Q) Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two triangles whose sides are 35, 53, 66 and 33, 56, 65 measured in centimeters (Use π = ) Ans: Let’s start with calculating area of triangles: In 1st triangle: sides a = 35 cm, […]
December 2023
Q) In a hospital the ages of diabetic patients were recorded as follows. Find the median age. Ans: Let’s re-organize the data in the frequency table to find out each part: To find the median, we need to identify middle value of the data. Let’s rearrange the data: First, we need to find the cumulative
Q) Find the HCF of 506 and 1155. Ans: By prime factorisation, we get: 506 = 2 x 11 x 23 1155 = 3 x 5 x 7 x 11 Since HCF is all the factors between the two numbers and here 11 is the only factor between the two numbers ∴ HCF = 11
Find the HCF of 506 and 1155. Read More »
Q) Find the LCM and HCF of 404 and 96 and verify that LCM x HCF = product of the two numbers.120. Ans: By prime factorisation, we get: 404 = 22 x 101 96 = 25 x 3 ∴ LCM = 25 x 3 x 101 = 9696 And HCF = 22 = 4 Now
Q) Two rails are represented by the linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically. Ans: Step 1: Let’s try to find the intersection points on X – axis and Y – axis for each of the lines: A. For linear equation
Two rails are represented by the linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Read More »
Q) If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p. Ans: sec θ + tan θ = p ………….. (i) ∵ sec2 θ – tan2 θ = 1 ∴ (sec θ + tan θ) (sec θ – tan θ) = 1 ∴ p (sec θ – tan θ)
If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p. Read More »
Q) In the given figure, ABC is a triangle in which ∠B = 900, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle. Ans: By Pythagorus theorem, AC = = = = 50 cm Method 1: OP = OQ (radius
In the given figure, ABC is a triangle in which ∠B = 90, BC = 48 cm and AB = 14 cm. Read More »
Q) A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC Ans: By tangents property, we know that the tangents drawn on a circle from an external point are always equal, ∴ from Point A: AP = AS ………….. (i) from Point B:
Q) If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB and P lies on the line segment AB. Ans: Let the coordinates of P are (X, Y) Since P lies on the line AP, ∴ AP + PB = AB … (1) Given
If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that Read More »
Q) Two vertices of a triangle have coordinates (-8,7) and (9,4). If the centroid of the triangle is at the origin, what are the coordinates of the third vertex? Ans: Given that two vertices of a triangle are (-8,7) and (9,4); Centroid is (0,0) Let the third vertex be (X, Y) We know that if a