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
Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30° Read More »
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. From the given pack of 52
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 »
Q) Find the ratio in which the point (8/5, y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y. ns: Let’s make a diagram for the given question: Let’s consider the point C(8/5, y) divides the line AB in ratio of P : 1 Now, by
Find the ratio in which the point (8/5, y) divides the line segment joining the points Read More »
Q) In a chemistry lab, there is some quantity of 50% acid solution and some quantity of 25% acid solution. How much of each should be mixed to make 10 litres of 40% acid solution? Ans: Let consider quantity of 50% acid solution be V litres ∵ total quantity of final solution is 10 litres ∴
In a chemistry lab, there is some quantity of 50% acid solution and some quantity of 25% Read More »
Q) Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ + cosec θ Ans: Here, let’s start by simplifying the LHS in given equation: LHS = = = = = = Now, we know that a3 – b3 = (a – b) (a2
Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosec θ Read More »
Q) In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that ∠POQ = 90°. Ans: Let’s connect Point O with Point R where tangent PQ touches the circle. Let’s consider ∠ POR = x and ∠ QOR = y Step 1:
In the given figure, AB is a diameter of the circle with centre O. AQ, BP and Read More »