MCQOPTIONS
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MCQOPTIONS
This section includes 1274 Mcqs, each offering curated multiple-choice questions to sharpen your SRMJEEE knowledge and support exam preparation. Choose a topic below to get started.
| 451. |
In a ΔABC, the bisectors of ∠B and ∠C meet at O. If ∠BOC = 142°, then the measure of ∠A is: |
| A. | 52° |
| B. | 68° |
| C. | 116° |
| D. | 104° |
| Answer» E. | |
| 452. |
In a circle with centre O, an arc ABC subtends an angle of 132° at the center of the circle. Chord AB is produced to point P. Then ∠CBP is equal to∶ |
| A. | 76° |
| B. | 68° |
| C. | 66° |
| D. | 48° |
| Answer» D. 48° | |
| 453. |
An equilateral triangle has sides of 10 cm each. Find the ratio of in-radius to the circum-radius of the triangle. |
| A. | 1 : 1 |
| B. | 1 : 2 |
| C. | 2 : 1 |
| D. | 1 : 3 |
| Answer» C. 2 : 1 | |
| 454. |
In the figure given below, XA and XB are two tangents to a circle. If ∠AXB = 50° and AC is parallel to XB, then what is ∠ ACB equal to? |
| A. | 70° |
| B. | 65° |
| C. | 60° |
| D. | 55° |
| Answer» C. 60° | |
| 455. |
ΔABC ~ ΔDEF and their perimeters are 64 cm and 48 cm respectively. What is the length AB, if DE is equal to 9 cm? |
| A. | 16 cm |
| B. | 12 cm |
| C. | 17.5 cm |
| D. | 18 cm |
| Answer» C. 17.5 cm | |
| 456. |
In ΔABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of BD is |
| A. | 8 cm |
| B. | 9.6 cm |
| C. | 7.5 cm |
| D. | 9 cm |
| Answer» B. 9.6 cm | |
| 457. |
In the given figure, ΔPQR is a right angled triangle at Q. If PQ = 35 cm and QS = 28 cm and a semicircle passes from the point QRS, then what is the value (in cm) of SR? |
| A. | 35.33 |
| B. | 37.33 |
| C. | 41.33 |
| D. | 43.33 |
| Answer» C. 41.33 | |
| 458. |
In ΔABD, C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ? |
| A. | 2√10 cm |
| B. | √10 cm |
| C. | √41 cm |
| D. | 2√41 cm |
| Answer» E. | |
| 459. |
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Find the length of PQ. |
| A. | 12 cm |
| B. | 13 cm |
| C. | 8.5 cm |
| D. | √119 cm |
| Answer» E. | |
| 460. |
In a circle of radius 13 cm, a chord is at a distance of 5 cm from its centre. What is the length of chord? |
| A. | 12 cm |
| B. | 20 cm |
| C. | 24 cm |
| D. | 18 cm |
| Answer» D. 18 cm | |
| 461. |
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 148°. ∠BAC is equal to: |
| A. | 60° |
| B. | 58° |
| C. | 40° |
| D. | 150° |
| Answer» C. 40° | |
| 462. |
In an isosceles triangle ABC, AB = AC and D is the mid point of BC. Which of the following relations is always true? |
| A. | AB > AD |
| B. | AB < AD |
| C. | AB = AD |
| D. | AB = 2AD |
| Answer» B. AB < AD | |
| 463. |
In ΔPQR, ∠PQR = 90°, PQ = 5 cm and QR = 12. What is the radius (in cm) of the circum circle of ΔPQR? |
| A. | 6.5 |
| B. | 7.5 |
| C. | 13 |
| D. | 15 |
| Answer» B. 7.5 | |
| 464. |
If S is the midpoint of a straight line PQ and R is a point different from S, such that PR = RQ, then |
| A. | ∠PRS = 90° |
| B. | ∠QRS = 90° |
| C. | ∠PSR = 90° |
| D. | ∠QSR > 90° |
| Answer» D. ∠QSR > 90° | |
| 465. |
In a triangle ABC, the side BC is extended upto D. if ∠ACD = 120° and ∠B = \(\frac{2}{3}\) ∠A, then ∠BAC is |
| A. | 72° |
| B. | 105° |
| C. | 70° |
| D. | 100° |
| Answer» B. 105° | |
| 466. |
PA and PB are two tangents to a circle with center O, from a point P outside the circle. A and B are points on the circle. If ∠APB = 86°, then ∠OAB is equal to: |
| A. | 43° |
| B. | 45° |
| C. | 50° |
| D. | 20° |
| Answer» B. 45° | |
| 467. |
A and S are two points on a circle with centre O. AT is a tangent, such that ∠SAT = 45°. N is a point on OA, such that SN = 10 cm. The length of the median OM of ΔSON is: |
| A. | 53 cm |
| B. | 5 cm |
| C. | 102 cm |
| D. | 52 cm |
| Answer» C. 102 cm | |
| 468. |
In the given figure, ABCD is a rectangle and P is a point on DC such that BC = 24 cm, DP = 10 cm, and CD = 15 cm. If AP produced intersects BC produced at Q, then find the length of AQ. |
| A. | 26 cm |
| B. | 39 cm |
| C. | 35 cm |
| D. | 24 cm |
| Answer» C. 35 cm | |
