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Q) Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5 Ans: Given equations are: 2 x + 5 y = – 4 …………………… (i) 4 x – 3 y = 5 …………………..(ii) To get the value of variables, we need to […]
Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5 Read More »
Q) In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that: (i) Δ ABD ~ Δ CBD (ii) AB = BC Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given: (i) ABCD is a quadrilateral and (ii) BD is angle bisector of ∠ B and ∠ D.
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 »