MCQOPTIONS
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MCQOPTIONS
This section includes 78 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Three points \[A(1,-2)\]\[B(3,4)\] and \[C(4,7)\]form |
| A. | A straight line |
| B. | An equilateral triangle |
| C. | A right-angled triangle |
| D. | None of these |
| Answer» B. An equilateral triangle | |
| 2. |
One set of ordered pair which belongs to a straight line represented by an equation \[y=2x-1\]is____. |
| A. | (1, 1) |
| B. | (2, 1) |
| C. | (1, 2) |
| D. | (3, 1) |
| Answer» B. (2, 1) | |
| 3. |
If \[A(2,2),\,B(4,4)\] and \[C(2,6)\] are the vertices of a triangle ABC and D, E and F are the mid point of AB, BC and AC respectively, then (i) Find the area of MBC. (ii)Find the area of ADEF. (iii) Find the ratio of area of ADEF to MSQ |
| A. | (i) (ii) (iii) 8 sq. units 2 sq. units \[1:4\] |
| B. | (i) (ii) (iii) 6 sq. units 3 sq. units \[1:2\] |
| C. | (i) (ii) (iii) 4 sq. units 1 sq. units \[1:4\] |
| D. | (i) (ii) (iii) 3 sq. units 1 sq. units \[1:3\] |
| Answer» D. (i) (ii) (iii) 3 sq. units 1 sq. units \[1:3\] | |
| 4. |
A well planned locality, has two straight roads perpendicular to each other. There are 5 lanes parallel to Road - I. Each lane has 8 houses as seen in figure. Chaitanya lives in the 6th house of the 5th lane and Hamida lives in the 2nd house of the 2nd lane. What will be the shortest distance between their houses? |
| A. | 10 units |
| B. | 12 units |
| C. | 6 units |
| D. | 5 units |
| Answer» E. | |
| 5. |
Find the coordinates of the point on X-axis which are equidistant from the points \[(-3,4)\] and (2, 5). |
| A. | \[(20,0)\] |
| B. | \[(-23,0)\] |
| C. | \[\left( \frac{4}{7},0 \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 6. |
The coordinates of two points are A(3, 4) and B(-2, 5), then (abscissa of A) - (abscissa of B) is____. |
| A. | 1 |
| B. | -1 |
| C. | 5 |
| D. | -5 |
| Answer» D. -5 | |
| 7. |
What is the perimeter of the triangle PQR shown alongside |
| A. | 11.7 |
| B. | 12.7 |
| C. | 14.7 |
| D. | 13.7 |
| Answer» E. | |
| 8. |
In the given figure, \[\mathbf{P}\left( \mathbf{4},\mathbf{2} \right)\] and \[\mathbf{R}\left( -\mathbf{2},\mathbf{0} \right)\]are vertices of a. rhombus PQRS. What is the equation of diagonal QS? |
| A. | \[x-3y=-2\] |
| B. | \[3x+y=4\] |
| C. | \[3x+y=-4\] |
| D. | \[x-3y\text{=}2\] |
| Answer» C. \[3x+y=-4\] | |
| 9. |
Let the vertices of a triangle ABC be\[\left( \mathbf{7},\mathbf{9} \right),\left( \mathbf{3},-\mathbf{7} \right)\], and (-3,3) then the triangle is |
| A. | Right angled |
| B. | Equilateral |
| C. | Isosceles |
| D. | Bothand |
| Answer» E. | |
| 10. |
For what value of 'x' are A(2,3), B(x, y) and C(4,3) the vertices of a right triangle with right angle at A? |
| A. | 2 |
| B. | 4 |
| C. | 5 |
| D. | 3 |
| Answer» B. 4 | |
| 11. |
The area of rectangles whose vertices are (0,1), (6, 7), \[\left( \text{-2},\text{ 3} \right)\]and (8, 3) is |
| A. | \[10\sqrt{5}\]sq. units |
| B. | \[\sqrt{5}\]sq. units |
| C. | 40 sq. units |
| D. | \[\sqrt{15}\]sq. units |
