Class 11th Applied Mathematics - Coordinate Geometry Case Study Questions and Answers 2022 - 2023
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Coordinate Geometry Case Study Questions With Answer Key
11th Standard CBSE
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Reg.No. :
Applied Mathematics
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A market is in the form of a triangle whose vertices are B(–2, 0), C(1, 12). The third vertex A of this trianagle lies on the mid point of the line joining the points (2, 1) and (4, 13).
On the basis of this information answer the following questions:
(i) What will be the coordinates of A ?(a) (5, 8) (b) (3, 7) (c) (3, 9) (d) (4, 8) (ii) Find the slope of the line joining the points B and C?
(a) 4 (b) 3 (c) 2 (d) 1 (iii) Equation of the line joining the points B and C?
(a) y – 2 = 4 x (b) y + 2 = 5x (c) y + 2 = 3x (d) y + 2 = x (iv) Does point A lies on the line BC?
(a) it lies on the line BC (b) it will not lie on the line BC (c) can’t say (d) None of these (v) If slope between two lines are – 2 and \(\frac{1}{2}\) then these lines are
(a) parallel (b) perpendicular (c) coincident lines (d) Perpendicular -
A farming land is in the form of a quadrilateral. Vertices of this quadrilateral are A(1, 3), B(8, 3), C(8, 16), and D(16, 1).
On the basis of this information answer the following questions:
(i) Slope of side AB is(a) 1 (b) \(\frac{1}{2}\) (c) 0 (d) \(\frac{1}{3}\) (ii) Slope of side AC is
(a) \(\frac{1}{3}\) (b) \(\frac{13}{14}\) (c) \(\frac{13}{14}\) (d) \(\frac{2}{3}\) (iii) If the slope of the line is zero, then such line is
(a) parallel to x-axis (b) parallel to y-axis (c) none of these (iv) Equation of line AC is
(a) 13x + y = – 21 (b) 3x + y = – 11 (c) 3x – y = – 21 (d) 13x – 7y = –8 (v) If slope of line L1 is m1 and slope of line L2 is m2 then angle between two lines is
(a) \(\tan ^{-1}\left(\frac{m_{2}-m_{1}}{1+m_{1} m_{2}}\right)\) (b) \(\tan ^{-1}\left(\frac{m_{2}+m_{1}}{1+2 m_{1} m_{2}}\right)\) (c) \(\tan ^{-1}\left(\frac{m_{2}+m_{1}}{2-2 m_{1} m_{2}}\right)\) (d)\(\tan ^{-1}\left(\frac{m_{2}+m_{1}}{1-m_{1} m_{2}}\right)\) -
A student was standing at point P (as shown in figure. From point P, he was looking at a sphere at two different points T and R. O is the centre of the sphere. Given ∠TPR = 60° and distance between point P and O is \(a \sqrt{3}\).
On the basis of the given information answer the following questions :
(i) What is the measure of the angle OTP?(a) 30° (b) 75° (c) 45° (d) 90° (ii) What is the measure of angle OPT?
(a) 45° (b) 35° (c) 30° (d) 60° (iii) The value of OP in terms of a is
(a) 3a (b) 2a (c) 4a (d) a (iv) The value of PT in terms of a is
(a) \(\sqrt{2} a\) (b) a (c) \(\sqrt{3} a\) (d) \(\sqrt{4} a\) (v) If OT = 2 units and coordinates of centre are (0,0). then equation of circle is
(a) x2 + y2 = 6 (b) x2 – y2 = 4 (c) 2x2 + 2y2 = 9 (d) x2 + y2 = 4 -
A farmer has a circular field in which a square area is there. In that square area, he was able to crop the field and rest of the area outside the square was not good for crops.
On the basis of this information, answer the following questions:
(i) If the coordinates of centre of the circle are (2, – 3), then which of the following equation of the diameter will pass through the centre?(a) x + 2y = –1 (b) x + y = – 1 (c) x + y = 2 (d) x – y = – 1 (ii) If the centre of the circle is (2, –3) and radius is 8 then equation of circle is
(a) x2 – y2 – x + 3y – 41 = 0 (b) x2 + y2 – x + y – 51 = 0 (c) x2 + y2 – 4x – 5y – 51 = 0 (d) x2 + y2 – 4x + 6y – 51 = 0 (iii) If radius of circle is double, then its area will
(a) remain same (b) double (c) three times (d) four times (iv) If the square has side 2m, then difference between the area of circle and square is
(a) \(2 \pi+4\) (b) \(2 \pi-4\) (c) \(2 \pi-1\) (d) \(2 \pi-2\) (v) Line which is perpendicular to the tangent will always pass through the centre of the circle, this statement is
(a) true (b) false (c) can’t say (d) none of these -
Rahul is playing with long string, he hang the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10m high and 5 m wide at its base as shown in the following figure:
On the basis of the above information answer the following questions:
(i) What is the standard equation of parabola in this case ?(a) y2 = 4ax (b) y2 = - 4ax (c) x2 = 4 ay (d) x2 = - 4 ay (ii) Parabola passes through the point :
(a) \(\left(\frac{5}{2}, 10\right)\) (b) \(\left(10, \frac{5}{2}\right)\) (c) \(\left(0, \frac{5}{2}\right)\) (d) \(\left(\frac{5}{2}, 0\right)\) (iii) Find the value of a in the standard equation
(a) \(\frac{32}{5}\) (b) \(\frac{5}{32}\) (c) \(\frac{5}{2}\) (d) \(\frac{2}{5}\) (iv) What is particular equation of parabola ?
(a) x2 = 5y (b) x2 = 8y (c) \(x^{2}=\frac{5}{8} y\) (d) x2 = y (v) How wide is it 2 m from the vertex of the parabola ?
(a) 2m (b) 3m (c) 2.23 m (d) 2.5 m -
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)
On the basis of the above information answer the following questions:
(i) What is the standard equation of parabola in this case ?(a) y2 = 4ax (b) y2 = - 4ax (c) x2 = 4 ay (d) x2 = - 4 ax (ii) What are the coordinates of point A ?
(a) (50, 30) (b) (50, 24) (c) (30,50) (d) (24, 50) (iii) Find the value of a in the standard equation
(a) \(\frac{24}{625}\) (b) \(\frac{18}{625}\) (c) \(\frac{625}{24}\) (d) \(\frac{625}{18}\) (iv) What is particular equation of parabola ?
(a) x2 = 25y (b) x2 = -24y (c) x2 = 625y (d) 6x2 = 625y (v) Find the length of a supporting wire attached to the roadway 18 m from the middle
(a) 3.11 m (b) 6 m (c) 9.11 m (d) none of these
Case Study
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