MCQOPTIONS
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MCQOPTIONS
This section includes 564 Mcqs, each offering curated multiple-choice questions to sharpen your Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 301. |
For a triangle circumcentre lies on one of its sides. The triangleis |
| A. | right angled |
| B. | obtused angled |
| C. | isosceles |
| D. | equilatera |
| Answer» B. obtused angled | |
| 302. |
A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of 65 at any point C on the circumference of the circle. If P is the point of intersection of the two lines, then the measure of APO is |
| A. | 25 |
| B. | 65 |
| C. | 90 |
| D. | 40 |
| Answer» B. 65 | |
| 303. |
Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is |
| A. | 5 cm |
| B. | 7.35 cm |
| C. | 6 cm |
| D. | 4 cm |
| Answer» C. 6 cm | |
| 304. |
Two circles of same radius 5 cm, intersect each other at A and B. If AB = 8 cm, then the distance between the centre is : |
| A. | 6 cm |
| B. | 8 cm |
| C. | 10 cm |
| D. | 4 cm |
| Answer» B. 8 cm | |
| 305. |
Two circles with centre P and Q intersect at B and C. A, D are points on the circle such that A, C, D are collinear. If APB = 130 , and BQD = x , then the value of x is |
| A. | 65 |
| B. | 130 |
| C. | 195 |
| D. | 135 |
| Answer» C. 195 | |
| 306. |
Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is |
| A. | PT = 2PQ |
| B. | PT < PQ |
| C. | PT > PQ |
| D. | PT = PQ |
| Answer» E. | |
| 307. |
In the given figure, find the length of BD. |
| A. | 13.5 cm |
| B. | 12 cm |
| C. | 14.5 cm |
| D. | 15 cm |
| E. | None of these |
| Answer» B. 12 cm | |
| 308. |
AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17 cm. The length of AB and CD are 10 cm and 24 cm respectively. The radius (in cm) of the circle is : |
| A. | 13 |
| B. | 9 |
| C. | 18 |
| D. | 15 |
| Answer» B. 9 | |
| 309. |
A, B and C are the three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90 and 110 respectively. BAC is equal to |
| A. | 70 |
| B. | 80 |
| C. | 90 |
| D. | 100 |
| Answer» C. 90 | |
| 310. |
Two circles touch each other externally. The distance between their centre is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle is |
| A. | 3.5 cm |
| B. | 3 cm |
| C. | 4 cm |
| D. | 2 cm |
| Answer» C. 4 cm | |
| 311. |
A square ABCD is inscribed in a circle of unit radius. Semicircles are described on each side as a diameter. The area of the region bounded by the four semicircles and the circle is |
| A. | 1 sq. unit |
| B. | 2 sq. unit |
| C. | 1.5 sq. unit |
| D. | 2.5 sq. unit |
| Answer» C. 1.5 sq. unit | |
| 312. |
In a circle of radius 17 cm, two parallel chords of length 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is |
| A. | 9 cm |
| B. | 7 cm |
| C. | 23 cm |
| D. | 11 cm |
| Answer» C. 23 cm | |
| 313. |
A chord 12 cm long is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is |
| A. | 8 cm |
| B. | 6 cm |
| C. | 10 cm |
| D. | 16 cm |
| Answer» B. 6 cm | |
| 314. |
If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is |
| A. | 6 cm |
| B. | 7 cm |
| C. | 10 cm |
| D. | 8 cm |
| Answer» E. | |
| 315. |
A, B, C, D are four points on a circle. AC and BD intersect at a point E such that BEC = 130 and ECD = 20 . BAC is |
| A. | 120 |
| B. | 90 |
| C. | 100 |
| D. | 110 |
| Answer» E. | |
| 316. |
Two circles intersect each other at the points A and B, A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is |
| A. | 1.50 cm |
| B. | 2.25 cm |
| C. | 4.50 cm |
| D. | 9.00 cm |
| Answer» D. 9.00 cm | |
| 317. |
Chords AC and BD of a circle with centre O intersect at right angles at E. If OAB = 25 , then the value of EBC is |
