MCQOPTIONS
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MCQOPTIONS
This section includes 27 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The figure given is made up of a circle and 3 identical semicircles. 0 is the centre of the circle and XY is the diameter of the circle. Given that XY is 28 cm, find the perimeter of the shaded part of the figure. (Use \[\pi =\frac{22}{7}\].) |
| A. | 67 cm |
| B. | 50 cm |
| C. | 80 cm |
| D. | 15 cm |
| Answer» D. 15 cm | |
| 2. |
In the given figure, a circle with centre B overlaps another circle with centre A and a square. The ratio of areas of P and Q is 5 :4 and the area of Q is\[\frac{1}{8}\]the area of circle B. The radii of circle A and circle B are 10 cm and 8 cm respectively. Find the area of the unshaded part of the figure. (Take\[\pi =\text{3}.\text{14}\].) |
| A. | \[\text{449}.\text{75 c}{{\text{m}}^{\text{2}}}\] |
| B. | \[\text{52}0.\text{6}0\text{ c}{{\text{m}}^{\text{2}}}\] |
| C. | \[\text{563}.\text{72 c}{{\text{m}}^{\text{2}}}\] |
| D. | \[\text{45}0.\text{92 c}{{\text{m}}^{\text{2}}}\] |
| Answer» E. | |
| 3. |
In given figure, ABC is a triangle right- angled at B, with AB = 14 cm and BC = 24 cm. With the vertices A, B and C as centres, arcs are drawn each of radius 7 cm. Find the area of the shaded region. [Use \[\pi =\frac{22}{7}\]] |
| A. | \[91\text{ }c{{m}^{2}}\] |
| B. | \[95\,c{{m}^{2}}\] |
| C. | \[97\,c{{m}^{2}}\] |
| D. | \[88\,c{{m}^{2}}~\] |
| Answer» B. \[95\,c{{m}^{2}}\] | |
| 4. |
If the ratio of areas of two circles is 16:25, what is the respective ratio of their circumferences? |
| A. | 1.0527777777778 |
| B. | 5:4 |
| C. | 0.17013888888889 |
| D. | 3:5 |
| Answer» D. 3:5 | |
| 5. |
The areas of two concentric circles are \[962.5\text{ }c{{m}^{2}}\]and \[1386\text{ }c{{m}^{2}}\]respectively. The width of the ring is _____. |
| A. | \[3.4\text{ }cm\] |
| B. | \[3.5\text{ }cm\] |
| C. | \[3.2\text{ }cm\] |
| D. | \[3.1\text{ }cm\] |
| Answer» C. \[3.2\text{ }cm\] | |
| 6. |
If the length of the arc of a circle having a central angle 36° is 22 cm, what is the area of the circle? |
| A. | \[\text{358}0\text{ c}{{\text{m}}^{\text{2}}}\] |
| B. | \[\text{385}0\text{ c}{{\text{m}}^{\text{2}}}\] |
| C. | \[\text{3}0\text{58 c}{{\text{m}}^{\text{2}}}\] |
| D. | \[~\text{38}0\text{5 c}{{\text{m}}^{\text{2}}}\] |
| Answer» C. \[\text{3}0\text{58 c}{{\text{m}}^{\text{2}}}\] | |
| 7. |
The figure shows a right-angled triangle and a semicircle. PQ is the diameter of the semicircle. Find the perimeter of the whole figure. |
| A. | \[13+8\pi \] |
| B. | \[\text{3}0+5\pi \] |
| C. | \[\text{18}+\text{6}\pi \] |
| D. | \[\text{18}+\text{1}0\pi \] |
| Answer» C. \[\text{18}+\text{6}\pi \] | |
| 8. |
A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per\[{{m}^{2}}\]. |
| A. | Rs.31425 |
| B. | Rs. 28260 |
| C. | Rs.352.40 |
| D. | Rs. 282.60 |
| Answer» E. | |
| 9. |
The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of one of the three concentric circles. |
