## KC Sinha Mathematics Solution Class 10 Chapter 7 Quadratic Equations Exercise 7.2

Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.2 Question 1 A  Check whether the following are quadratic equations: (x − 2) (x + 1) = (x − 1) (x + 3) Sol : Given; (x − 2) (x + 1) = (x − 1) (x + 3) ⇒ x2 + x − 2x …

## KC Sinha Mathematics Solution Class 10 Chapter 7 Quadratic Equations Exercise 7.1

Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.1 Question 1 A  Which of the following is a quadratic polynomial? (i) 2 –x2 (ii) x+ (iii) x+ (iv) x2 +3+2 Sol : (i) On solving the equations, Re-writing in the format of ax2 + bx + c = 0 ∵  b = 0 & c = 2 So, …

## KC Sinha Mathematics Solution Class 10 Chapter 6 Statistics Exercise 6.4

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.4 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 type cumulative frequency distribution, and …

## KC Sinha Mathematics Solution Class 10 Chapter 6 Statistics Exercise 6.3

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.3 Question 1  Find the median of the following data: Sol : Now, items from 23 to 32 have value of variate 14 as shown by cumulative frequency. ∴ Median = 14 Question 2  Find the median of the following distribution: Sol : Now, persons from 100 …

## KC Sinha Mathematics Solution Class 10 Chapter 6 Statistics Exercise 6.2

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.2 Question 1  Find mode of the following data: 64, 61, 62, 62, 63, 61, 63, 64, 64, 60, 65, 63, 64, 65, 66, 64 Sol : Here, we can see that 64 observation has the maximum frequency. Hence, Mode = 64 Question 2  Find the …

## KC Sinha Mathematics Solution Class 10 Chapter 6 Statistics Exercise 6.1

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.1 Question 1  The mean of 11 results is 30. If the mean of the first 6 results is 28 and that of last 6 results is 32, find the 6th result. Sol : Let the 6th number be x Given that mean of 11 results = …

## KC Sinha Mathematics Solution Class 10 Chapter 5 Triangles Exercise 5.5

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.5 Question 1  Sides of some triangles are given below. Determine which of them are right triangles (i) 8 cm, 15 cm, 17 cm (ii) (2a —1) cm,  cm and (2a + 1) cm (iii) 7 cm, 24 cm, 25 cm (iv) 1.4 cm, 4.8 …

## KC Sinha Mathematics Solution Class 10 Chapter 5 Triangles Exercise 5.4

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.4 Question 1  In two similar triangles ABC and DEF, AC = 3 cm and DF = 5 cm. Find the ratio of the areas of the two triangles. Sol : Given: ΔABC ~ ΔDEF and AC = 3 cm and DF = 5 …

## KC Sinha Mathematics Solution Class 10 Chapter 5 Triangles Exercise 5.3

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.3 Question 1  State which of the following pairs of triangles are similar. Write the similarity criterion used and write the pairs of similar triangles in symbolic form (all lengths of sides are in cm). (i)  (ii)  (iii)  (iv)  (v)  (vi)  (vii)  Sol : …

## KC Sinha Mathematics Solution Class 10 Chapter 5 Triangles Exercise 5.2

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.2 Question 1  In ΔABC, P and Q are two points on AB and AC respectively such that PQ || BC and , then find. Sol : Given: PQ || BC and  By Basic Proportionality theorem which states that if a line is drawn parallel to one …

## KC Sinha Mathematics Solution Class 10 Chapter 5 Triangles Exercise 5.1

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.1 Question 1  Fill in the blanks with the correct word given in brackets: (i) All squares are having the same length of sides are………. [similar, congruent, both congruent and similar] (ii) All circles having the same radius are ………. [similar, congruent, both congruent …

## KC Sinha Mathematics Solution Class 10 Chapter 4 Trigonometric Ratios and Identities Exercise 4.4

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.4 Question 1 Fill in the blanks (i) sin2 θ cosec2 θ = …….. (ii) 1 + tan2 θ = …… (iii) Reciprocal sin θ. cot θ = …… (iv) 1–…….= cos2θ (v)  (vi)  (vii) cos θ is reciprocal of ……… (viii) Reciprocal of sin θ is……… (ix) Value of sin θ in terms of …

## KC Sinha Mathematics Solution Class 10 Chapter 4 Trigonometric Ratios and Identities Exercise 4.3

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.3 Question 1  Express the following as trigonometric ratio of complementary angle of θ. (i) cos θ (ii) sec θ (iii) cot θ (iv) cosec θ (v) tan θ Sol : (i) We know that ⇒ cosθ = sin (90° – θ) (ii) We know that (iii) We know that …