| Answer» D. \[\sqrt{15}\]sq. units | |
| 12. |
What is the distance of a point \[(0,\,\,-3)\] from the origin? |
| A. | \[0\] units |
| B. | \[-3\] units |
| C. | cannot be determined |
| D. | \[3\] units |
| Answer» E. | |
| 13. |
In the rectangular co-ordinate system above, if the equation of \[{{l}_{1}}\] is y = x and parallel to \[{{l}_{2}}\], the shortest distance between \[{{l}_{1}}\] and \[{{l}_{2}}\]is |
| A. | \[\sqrt{2}\] |
| B. | 1 |
| C. | \[\frac{\sqrt{2}}{2}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 14. |
Which of the following is an equation of the line that contains diagonal AC of square of ABCD shown in the figure? |
| A. | \[y=2x+1\] |
| B. | \[y=x+1\] |
| C. | \[y=\frac{1}{2}x-2\] |
| D. | \[y=x-1\] |
| Answer» E. | |
| 15. |
If points A (2, 0) and B (8, -4) are the end points of diameter AB of circle 0, then area of circle 0 is |
| A. | \[10\,\pi \] |
| B. | \[13\,\pi \] |
| C. | \[24\,\pi \] |
| D. | \[26\,\pi \] |
| Answer» C. \[24\,\pi \] | |
| 16. |
The area of a triangle whose vertices are (-4, 0), (2, 4) and (4, 0) is |
| A. | 8 |
| B. | 12 |
| C. | 16 |
| D. | 32 |
| Answer» D. 32 | |
| 17. |
In the given figure, which of the following points lies within the circle? |
| A. | (3.5, 9.5) |
| B. | \[(-7,7)\] |
| C. | (-10,1) |
| D. | \[(-10,1)\] |
| Answer» C. (-10,1) | |
| 18. |
In the given figure, if AB is a diameter of circle P then perimeter of the shaded region is |
| A. | \[4\pi +8\] |
| B. | \[8\pi +4\] |
| C. | \[8\pi +8\] |
| D. | \[16\pi +4\] |
| Answer» B. \[8\pi +4\] | |
| 19. |
What is the value of 'x' if (4, 3) and\[(x,5)\] are points on the circumference of a circle with centre O (2, 3)? |
| A. | 4 |
| B. | 2 |
| C. | 0 |
| D. | -2 |
| Answer» C. 0 | |
| 20. |
In the given figure co-ordinates of the midpoint of AB are |
| A. | (0, 2) |
| B. | (0,3) |
| C. | (1' 2) |
| D. | (3, 1) |
| Answer» E. | |
| 21. |
If the distance between the points (k, - 1) and (3, 2) is 5, then the value of k is |
| A. | 2 |
| B. | -2 |
| C. | -1 |
| D. | 1 |
| Answer» D. 1 | |
| 22. |
If A = (-3,4) and B = (2,1). what are the coordinates of the point C on AB produced such that AC = 2BC? |
| A. | (2, 4) |
| B. | (3, 7) |
| C. | (7,-2) |
| D. | (3, -2) |
| Answer» D. (3, -2) | |
| 23. |
The coordinates of the vertices of a rectangle are (0, 0), (4, 0), (4, 3) and (0, 3). The length of its diagonal is |
| A. | 4 |
| B. | 5 |
| C. | 7 |
| D. | 3 |
| Answer» C. 7 | |
| 24. |
The mid-point of the line segment AB is shown in the figure is (4, - 3). Then the co-ordinates of A and B are |
| A. | (8, 0) and (0, - 6) |
| B. | (0, 8) and (0, - 6) |
| C. | (8, 0) and (-6, 0) |
| D. | None of these |
| Answer» B. (0, 8) and (0, - 6) | |
| 25. |
Reshma moves \[5\] units right and then \[3\] units downwards. She then moves \[4\] units to the left, finally stops at a point represented by \[(-2,\,\,-2)\] on the cartesian plane. What was her starting point on the plane? |
| A. | \[(-3,\,\,1)\] |
| B. | \[(0,\,\,0)\] |
| C. | \[(2,\,\,-1)\] |
| D. | \[(-5,\,\,-3)\] |