| 469. |
In a circle of radius 17 cm, a chord is at a distance of 8 cm from the centre of the circle. What is the length of the chord? |
| A. | 20 cm |
| B. | 25 cm |
| C. | 15 cm |
| D. | 30 cm |
| Answer» E. | |
| 470. |
A regular hexagon of side 6 cm is inscribed in a circle. The area (in cm2) of the region in the circle that is outside the hexagon is closest to (use π = 3.14)∶ |
| A. | 18.5 |
| B. | 19.4 |
| C. | 19.5 |
| D. | 20.4 |
| Answer» D. 20.4 | |
| 471. |
If the interior angle of five-sided polygon are in the ratio 1 : 2 : 3 : 4 : 5 then sum (in degrees) of measure of smaller and largest angles, is: |
| A. | 240 |
| B. | 252 |
| C. | 108 |
| D. | 324 |
| Answer» B. 252 | |
| 472. |
In the given figure, O is the center of the circle, OQ is perpendicular to RS and ∠SRT = 30°. If RS = 10√2, then what is the of PR2? |
| A. | 200 (1 + √3) |
| B. | 300 (2 + √3) |
| C. | 200 (2 + √3) |
| D. | 100 (3 + 2√3) |
| Answer» D. 100 (3 + 2√3) | |
| 473. |
A line cuts two concentric circles. The length of the chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in cm2) in squares of radii of two circles? |
| A. | 240 |
| B. | 120 |
| C. | 60 |
| D. | 90 |
| Answer» D. 90 | |
| 474. |
At what point does the line 2x + 5y = -6 cuts the X - axis? |
| A. | (3, 0) |
| B. | (0, 3) |
| C. | (-3, 0) |
| D. | (0, -3) |
| Answer» D. (0, -3) | |
| 475. |
Circumcentre of ΔABC is O. If ∠BAC = 75° and ∠BCA = 80°, then what is the value (in degrees) of ∠OAC? |
| A. | 45 |
| B. | 65 |
| C. | 90 |
| D. | 95 |
| Answer» C. 90 | |
| 476. |
In ΔABC with sides 6 cm, 7 cm and 8 cm, the angle bisector of the largest angle divides the opposite side into two segments. What is the length of the shorter segment? |
| A. | 56/13 cm |
| B. | 48/13 cm |
| C. | 21/5 cm |
| D. | 24/5 cm |
| Answer» C. 21/5 cm | |
| 477. |
Consider a circle with centre at O and radius 7 cm. Let QR be the chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct?(1) ∠QPD = 135°(2) If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0(3) The ratio of triangle OPR to the area of triangle OMP is 1 ∶ 2√2Select the correct answer using the code given below. |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» B. 2 and 3 only | |
| 478. |
Consider a trapezium ABCD, in which AB is parallel to CD and AD is perpendicular to AB. If the trapezium has an incircle which touches AB at E, CD at F and BC at P, where EB = 25 cm and FC = 16 cm, then what is the diameter of the circle? |
| A. | 16 cm |
| B. | 25 cm |
| C. | 36 cm |
| D. | 40 cm |
| Answer» E. | |
| 479. |
Find the distance between the following pairs of points:(2, 3); (4, 1) in units of length. |
| A. | 2√2 |
| B. | 2√3 |
| C. | 2 |
| D. | 2√5 |
| Answer» B. 2√3 | |
| 480. |
Consider the following inequalities in respect of any triangle ABC:1. AC - AB < BC2. BC - AC < AB3. AB - BC < ACWhich of the above are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 481. |
A person goes to a market between 4 p.m. and 5 p.m. When he comes back he finds that the hour hand and the minute hand of the clock have interchanged their positions. For how much time (approximately) was he out of his house? |
| A. | 55.38 minutes |
| B. | 55.48 minutes |
| C. | 55.57 minutes |
| D. | 55.67 minutes |
| Answer» B. 55.48 minutes | |
| 482. |
In the given figure, triangle ABC is drawn such that AB is tangent to a circle at A whose radius is 10cm and BC passes through centre of the circle. Point C lies on the circle. If BC = 36cm and AB = 24cm, then what is the area (in cm2) of triangle ABC? |
| A. | 134.5 |
| B. | 148 |
| C. | 166.15 |
| D. | 180 |
| Answer» D. 180 | |
| 483. |
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 110° then ∠POA is: |
| A. | 50° |
| B. | 70° |
| C. | 35° |
| D. | 45° |
| Answer» D. 45° | |
| 484. |
ΔPQR is such that PR = 7.5 cm and ΔPQR is similar to ΔXYZ. If XY = 18 and YZ = 12 cm, then find the ratio of PQ ∶ QR. |
| A. | 1 ∶ 2 |
| B. | 3 ∶ 2 |
| C. | 4 ∶ 5 |
| D. | 5 ∶ 2 |
| Answer» C. 4 ∶ 5 | |
| 485. |
