Q) Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots: x2 + 2 (m – 1) x + (m + 5) = 0 Ans: Step 1: First, let’s compare the given equation with standard quadratic equation ax2 + bx + c = 0, […]
Without solving the following quadratic equation, find the value of ‘m’ for which Read More »
Q) Using graphical method, solve the following system of equations : 3 x – 2 y = 10 and 5 x + 3 y = 4 Ans: Ans: (i) Solution of the equations: Step 1: Let’s find the points on both lines and plot on the graph paper: a) 3 x – 2 y =
Q) If three times the greater of two numbers is divided by the smaller one, we get 4 as the quotient and 3 as the remainder. Also, if seven times the smaller number is divided by greater one, we get 5 as the quotient and 1 as the remainder. Find the numbers. Ans: STEP BY
Q) Find , if Ans: Given Taking log both sides log = log Since log (a) b = b. log a ∴ y log (cos x) = x log (cos y) Differentiating both sides w.r.t. x (y log cos x) = (x log cos y) . log cos x + . y = . log
Find dy/dx, if (cos x)y = (cos y)x Read More »
Q) Find the co-ordinates of the foot of the perpendicular drawn from the point (2, 3, – 8) to the line (4 – x)/2 = y/6 = (1 – z )/3Also, find the perpendicular distance of the given point from the line. On the basis of the above information, answer the following questions :(i) Write
Find the co-ordinates of the foot of the perpendicular drawn from the point (2, 3, – 8) Read More »
Q) A rectangular visiting card is to contain 24 sq.cm. of printed matter. The margins at the top and bottom of the card are to be 1 cm and the margins on the left and right are to be 1½ cm as shown below : On the basis of the above information, answer the following questions
Q) A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who
A departmental store sends bills to charge its customers once a month. Past experience Read More »
Q) Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Ans: Let’s take both numbers one by one and analyse: (i) 7 × 11 × 13 + 13 = 13 (7 x 11 + 1) = 13
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Read More »
Q) The vertices of Δ ABC are A (- 2, 4), B(4, 3) and C(1, – 6). Find length of the median BD. Ans: Let’s plot the points on the graph: Step 1: To draw median BD, point D lies on AC Let’s consider the coordinates of D are (X, Y) Since D is the midpoint of
Q) Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three integers. Ans: STEP BY STEP SOLUTION Let’s consider the three consecutive integers as (X – 1), X and (X + 1) By given condition, X 2 + (X – 1) (X +