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Q)Â Â In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression: (a) Write the AP for […]
Q)Â PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn such that PQ = QR = RS. Semicircles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of the shaded region. Ans:Â Given that the
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 Ï€ = ) Ans: Let’s start with calculating area of triangles: In 1st triangle: sides a = 35 cm,
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
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:Â 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: