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Class 10 Chapter 2(Poloynomials) Case based 4:- The pictures are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures,their curve represents an efficient method of carrying load and so can be found in bridges and in architecture … Read more
Class 10 Chapter 2(Poloynomials) Case based 2:- While passing over an iron bridge, Hema noticed that the shape resembles a curve about which she had studied in mathematics.(Class 10 Case based problem of Chapter 2 Polynomials 2) (A) What type of ploynomial does the shape of the bridge represents ? (B) Find the zeroes of … Read more
Class 10 Chapter 2(Poloynomials) Case based 1: SLV-3 was successfully launched on july 18, 1980 from Shriharikota Range (SHAR), when Rohini satellite, RS-1, was placed in orbit, thereby making India the sixth member of an exclusive club of space-faring nations. SLV-3 employed an open loop guidance (with stored pitch programme) to steer the vehicle in … Read more
Question:- Prove that root n is not a rational number, if n is not perfect square Solution:- Let √n be a rational number. ∴ , where p and q are co-prime integers q≠ 0. On squaring both side we get ….(i) ⇒ n divides p² ⇒ n divides p … (ii) [If n divides p², … Read more
Question :- Prove that √2 + √5 is irrational Solution:- Let us suppose that √2 + √5 is rational. Let , where a and b coprime integers and b ≠ 0. Now Squaring both side ⇒ √2 is rational, since is rational. This contradict the fact that √2 is an irrational number. So, our assumption … Read more
Question:- Prove that √p + √q is irrational, where p and q are primes Solution:- Let us suppose that √p + √q is rational. Let √p + √q = a where a is rational number. ⇒ √p = a – √q On squaring both side we get ⇒ [Using formula ] The above statement is a … Read more
Exercise 1.2(Real numbers) Question 1: Prove that √5 is irrational. Solutions: Let us assume, that √5 is rational number.where, x and y are co-primes and y ≠ 0. i.e. √5 = x/y. ⇒ y√5= x Squaring both the sides, we get, (y√5)2 = x2 ⇒5y2 = x2……………………………….. (1) Thus, x2 is divisible by 5, so x is also divisible by 5. Let … Read more
Exercise 1.1(Real numbers) Exercise 1.1 real number class 10 ncert maths solutions Question 1: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Solutions: (i) 140 we will get the product of its prime factor. Therefore, 140 = 2 × 2 × 5 × … Read more
Question:- Prove that 2 – √ 3 is irrational, given that √3 is irrational Solution: Let 2 – √3 be a rational number. Then there exist positive integers ‘a’ and ‘ b’, where a and b are integers having no common factor other than 1 and b ≠ 0 such that ⇒ Since a and … Read more
Question:- Prove that root 5 is an irrational number Solution:- Let us assume that on the contrary that √5 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒ Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 5 then $a$ … Read more