| A. | 30 |
| B. | 25 |
| C. | 20 |
| D. | 15 |
| Answer» C. 20 | |
| 318. |
Chords PQ and RS of a circle, when produced, meet at a point O. If PQ = 6 cm, OQ = 8 cm and OS = 7 cm, then length (in cm) of the chord RS is |
| A. | 10 |
| B. | 12 |
| C. | 16 |
| D. | 9 |
| Answer» E. | |
| 319. |
Let O be the centre of a circle. A, B, C and D are four points on the circumference of the circle in the given order, such that AOC = 130 . Then the measure of ABC and ADC are respectively. |
| A. | 65 , 115 |
| B. | 65 , 65 |
| C. | 115 , 65 |
| D. | 115 , 115 |
| Answer» C. 115 , 65 | |
| 320. |
The length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm is : |
| A. | 18 cm. |
| B. | 24 cm. |
| C. | 25 cm. |
| D. | 30 cm. |
| Answer» C. 25 cm. | |
| 321. |
Two chords AB and CD of a circle with centre O intersect at P. If APC = 40 . Then the value of AOC + BOD is |
| A. | 50 |
| B. | 60 |
| C. | 80 |
| D. | 120 |
| Answer» D. 120 | |
| 322. |
In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of APB is |
| A. | 30 |
| B. | 45 |
| C. | 60 |
| D. | 90 |
| Answer» D. 90 | |
| 323. |
Points P, Q and R are on a circle such that PQR = 40 and QRP = 60 . Then the subtended angle by arc QR at the centre is : |
| A. | 80 |
| B. | 120 |
| C. | 140 |
| D. | 160 |
| Answer» E. | |
| 324. |
Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle will be |
| A. | 3 cm. |
| B. | 4 cm. |
| C. | 5.5 cm. |
| D. | 3.5 cm. |
| Answer» B. 4 cm. | |
| 325. |
The distance between the centre of two equal circles, each of radius 3 cm, is 10 cm. The length of a transverse common tangent is |
| A. | 8 cm |
| B. | 10 cm |
| C. | 4 cm |
| D. | 6 cm |
| Answer» B. 10 cm | |
| 326. |
A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is : |
| A. | 10 cm. |
| B. | 12 cm. |
| C. | 16 cm. |
| D. | 20 cm. |
| Answer» E. | |
| 327. |
In a circle, two arcs of unequal length subtend angles in the ratio 5 : 3. If the smaller angle is 45 then the measure of other angle in degrees is : |
| A. | 75 |
| B. | 72 |
| C. | 60 |
| D. | 78 |
| Answer» B. 72 | |
| 328. |
A chord of length 39 cm is at a distance of 10.4 cm from the centre of a circle. Find the radius of the circle. |
| A. | 19.5 cm. (appr.) |
| B. | 22.1 cm.(appr.) |
| C. | 28.6 cm. (appr.) |
| D. | 21 cm. (appr.) |
| Answer» C. 28.6 cm. (appr.) | |
| 329. |
Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are point of contact and PAB = 35 . Then ABP is |
| A. | 35 |
| B. | 55 |
| C. | 65 |
| D. | 75 |
| Answer» C. 65 | |
| 330. |
PR is tangent to a circle, with centre O and radius 4 cm, at point Q. If POR = 90 ,OR = 5 cm and OP = 20/3 cm, then (in cm) the length of PR is : |
| A. | 3 |
| B. | 16 3 |
| C. | 23 3 |
| D. | 25 3 |
| Answer» E. | |
| 331. |
Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is : |
| A. | 7.5 cm |
| B. | 9 cm |
| C. | 8 cm |
| D. | 10 cm |
| Answer» C. 8 cm | |
| 332. |
AB is a chord of a circle with 0 as centre. C is a point on the circle such that OC AB and OC intersects AB at P. If PC = 2 cm and AB = 6 cm then the diameter of the circle is |
| A. | 6 cm |
| B. | 6.5 cm |
| C. | 13 cm |
| D. | 12 cm |
| Answer» C. 13 cm | |
| 333. |
Two parallel chords of lengths 40 cm and 48 cm are drawn in a circle of radius 25 cm. What will be the distance between the two chords ? |
| A. | 8 cm |
| B. | 15 cm |
| C. | 22 cm |
| D. | Either 8 cm or 22 cm |
| Answer» E. | |
| 334. |
P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If PSQ = 20 , then PRQ = ? |
| A. | 80 |
| B. | 200 |
| C. | 160 |
| D. | 100 |
| Answer» E. | |
| 335. |
The perpendicular from the centre of a circle to a chord is 16 cm. If the diameter of the circle is 40 cm, what is the length of the chord ? |
