# preeti 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:  Let’s try to find the intersection points on X – axis and Y – axis for each of the lines: I. For linear equation x + …

Q) If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terns 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) …

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 …

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 …

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 …

Q)  The graph of the polynomial – ax²+bx+c is shown below. Write the signs of ‘a’ and ‘b² – 4ac’. Ans: Clearly, f(x) = ax² + bx + c represent a parabola opening upwards. Therefore, a>0 Since, the parabola cuts the x-axis at two points, this means that the polynomial will have two real solutions. Hence, …

Q) ABCD is a rectangle if the value of AB= 12 is given, find the values of x and y. Ans:  We know, opposite sides of a rectangle are equal, ∴ x + y = 12  —-(1) and, x – y = 8   —-(2) By elimination method, we subtract (2) from (1), Therefore, 2y = …

Q) From a group of 3 boys and 2 girls we select two children. What is the set representing the event: i. one girl is selected ii. at least one girl is selected Ans:  Let’s first find out all possible sets of selecting two children: Let 3 boys are B1, B2, B3 and 2 girls are G1, …

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