| A. | \[8\sqrt{3}\,cm\] |
| B. | \[2\sqrt{3}\,cm\] |
| C. | \[10\sqrt{3}\,cm\] |
| D. | \[14\sqrt{3}\,cm\] |
| Answer» D. \[14\sqrt{3}\,cm\] | |
| 10. |
Circle \[{{C}_{2}}\] passes through the centre of circle \[{{C}_{1}}\]and is tangential to it. If the area of \[{{C}_{1}}\]is \[4\text{ }c{{m}^{2}},\] then the area of \[{{C}_{2}}\] is _____. |
| A. | \[8\,c{{m}^{2}}\] |
| B. | \[8\,\sqrt{\pi \,}c{{m}^{2}}\] |
| C. | \[16\,c{{m}^{2}}\] |
| D. | \[16\sqrt{\pi }\,c{{m}^{2}}\] |
| Answer» D. \[16\sqrt{\pi }\,c{{m}^{2}}\] | |
| 11. |
If the ratio of circumference of two circles is 4:9, what is the ratio of their respective areas? |
| A. | 0.37777777777778 |
| B. | 16:81 |
| C. | 0.17291666666667 |
| D. | 2:3 |
| Answer» C. 0.17291666666667 | |
| 12. |
When the circumference and area of a circle are numerically equal, find the numerical value of its diameter. |
| A. | \[\frac{\pi }{2}\] |
| B. | 8 |
| C. | \[2\pi \] |
| D. | 4 |
| Answer» E. | |
| 13. |
Four horses are tethered at four corners of a square plot of 42 m so that they just cannot reach one another. The area left ungrazed is: |
| A. | \[378\,{{m}^{2}}\] |
| B. | \[438\,{{m}^{2}}\] |
| C. | \[786\,{{m}^{2}}\] |
| D. | None of these |
| Answer» B. \[438\,{{m}^{2}}\] | |
| 14. |
The minute hand of a wall clock is of length 10.5 cm. What is the area covered by it in 60 minutes? |
| A. | \[346.5\text{ }c{{m}^{2}}\] |
| B. | \[340\text{ }c{{m}^{2}}\] |
| C. | \[355\text{ }c{{m}^{2}}\] |
| D. | \[342\text{ }c{{m}^{2}}\] |
| Answer» B. \[340\text{ }c{{m}^{2}}\] | |
| 15. |
What is the Perimeter of the shaded region? |
| A. | 264 cm |
| B. | 352 cm |
| C. | 500 cm |
| D. | 528 cm |
| Answer» B. 352 cm | |
| 16. |
The area of the circle circumscribing three circles of unit radius touching each other is: |
| A. | \[(\pi /3){{\left( 2+\sqrt{3} \right)}^{2}}\] |
| B. | \[6\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] |
| C. | \[3\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] |
| D. | \[\left( \frac{\pi }{6} \right){{\left( 2+\sqrt{3} \right)}^{2}}\] |
| Answer» B. \[6\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] | |
| 17. |
In Fig, ABC is a right - angle triangle, \[\angle B=90{}^\circ ,AB=28\text{ }cm\] and \[BC=21\text{ }cm\]. With AC as diameter, a semicircle is drawn and with BC as radius, a quarter-circle is drawn. Find the area of the shaded region correct to two decimal places. |
| A. | \[428.75\,c{{m}^{2}}\] |
| B. | \[857.50\,c{{m}^{2}}\] |
| C. | \[214.37\,c{{m}^{2}}\] |
| D. | \[371.56\,c{{m}^{2}}\] |
| Answer» B. \[857.50\,c{{m}^{2}}\] | |
| 18. |
In the adjoining diagram ABCD is a square with side 'a' cm. In the diagram the area of the larger circle with centre 'O' is equal to the sum of the areas of all the rest four circles with equal radii, whose centers are P, Q, R and S. What is the ratio between the diagonal of square and radius of a smaller circle? |
| A. | \[\left( 2\sqrt{2}+3 \right)\] |