| Answer» B. \[(0,\,\,0)\] | |
| 26. |
If the area of the triangle given in the figure is 20, what are the coordinates of the point C? |
| A. | \[\left( 0,\frac{40}{a} \right)\] |
| B. | \[({{a}^{2}}+{{b}^{2}},0)\] |
| C. | \[\left( \frac{20}{b},0 \right)\] |
| D. | \[\left( \frac{40}{b},0 \right)\] |
| Answer» E. | |
| 27. |
The point which is equal-distant from the points (0, 0), (0, 8) and (4, 6) is |
| A. | \[\left( \frac{1}{2},-4 \right)\] |
| B. | \[\left( -\frac{1}{2},4 \right)\] |
| C. | \[\left( \frac{1}{2},4 \right)\] |
| D. | \[\left( -\frac{1}{2},-4 \right)\] |
| Answer» D. \[\left( -\frac{1}{2},-4 \right)\] | |
| 28. |
In the given figure Area of \[\Delta \mathbf{ABC}\] |
| A. | 3 unit |
| B. | \[4\frac{1}{2}\]unit |
| C. | \[1\frac{1}{2}\] unit |
| D. | 1 unit |
| Answer» D. 1 unit | |
| 29. |
In the adjoining figure, what is the area of \[\Delta \mathbf{ABC}\]? |
| A. | 24 |
| B. | 12 |
| C. | 30 |
| D. | 3 |
| Answer» D. 3 | |
| 30. |
In the given figure below, Area of \[\Delta \mathbf{AOB}=\] |
| A. | 4 |
| B. | 12 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 31. |
If (2, 1), (4, 5), (-1, - 3) are the mid points of the sides of a triangle, then the co-ordinates of its vertices are |
| A. | \[\left( -\text{3},-\text{7} \right),\text{ }\left( \text{17},\text{ 9} \right),\text{ }\left( \text{1},\text{1} \right)\] |
| B. | \[\left( -\text{3}.\text{ 7} \right),\text{ }\left( \text{7},\text{ 9} \right),\text{ }\left( -\text{ 1},\text{ 1} \right)\] |
| C. | \[\left( -\text{3},-\text{7} \right),\text{ }\left( \text{7},\text{ 9} \right),\text{ }\left( \text{1},\text{1} \right)\] |
| D. | none |
| Answer» D. none | |
| 32. |
Find the area of the quadrilateral the coordinates of whose angular points taken in order are (-1, 6), (-3, -9), (5, -8) and (3, 9). |
| A. | 48 |
| B. | 96 |
| C. | 192 |
| D. | 72 |
| Answer» C. 192 | |
| 33. |
The points (p - 1, p + 2), (p, p +1), (p + 1, p), are collinear for |
| A. | \[p=0\] |
| B. | \[p=1\] |
| C. | \[p=1/2\] |
| D. | Any value of p |
| Answer» E. | |
| 34. |
The area of the triangle with vertices at \[(a,b+c,)\text{ (}b,c+a)\] and \[(c,a+b)\] is |
| A. | \[0\] |
| B. | \[a+b+c\] |
| C. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] |
| D. | \[1\] |
| Answer» B. \[a+b+c\] | |
| 35. |
Find the distance between the points\[(\sqrt{3}+1,\sqrt{2}-1)\]and\[(\sqrt{3}-1,\sqrt{2}+1)\]. |
| A. | \[\sqrt{3}\] |
| B. | \[2\sqrt{3}\] |
| C. | \[\sqrt{2}\] |
| D. | \[2\sqrt{2}\] |
| Answer» E. | |
| 36. |
The co-ordinates of a point R which divides the line joining A(-3, 3) and B(2, - 7) internally in the ratio 2 : 3 are |
| A. | (1,1) |
| B. | (-1,-1) |
| C. | (2,-2) |
| D. | (3,3) |
| Answer» C. (2,-2) | |
| 37. |
What is the ordinate of a point on the \[y\text{-}\]axis? |
| A. | A positive number |
| B. | A negative number |
| C. | \[0\] |
| D. | All the above |
| Answer» E. | |
| 38. |
If the coordinates of opposite vertices of a square are (1, 3) and (6, 0), the length of a side a square is |
| A. | \[\sqrt{34}\] |
| B. | \[\sqrt{17}\] |
