Download free Class 3 chapter-wise NCERT solutions, textbook answers, sample question papers, syllabus, and study notes.
[mathjax] 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 = 2y + 7 …(ii) On...
[mathjax] Question 1 Divide 2x 3 + 3x + 1 by x + 2 and find the quotient and the reminder. Is q(x) a factor of 2x 3 + 3x + 1 ? Sol : Here, dividend and divisor both are in the standard form. Now, on...
[mathjax] Question 1 A Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients: x 2 – 3 Sol : Let f (x) = x 2 – 3 Now, if we recall...
add [mathjax] 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 $=\frac{p}{q}$ . Suppose p and q have a common...
add [mathjax] Exercise 8.3 (i) In a triangle, minimum number of acute angles is __ Sol : Two (ii) In figure (i) , if ∠ACD=130° , ∠ABC=48° , then ∠BAC=__ Sol : 82° (iii) If a side of a triangle is...
add [mathjax] 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....
[mathjax] 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...
add [mathjax] Exercise 5.1 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...
add [mathjax] Exercise 4.2 Type 1 Question 1 Factorize the following : (i) x 2 +4x+4 Sol: Using identity: a 2 +b 2 +2ab=(a+b) 2 =(a+b)(a+b) ⇒x 2 +2 2 +2(x)(2) ⇒(x+2) 2 ⇒(x+2)(x+2) (ii) x 2 -18x+81...
add [mathjax] 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)=x 2 +(a+b)x+ab ⇒x 2 +(3+3)x+3×3...
add [mathjax] Exercise 3.2 Question 1 Fill up the blanks : (i) When x 2 +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...
[mathjax] 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...
KC Sinha Class 10 Solutions is provided here. Mathematics is a subject that can be challenging for many students, and it’s not uncommon to feel overwhelmed or frustrated when trying to solve complex...
[mathjax] 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...
[mathjax] Question 1 Divide a line segment 4.2 cm long internally in the ratio 5:3 Also, write the steps of construction. Sol : Question 2 Divide a line segment of length 3.2 cm in the ratio of 3:5...
[mathjax] 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...
[mathjax] 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...
[mathjax] 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...
[mathjax] Question 1 D In which quadrants do the following points lie: Sol : Given coordinate \left(\frac{3}{2}, 5\right)lies, in Quadrant I because as shown in the figure that those coordinate who...
[mathjax] 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...