In ΔABC, ∠A = 52° and O is the orthocentre of the triangle (BO and CO meet AC and AB at E and F respectively when produced). If the bisectors of ∠OBC and ∠OCB meet at P, then the measure of ∠ BPC is∶ |
| A. | 138° |
| B. | 132° |
| C. | 154° |
| D. | 124° |
| Answer» D. 124° | |
| 486. |
In the given figure, radius of a circle is 14√2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are four identical squares. What is the total area (in cm2) of all the small squares? |
| A. | 31.36 |
| B. | 125.44 |
| C. | 62.72 |
| D. | 156.8 |
| Answer» C. 62.72 | |
| 487. |
If ΔABC ≅ ΔXYZ and ∠BAC = 55°, then ∠ZXY = ? |
| A. | 67.5° |
| B. | 55° |
| C. | 135° |
| D. | 65° |
| Answer» C. 135° | |
| 488. |
Let ABC be a right-angle triangle with BC = 5 cm and AC = 12 cm. Let D be a point on the hypotenuse AB such that ∠BCD = 30°. What is length of CD? |
| A. | 60/13 cm |
| B. | 17/2 cm |
| C. | \(\frac{{120}}{{5\; + \;12\sqrt 2 }}\) cm |
| D. | \(\frac{{120}}{{5\; + \;12\sqrt 3 }}\) cm |
| Answer» E. | |
| 489. |
If each of the two equal angles of an isosceles triangle is twice the third angle, the measure of the third angle is - |
| A. | 45° |
| B. | 90° |
| C. | 36° |
| D. | 72° |
| Answer» D. 72° | |
| 490. |
In the given figure, TB is a chord which passes through the centre of the circle. PT is a tangent to the circle at the point T on the circle. If PT = 10 cm, PA = 5 cm and AB = x cm, then the radius of the circle is: |
| A. | \(5\sqrt{3} \) cm |
| B. | \(6\sqrt{3} \) cm |
| C. | \(3\sqrt{3} \) cm |
| D. | \(10 \sqrt{3}\) cm |
| Answer» B. \(6\sqrt{3} \) cm | |
| 491. |
Find the point on the x-axis that is equidistant from points (1, -4) and (2, 6) |
| A. | (13.1, 0) |
| B. | (11.5, 0) |
| C. | (12, 0) |
| D. | (32.3, 0) |
| Answer» C. (12, 0) | |
| 492. |
A, B, C and D are points on the circle. The diameter AC and BD on E intersect each other inside the circle. The AB and CD lines are drawn. ∠BAE = 37° and ∠ACD = 83°, what is the measure of ∠BEC? |
| A. | 120° |
| B. | 140° |
| C. | 130° |
| D. | 110° |
| Answer» B. 140° | |
| 493. |
AB and CD are two parallel chords of a circle such that AB = 6 cm and CD = 2AB. Both chords are on the same side of the centre of the circle. If the distance between them is equal to one-fourth of the length of CD, then the radius of the circle is∶ |
| A. | 5√3 cm |
| B. | 4√3 cm |
| C. | 3√5 cm |
| D. | 4√5 cm |
| Answer» D. 4√5 cm | |
| 494. |
If the length of the side of a rhombus is equal to the length of its smaller diagonal, then what is the measure of its angle of larger magnitude? |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 120° |
| Answer» B. 45° | |
| 495. |
Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is |
| A. | 2√3 cm |
| B. | 8/√3 cm |
| C. | 8√3 cm |
| D. | 4√3 cm |
| Answer» C. 8√3 cm | |
| 496. |
In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.Consider the following statements:1. Triangle ADC is an isosceles triangle.2. D is the centroid of the triangle ABC.3. Triangle ABD is congruent to the triangle CBD.Which of the above statements are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» D. 1, 2 and 3 | |
| 497. |
In the figure given S is a point in on the side P̅R̅ of ΔPQR such that PS = PQ. If m∠PQR - m∠PRQ = 30°, how much is m∠SQR? |
| A. | \(22\frac{1}{2}^{\circ}\) |
| B. | 20° |
| C. | \(18\frac{1}{2}^{\circ}\) |
| D. | 15° |
| Answer» E. | |
| 498. |
ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and ∠ADC = 145°. What is the measure of ∠BAC? |
| A. | 40° |
| B. | 50° |
| C. | 35° |
| D. | 55° |
| Answer» E. | |
| 499. |
If the middle point of a straight line XY is Z and W is a different point from Z such that XW = WY, then which of the following is incorrect?A. XZ = ZYB. ∠XZW = 90°C. Triangle XZW is similar to triangle YZW.D.∠XZW > 90° |
| A. | C |
| B. | D |
| C. | A |
| D. | B |
| Answer» C. A | |
| 500. |
ΔABC is triangle, where ∠B is obtuse angle. AD is perpendicular on CB produced at D. If AB = 8 cm, BC = 7 cm and BD = 4 cm, then AC is equal to: |
| A. | 15 cm |
| B. | 13 cm |
| C. | 14 cm |
| D. | 12 cm |
| Answer» C. 14 cm | |