| A. | 12 cm |
| B. | 16 cm |
| C. | 24 cm |
| D. | 30 cm |
| Answer» D. 30 cm | |
| 336. |
In, ABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ADE and ABC. |
| A. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| B. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td></tr><tr><td style="text-align: center;">4</td></tr></table> |
| C. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">3</td></tr><tr><td style="text-align: center;">4</td></tr></table> |
| D. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td></tr><tr><td style="text-align: center;">8</td></tr></table> |
| E. | None of these |
| Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">3</td></tr><tr><td style="text-align: center;">4</td></tr></table> | |
| 337. |
Two chords AB and PQ of a circle intersect at D inside a circle. If AD = 4 cm., DB = 6 cm., QD = 3 cm., the length of PQ is equal to |
| A. | 11 cm. |
| B. | 8 cm. |
| C. | 9 cm. |
| D. | 10 cm. |
| Answer» B. 8 cm. | |
| 338. |
If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle (in cm) is : |
| A. | 15 |
| B. | 16 |
| C. | 17 |
| D. | 34 |
| Answer» D. 34 | |
| 339. |
Two circles touch each other internally. The greater circle has its radius as 6 cm and the distance between the centres of the circles is 2 cm. The radius of the other circle is |
| A. | 3 cm. |
| B. | 4 cm. |
| C. | 2 cm. |
| D. | 5 cm. |
| Answer» C. 2 cm. | |
| 340. |
Number of circles that can be drawn through three non-collinear points is : |
| A. | exactly one |
| B. | two |
| C. | three |
| D. | more than three |
| Answer» B. two | |
| 341. |
The tangents at two points A and B on the circle with centre O intersects at P ; If in quadrilateral PAOB, AOB: APB = 5 : 1, then measure of APB is : |
| A. | 30 |
| B. | 60 |
| C. | 45 |
| D. | 15 |
| Answer» B. 60 | |
| 342. |
AB is a chord to a circle and PAT is the tangent to the circle at A. If BAT = 75 and BAC = 45 , C being a point on the circle, then ABC is equal to |
| A. | 40 |
| B. | 45 |
| C. | 60 |
| D. | 70 |
| Answer» D. 70 | |
| 343. |
The tangents are drawn at the extremities of diameter AB of a circle with centre P. If a tangent to the circle at the point C intersects the other two tangents at Q and R, then the measure of the QPR is |
| A. | 45 |
| B. | 60 |
| C. | 90 |
| D. | 180 |
| Answer» D. 180 | |
| 344. |
If a chord of a circle of radius 5 cm is a tangent to another circle of radius 3 cm, both the circles being concentric, then the length of the chord is |
| A. | 10 cm |
| B. | 12.5 cm |
| C. | 8 cm |
| D. | 7 cm |
| Answer» D. 7 cm | |
| 345. |
Two circles touch each other externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then PAQ = |
| A. | 45 |
| B. | 90 |
| C. | 80 |
| D. | 100 |
| Answer» C. 80 | |
| 346. |
The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is |
| A. | 10 cm. |
| B. | 5 cm. |
| C. | 6 cm. |
| D. | 12 cm |
| Answer» B. 5 cm. | |
| 347. |
In a circle with centre at O (0, 0) and radius 5 cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is: |
| A. | 2.5 cm. |
| B. | 3 cm. |
| C. | 4 cm. |
| D. | 1 cm. |
| Answer» C. 4 cm. | |
| 348. |
AB is the diameter of a circle with centre O. P be a point on it. If POA = 120 . Then, PBO = ? |
| A. | 60 |
| B. | 120 |
| C. | 45 |
| D. | 50 |
| Answer» B. 120 | |
| 349. |
AB is the diameter of a circle with centre O and P is a point on its circumference. If POA = 120 , then the value of PBO is : |
| A. | 30 |
| B. | 60 |
| C. | 50 |
| D. | 40 |
| Answer» C. 50 | |
| 350. |
An arc of 30 in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |