Q) If 2x + y = 13 and 4x – y = 17, find the value of (x – y). Ans: We are given the following equations: 2 x + y = 13 …. (i) 4 x – y = 17 …. (ii) Step 1: To calculate values of x and y, let’s add both […]
If 2x + y = 13 and 4x – y = 17, find the value of (x – y). Read More »
Q) Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle. Ans: (i) value of y: We know that the center is the midpoint of the diameter, Therefore if AB
Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is Read More »
Q) Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). Ans: We know that the distance between two points (X1, Y1) and (X2, Y2) is given by: S = √ [(X2 – X1)2 + (Y2 – Y1)2 ] Now distance between A(7,1)
Find a relation between x and y such that the point P(x, y) is equidistant Read More »
Q) In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Ans: Step 1: It is given that: ∴ by cross multiplying, we can say that: Step 2: Let’s look at Δ EAB and Δ ECD: ∠ AEB = ∠ DEC (∵ Vertically Opposite Angles) Step 3: Let’s compare Δ EAB
In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Read More »
Q) Evaluate : (cos 450 + sin 600) / (sec 300+ cosec 300). Ans: We know that: cos 450 = ; sin 600 = ; sec 300 = ; cosec 300 = 2 By submitting these values in the given expression, we get: (cos 450 + sin 600) / (sec 300+ cosec 300) = =
Evaluate : (cos 45° + sin 60°) / (sec 30° + cosec 30°). Read More »
Q) If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms. Ans: Let’s consider the first term be A and the common difference be D. Step 1: We know that sum of first n terms of an A.P.
If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289 Read More »
Q) The ratio of the 10th term to its 30th term of an A.P. is 1 : 3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P. Ans: Step 1: We know that nth term of an A.P. = a + (n-1) d Therefore,
The ratio of the 10th term to its 30th term of an A.P. is 1 : 3 and the sum of Read More »
Q) Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship between the zeroes and the coefficients of the polynomial. Ans: In the given polynomial equation, to find zeroes, we will start with f(x) = 0 Therefore, x2 – 15 = 0 Step 1: Let’s start calculating the zeroes of the
Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship Read More »
Q) Solve the following system of linear equations graphically: 3 x – y + 1 = 0 x + y = 5 Ans: Step 1: To plot the equations, let’s first find out the coordinates of points lying on these lines: For line: 3 x – y + 1 = 0,, we calculate coordinates of
Solve the following system of linear equations graphically: 3 x – y + 1 = 0 Read More »
Q) Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis. Ans: Method 1: Step 1: By section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be given by: P (X,Y) = here, the point divides