| B. | \[\left( 2+3\sqrt{2} \right)\] |
| C. | \[\left( 4+3\sqrt{2} \right)\] |
| D. | can't be determined |
| Answer» C. \[\left( 4+3\sqrt{2} \right)\] | |
| 19. |
Three circles of equal radii touch each other as shown in the figure. The radius of each circle is 1 cm. What is the area of the shaded region? |
| A. | \[\left( \frac{2\sqrt{3}-\pi }{2} \right)c{{m}^{2}}\] |
| B. | \[\left( \frac{3\sqrt{2}-\pi }{3} \right)c{{m}^{2}}\] |
| C. | \[\frac{2\sqrt{3}}{\pi }c{{m}^{2}}\] |
| D. | \[\frac{\sqrt{6}}{2\pi }c{{m}^{2}}\] |
| Answer» B. \[\left( \frac{3\sqrt{2}-\pi }{3} \right)c{{m}^{2}}\] | |
| 20. |
ABCD is a squares, inside of it four circles with radius 1 cm. and touching each other are drawn. What is the area of the shaded region? |
| A. | \[(2\pi -3)c{{m}^{2}}\] |
| B. | \[(4-\pi )c{{m}^{2}}\] |
| C. | \[(16-4\pi )c{{m}^{2}}\] |
| D. | None of these |
| Answer» C. \[(16-4\pi )c{{m}^{2}}\] | |
| 21. |
There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle? |
| A. | \[4\pi \text{ }c{{m}^{2}}\] |
| B. | \[2\pi \text{ }c{{m}^{2}}\] |
| C. | \[\frac{4}{\pi }\text{ }c{{m}^{2}}\] |
| D. | \[\frac{\pi }{4}\text{ }c{{m}^{2}}\] |
| Answer» B. \[2\pi \text{ }c{{m}^{2}}\] | |
| 22. |
In the given figure, ABCD is a square of side 10 cm and a circle is inscribed in it. What is the area of the shaded part? (\[in\text{ }c{{m}^{2}}\]) |
| A. | \[\frac{100-36\pi }{41}\] |
| B. | \[\frac{100-25\pi }{8}\] |
| C. | \[\frac{100+25\pi }{8}\] |
| D. | None of these |
| Answer» C. \[\frac{100+25\pi }{8}\] | |
| 23. |
What is the area of the sector of a circle, whose radius is 6 m and the angle at the centre is\[42{}^\circ \]? |
| A. | \[13.2\text{ }{{m}^{2}}\] |
| B. | \[14.2\text{ }{{m}^{2}}\] |
| C. | \[13.4\text{ }{{m}^{2}}\] |
| D. | \[14.4\text{ }{{m}^{2}}\] |
| Answer» B. \[14.2\text{ }{{m}^{2}}\] | |
| 24. |
An ink pen, with a cylindrical barrel of diameter 2 cm and height 10.5 cm, completely filled with ink, can be used to write 4950 words. How many words can be written using 400 ml of ink? |
| A. | 40000 |
| B. | 60000 |
| C. | 450000 |
| D. | 80000 |
| Answer» C. 450000 | |
| 25. |
What is area of the shaded figure below? |
| A. | \[\frac{\pi }{\sqrt{3}}{{a}^{2}}\] |
| B. | \[\frac{\pi {{a}^{2}}}{16}\] |
| C. | \[\frac{\left( \pi -\sqrt{2} \right)}{4}{{a}^{2}}\] |
| D. | \[\frac{2\sqrt{3}}{\pi }{{a}^{2}}\] |
| Answer» C. \[\frac{\left( \pi -\sqrt{2} \right)}{4}{{a}^{2}}\] | |
| 26. |
Find the area of the shaded region, given that the radius of each circle is equal to 5 cm. |
| A. | \[(400-100\pi )\] |
| B. | \[(360-100\pi )\] |
| C. | \[(231-100\pi )\] |
| D. | \[(400-50\pi )\] |
| Answer» B. \[(360-100\pi )\] | |
| 27. |
A circular garden of radius is 15 m is surrounded by a circular path of width 7 m. If the path is to be covered with tiles at a rate of Rs. 10 per\[{{m}^{2}}\], then what is the total cost of the work? |
| A. | Rs. 8410 |
| B. | Rs. 7140 |
| C. | Rs. 8140 |
| D. | Rs. 7410 |
| Answer» D. Rs. 7410 | |