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Q) Solve the following system of linear equations : 7 x – 2 y = 5 and 8 x + 7 y = 15 and verify your answer. Ans: Given equations are: 7 x – 2 y = 5 …………………… (i) 8 x + 7 y = 15 …………………..(ii) To get the value of variables, […]
Q. Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now? Ans: Let’s consider Rashmi’s present age be X and Nazma’s present age be Y Hence, Rashmi’s age 3 years ago = X – 3 Nazma’s age
Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be Read More »
Q) Diagonals AC and BD of a trapezium ABCD intersect at O, where AB || DC. If DO/OB = 1/2, then show that AB = 2CD Ans: Let’s make a diagram for the given question: In Δ AOB and Δ COD, ∠ ABO = ∠ CDO (being traversal alternate angles with AB ǁ CD) similarly ∠
Q) Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering 5 – 2 √3 is a rational number. ∴ 5 – 2 √3 = (here p and q are integers and q ≠ 0) ∴ – 2 √3
Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Read More »
Q) Show that the number 5 × 11 × 17 + 3 × 11 is a composite number Ans: STEP BY STEP SOLUTION Let’s start solving the given expression: 5 ×11 × 17 + 3 × 11 = 11 (5 x 17 + 3) = 11 (88) = 11 x 11 x 8 it has
Show that the number 5×11×17+3×11 is a composite number Read More »
Q) Solve the following system of linear equations : 2p + 3q = 13 and 5p – 4q = – 2 Ans: Given equations are: 2p + 3q = 13 …… ………….. (i) and 5p – 4q = – 2 …………… (ii) To get the value of variables, we need to drop one variable. Let’s
Solve the following system of linear equations : 2p + 3q = 13 Read More »
Q) Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30° Ans: Here, let’s start values of sin & cosine for θ = 300 and 450 We know that sin 300 = , cos 300 = , cos 450 = We submit these values in the given question, we get: 2√2 cos 45° sin
Q) If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B Ans: Here, let’s calculate the values of LHS & RHS one by one and check if it is verified. LHS = sin (A + B) = sin (60
If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B Read More »
Q) In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card. Ans: We have 52 cards in a pack. Step 1: From the given pack
In a pack of 52 playing cards one card is lost. From the remaining cards, Read More »
Q) ABCD is a rectangle formed by the points A (−1, −1), B (−1, 6), C (3, 6) and D (3, −1). P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other. Ans: Let’s make a diagram for the given
ABCD is a rectangle formed by the points A (−1, −1), B (−1, 6), C (3, 6) and D (3, −1). Read More »