## KC Sinha Mathematics Solution Class 10 Chapter 4 Trigonometric Ratios and Identities Exercise 4.2

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.2 Question 1  Find the value of the following : (i) sin 30o + cos 60o (ii) sin2 45o+cos245o (iii) sin 30o + cos 60o – tan45o (iv)  (v) tan 60o x cos30o Sol : (i) sin 30o + cos 60o We know that, > So, sin(30o) + cos(60o) =1 (ii) sin2 45o+cos245o …

## KC Sinha Mathematics Solution Class 10 Chapter 4 Trigonometric Ratios and Identities Exercise 4.1

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.1 Question 1 From the given figure, find the value of the following: (i) sin C (ii) sin A (iii) cos C (iv) cos A (v) tan C (vi) tan A Sol : (i) Sin C We know that, So, here θ = C Side opposite to ∠C …

## KC Sinha Mathematics Solution Class 10 Chapter 3 Pairs of Linear Equations in Two Variables Exercise 3.5

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.5 Question 1  The sum of the two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers. Sol : Let the two numbers be x and y. According to the question, x + y = 18 …(i)  …(ii) Eq. (ii) …

## KC Sinha Mathematics Solution Class 10 Chapter 3 Pairs of Linear Equations in Two Variables Exercise 3.4

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.4 Question 1 A  Solve the following pair of linear equation by cross – multiplication method: 8x + 5y = 9 3x + 2y = 4 Sol : Given, pair of equations is 8x + 5y – 9 = 0 and 3x + 2y …

## KC Sinha Mathematics Solution Class 10 Chapter 3 Pairs of Linear Equations in Two Variables Exercise 3.3

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.3 Question 1 A  Solve the following system of equations by elimination method: 3x – 5y – 4 = 0 9x = 2y + 7 Sol : Given pair of linear equations is 3x – 5y – 4 = 0 …(i) And 9x = …

## KC Sinha Mathematics Solution Class 10 Chapter 3 Pairs of Linear Equations in Two Variables Exercise 3.2

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.2 Question 1 A  Solve the following pair of linear equations by substitution method: 7x— 15y = 2 x + 2y = 3 Sol : Given equations are 7x – 15y = 2 …(i) x + 2y = 3 …(ii) From eqn (ii), x = …

## KC Sinha Mathematics Solution Class 10 Chapter 3 Pairs of Linear Equations in Two Variables Exercise 3.1

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.1 Question 1  Sudha went to market with her friends. They wanted to eat `gol – gappa’ as well as `dahi – bhalla’. The number of plates of gol – gappa taken by them is half that of dahi – bhalla. The cost of …

## KC Sinha Mathematics Solution Class 10 Chapter 2 Polynomials Exercise 2.3

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.3 Question 1  Divide 2×3 + 3x + 1 by x + 2 and find the quotient and the reminder. Is q(x) a factor of 2×3 + 3x + 1 ? Sol : Here, dividend and divisor both are in the standard form. Now, on dividing p(x) by g(x) we …

## KC Sinha Mathematics Solution Class 10 Chapter 2 Polynomials Exercise 2.2

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.2 Question 1 A  Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients: x2 – 3 Sol : Let f (x) = x2 – 3 Now, if we recall the identity (a2 – b2) = (a – b)(a + b) Using this …

## KC Sinha Mathematics Solution Class 10 Chapter 2 Polynomials Exercise 2.1

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.1 Question 1  Examine, seeing the graph of the polynomials given below, whether they are a linear or quadratic polynomial or neither linear nor quadratic polynomial: (i) (ii)  (iii) (iv)  (v)  (vi)  (vii) (viii)  Sol : (i) In general, we know that for a linear polynomial ax + b, a≠0, the graph of y …

## KC Sinha Mathematics Solution Class 10 Chapter 1 Real nuambers Exercise 1.4

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.4 Question 1 A  Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion. Sol : Given rational number is   is terminating if a) p and q are co-prime & b) q is of the form …

## KC Sinha Mathematics Solution Class 10 Chapter 1 Real numbers Exercise 1.3

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.3 Question 1  Prove that √2 is irrational. Sol : Let us assume that √2 is rational. So, we can find integers p and q (≠ 0) such that √2 =  . Suppose p and q have a common factor other than 1. Then, we divide by …

## KC Sinha Mathematics Solution Class 10 Chapter 1 Real numbers Exercise 1.2

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.2 Question 1 A  Express each of the following numbers as a product of its prime factors: Sol : Given number is 4320 Factorization of 4320 is Hence, 4320 = 25 × 33 × 5 (Product of its prime factors) Question 1 B  Express each of the following …

## KC Sinha Mathematics Solution Class 10 Chapter 1 Real numbers Exercise 1.1

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.1 Question 1 A  Using Euclid’s division algorithm, find the HCF of 156 and 504 Sol : Given numbers are 156 and 504 Here, 504 > 156 So, we divide 504 by 156 By using Euclid’s division lemma, we get 504 = 156 × 3 + 36 …

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