The next term of the A.P. , and is [1]18−−√ 32−−√ 50−−√72−−√ 84−−√64−−√ 80−−√a) scalene b) equilateralc) isosceles d) right angled6. The points P(0, 6), Q(-5, 3) and R( 3,1) are the vertices of a triangle, which is [1]a) III quadrant b) II quadrantc) I quadrant d) IV quadrant7. The point which divides the line segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the [1]a) 20o, 30o. b) 30o, 20o.c) 50o, 40o. d) 40o, 50o.8. In the given figures the measures of D and F are respectively [1]∠ ∠a) 120° b) 150°9. In figure, AB is a chord of a circle and AT is a tangent at A such that , measure of is : [1]∠BAT = 60o ∠ACBPage 2 of 22

To find the next term of the given arithmetic progression (A.P.), we need to identify the common difference between consecutive terms.

The common difference can be calculated by subtracting any two consecutive terms. Let's take the second and first terms:

32√18 - 18√1 = 32 - 18 = 14

Now, we can find the next term by adding the common difference to the last term:

84√1 + 14 = 84 + 14 = 98

Therefore, the next term of the A.P. is 98.

To determine the type of triangle formed by the points P(0, 6), Q(-5, 3), and R(3, 1), we need to analyze the coordinates of the vertices.

The x-coordinate of P is 0, which means it lies on the y-axis. The y-coordinate of P is 6, which is positive.

Similarly, the x-coordinate of Q is -5, which is negative, and the y-coordinate is 3, which is positive.

Finally, the x-coordinate of R is 3, which is positive, and the y-coordinate is 1, which is positive.

Based on these coordinates, we can conclude that the triangle formed by P, Q, and R lies in the first quadrant (I quadrant).

To find the point that divides the line segment joining (7, -6) and (3, 4) in the ratio 1:2 internally, we can use the section formula.

The section formula states that the coordinates of the point dividing the line segment in the ratio m:n internally are given by:

( (n * x1) + (m * x2) ) / (m + n), ( (n * y1) + (m * y2) ) / (m + n)

Applying this formula, we have:

x = ( (2 * 7) + (1 * 3) ) / (1 + 2) = (14 + 3) / 3 = 17 / 3

y = ( (2 * -6) + (1 * 4) ) / (1 + 2) = (-12 + 4) / 3 = -8 / 3

Therefore, the point that divides the line segment in the ratio 1:2 internally lies at (17/3, -8/3).

In the given figures, the measures of angles D and F are not provided, so we cannot determine their values.

In the figure where AB is a chord of a circle and AT is a tangent at A, the measure of angle BAT is given as 60 degrees.