| C. | 17 |
| D. | 12 |
| Answer» C. 17 | |
| 39. |
What is the distance of the point \[(3,\,\,2)\] from the \[Y-\]axis? |
| A. | \[2\] units |
| B. | \[3\] units |
| C. | \[5\] units |
| D. | \[6\] units |
| Answer» C. \[5\] units | |
| 40. |
The equation of the straight line which is perpendicular to \[7x-8y=6\] is |
| A. | \[8x\text{ }+\text{ 7y }=\text{ 3}\] |
| B. | \[7x+8\text{y}=\text{3}\] |
| C. | \[8x-\text{7y}=\text{3}\] |
| D. | \[7x-8\text{y}=\text{3}\] |
| Answer» D. \[7x-8\text{y}=\text{3}\] | |
| 41. |
Find the third vertex of an equilateral triangle whose two vertices are (2, 4) and (2, 6). |
| A. | \[(\sqrt{3},5)\] |
| B. | \[(2\sqrt{3},5)\] |
| C. | \[(2+\sqrt{3},5)\] |
| D. | (2,5) |
| Answer» D. (2,5) | |
| 42. |
Determine the ratio in which \[y-x+2=0\] divides the line joining (3, - 1) and (8, 9): |
| A. | \[3:5\] |
| B. | \[4:3\] |
| C. | \[2:3\] |
| D. | \[2:5\] |
| Answer» D. \[2:5\] | |
| 43. |
Find (x, y) if (3, 2), (6, 3), (x, y) and (6, 5) are the vertices of a parallelogram: |
| A. | (5, 6) |
| B. | (6, 5) |
| C. | (9, 6) |
| D. | (9, 5) |
| Answer» D. (9, 5) | |
| 44. |
If the coordinates of the midpoint of the sides of a triangle are (1, 2), (0, - 1) and (2, - 1). Find the coordinates of its vertices: |
| A. | (1, - 4), (3, 2), (-1, 2) |
| B. | (1, 2), (2, 3), (3, - 4) |
| C. | (3, 4), (5, 2), (1, 2) |
| D. | (3, 2), (-1, 2), (1, - 4) |
| Answer» E. | |
| 45. |
What is the centroid of \[\Delta \mathbf{ABC}\] whose vertices, are \[\mathbf{A}\left( \mathbf{2},-\mathbf{4} \right),\] \[\mathbf{B}\left( -\mathbf{4},-\mathbf{2} \right)\] and \[\mathbf{C}\left( -1,\text{ }\mathbf{3} \right).\] |
| A. | \[\left( -1,-1 \right)\] |
| B. | \[\left( -2,-2 \right)\] |
| C. | \[\left( 3,\text{ }4 \right)\] |
| D. | \[\left( 4,\text{ }4 \right)\] |
| Answer» B. \[\left( -2,-2 \right)\] | |
| 46. |
What is the area of the triangle formed by the mid-points of the sides of\[\Delta \mathbf{ABC}\]. With coordinate A (3, 2), B(-5, 6) and C (8,3). |
| A. | 7 sq. units |
| B. | 14 sq. units |
| C. | 2.5 sq. units |
| D. | 5 sq. units |
| Answer» C. 2.5 sq. units | |
| 47. |
Find the fourth vertex of the rhombus formed by \[\left( -\mathbf{1},-\mathbf{1} \right),\left( \mathbf{6},\mathbf{1} \right)\] and (8, 8). |
| A. | (3, 4) |
| B. | (2, 5) |
| C. | (2, 3) |
| D. | (1, 6) |
| Answer» E. | |
| 48. |
Find the perimeter of a triangle formed by (0, 0), (1, 0) and (0, 1). |
| A. | \[1\pm \sqrt{2}\] |
| B. | \[\sqrt{2}+1\] |
| C. | 3 |
| D. | \[2+\sqrt{2}\] |
| Answer» E. | |
| 49. |
The slope of the line joining the points (-8, - 3) and (8, 3) is |
| A. | \[\frac{8}{3}\] |
| B. | \[\frac{3}{8}\] |
| C. | 0 |
| D. | -1 |
| Answer» C. 0 | |
| 50. |
The perpendicular distance of a point from the \[x\text{-}\]axis is \[2\] units and its perpendicular distance from the \[y\text{-}\]axis is \[3\] units. Find the co-ordinates of the point if it lies in the III Quadrant. |
| A. | \[(-3,\,\,-2)\] |
| B. | \[(-2,\,\,-3)\] |
| C. | \[(3,\,\,-2)\] |
| D. | \[(-3,\,\,2)\] |
| Answer» B. \[(-2,\,\,-3)\] | |