Q) If (-5,3) coordinates and (5,3) are two vertices of an equilateral triangle, then find of the third vertex, given that origin lies inside the triangle. (Take √3 = 1.7) Ans: Let the third vertex be (x, y)Hence, 3 vertex of the triangle will be A (-5,3) B (5,3) C (x y) Step 1: Since it […]
Q) Prove that √5 is an irrational number. Ans: Let √5 be a rational number. Therefore √5 = p/q, where q ≠ 0 and let p & q be co-primes. ⇒ 5q² = p² ⇒ p² is divisible by 5 ⇒ p is divisible by 5………………….. ……………….. (i) ⇒ p = 5a, where a is some
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Q) Half of the difference between two numbers is 2. The sum of the greater and twice the smaller number is 13. Find the numbers. Ans: Step 1: Let the numbers be x and y. Here, x is the greater number and y is the smaller number. Step 2: by 1st condition, we get: ½ (x-
Q) If sin α = 1/√2 and cot β = √3, then find the value of cosec α + cosec β. Ans: Given that, sin α = 1/√2 ⇒ cosec α = 1 / sin α = 1/ (1/√2) ⇒ cosec α = √2 …………(i) Next, we have value of cot β and need to arrive
If Sin α = 1/√2 and Cot β = √3, then find the value of Cosec α + Cosec β. Read More »
Q) A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is (i) red (ii) yellow. Ans:
Q) Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively. Ans: Question is asking for highest number which is dividing other numbers…. . clearly, we need to find HCF Since there are remainders after dividing, hence if we subtract remainder from the given number, we will get the actual
Q) If Sin θ + cos θ = √3, then find the value of Sin θ . Cos θ Ans: Given that Sin θ + cos θ = √3 Let’s square on both sides => (Sin θ + cos θ)2 = (√3) 2 ⇒ Sin2 θ + Cos2 θ +2 Sin θ Cos θ =
If Sin θ + Cos θ = √3, then find the value of Sin θ . Cos θ Read More »
Q) In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY. Ans: Since XZ ǁ BC, Therefore, (BPT Theorem) ∴ ………….. (i) Since XZ ǁ BC, ∴ XY ǁ BM ∠ AXY = ∠
Q) Solve the pair of equations x = 3 and y = – 4 graphically. Ans: Lets plot both the equations on the graph. Increase till these lines intersect each other. Get the intersection point as (3,-4)
Solve the pair of equations x = 3 and y =- 4 graphically. Read More »
Class 10 Mathematics Chapter 1 – Real Numbers Exercise 1.2 1). Express each number as a product of its prime factors: (i) 140(ii) 156(iii) 3825(iv) 5005(v) 7429 Solution: (i) 140: To find the prime factorization of 140, we can use either trial division or prime decomposition (factor tree). Let’s use prime decomposition here: Factor tree
NCERT Solutions: Class 10 Mathematics Chapter 1 – Real Numbers Exercise 1.2 Read More »