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.
| 1. |
PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be |
| A. | 3 cm |
| B. | 4 cm |
| C. | 5 cm |
| D. | 2 cm |
| Answer» C. 5 cm | |
| 2. |
If the sum of all interior angles of a regular polygon is twice the sum of all its exterior angles then the polygon is |
| A. | Hexagon |
| B. | Octagon |
| C. | Nonagon |
| D. | Decagon |
| Answer» B. Octagon | |
| 3. |
In an isosceles right-angled triangle, the perimeter is 30 m. Find its area (Approximate) |
| A. | 38.63 m2 |
| B. | 40 m2 |
| C. | 39.60 m2 |
| D. | 37.86 m2 |
| Answer» B. 40 m2 | |
| 4. |
In ΔPQR, S and T are mid-points of PQ and PR, respectively. If ∠QPR = 75° and ∠PRQ = 40°, then ∠TSQ is: |
| A. | 115° |
| B. | 105° |
| C. | 120° |
| D. | 135° |
| Answer» B. 105° | |
| 5. |
In the circle below, chord AB is extended to meet the tangent DC at D. If AB = 12 cm and DC = 8 cm, find the length of BD. |
| A. | 4√6 cm |
| B. | 6 cm |
| C. | 4 cm |
| D. | 5 cm |
| Answer» D. 5 cm | |
| 6. |
If the base and height of a triangle is doubled and tripled respectively. Find the difference between the final and initial area of the triangle. |
| A. | bh/2 |
| B. | 3bh/2 |
| C. | 5bh/2 |
| D. | 7bh/2 |
| Answer» D. 7bh/2 | |
| 7. |
In a circle with centre O, AC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and ∠AEB = 68°, then the measure of ∠DOC is: |
| A. | 22° |
| B. | 30° |
| C. | 44° |
| D. | 32° |
| Answer» D. 32° | |
| 8. |
In the following figure (not to scale), AB = CD and \(\rm\overline{AB}\) and \(\rm\overline{CD}\) are produced to meet at point P. If ∠BAD = 70°, then find ∠P |
| A. | 50° |
| B. | 30° |
| C. | 40° |
| D. | 45° |
| Answer» D. 45° | |
| 9. |
Consider the following statements:1. The diagonals of a trapezium divide each other proportionally.2. Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.Which of the above statements is / are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 10. |
DEF is an isosceles triangle with such that DE = DF = 60 cm and EF = 96 cm. DG is a median to base EF. What is the length (in cm) of DG? |
| A. | 22 |
| B. | 36 |
| C. | 24 |
| D. | 32 |
| Answer» C. 24 | |
| 11. |
Let O be the centre of a circle and AC be its diameter. BD is a chord intersecting AC at E. Point B is joined to C and D. If ∠BOC = 50° and ∠AOD = 110°, then ∠BEC = ? |
| A. | 70° |
| B. | 80° |
| C. | 55° |
| D. | 90° |
| Answer» C. 55° | |
| 12. |
In ΔABC, AD is median and G is the point on AD such that AG ∶ GD = 2 ∶ 1. Then ar (ΔABG) ∶ ar(ΔABC) is equal to: |
| A. | 1 ∶ 6 |
| B. | 1 ∶ 3 |
| C. | 3 ∶ 1 |
| D. | 1 ∶ 5 |
| Answer» C. 3 ∶ 1 | |
| 13. |
In a circle, PQ and RS are two diameters that are perpendicular to each other. Find the length of the chord PR. |
| A. | \(\frac{PQ}{\sqrt{2}}\) |
| B. | \(\sqrt{2} \ PQ\) |
| C. | 2 PQ |
| D. | \(\frac{PQ}{2}\) |
| Answer» B. \(\sqrt{2} \ PQ\) | |
| 14. |
Find the equation of the perpendicular to segment joining the points A (0, 4) and B(-5, 9) and passing through the point P. Point P divides segment AB in the ratio 2 : 3. |
| A. | x − y = 8 |
| B. | x − y = -8 |
| C. | x + y = -8 |
| D. | x + y = 8 |
| Answer» C. x + y = -8 | |
| 15. |
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is |
| A. | 24 |
| B. | 26 |
| C. | 28 |
| D. | 30 |
| Answer» B. 26 | |
| 16. |
In triangle ABC, AD divides ∠BAC in the ratio 2 : 3 and BD = AD. If side BA is produced to E such that ∠CAE = 115°, then ∠ACB = |
| A. | 95° |
| B. | 82° |
| C. | 89° |
| D. | 78° |
| Answer» D. 78° | |
| 17. |
In the given figure AB is parallel to CD and AC is parallel to BD. If ∠EAC = 40°, ∠FDG = 55°, ∠HAB = x°, then what is the value of x? |
| A. | 85° |
| B. | 80° |
| C. | 75° |
| D. | 65° |
| Answer» B. 80° | |
| 18. |
B1 is a point on the side AC of ΔABC and B1B is joined. A line is drawn through A parallel to B1B meeting BC at A1 and another line is drawn through C parallel to B1B meeting AB produced at C1. Then |
| A. | \(\frac{1}{{C{C_1}}} - \frac{1}{{A{A_1}}} = \frac{1}{{B{B_1}}}\) |
| B. | \(\frac{1}{{C{C_1}}} + \frac{1}{{A{A_1}}} = \frac{1}{{B{B_1}}}\) |
| C. | \(\frac{1}{{B{B_1}}} - \frac{1}{{A{A_1}}} = \frac{2}{{C{C_1}}}\) |
| D. | \(\frac{1}{{A{A_1}}} - \frac{1}{{C{C_1}}} = \frac{2}{{B{B_1}}}\) |
| Answer» C. \(\frac{1}{{B{B_1}}} - \frac{1}{{A{A_1}}} = \frac{2}{{C{C_1}}}\) | |
| 19. |
If the distance between center to chord is 12 cm and the length of the chord is 10 cm, then the diameter of the circle is |
| A. | 26 cm |
| B. | 14 cm |
| C. | 13 cm |
| D. | 30 cm |
| Answer» B. 14 cm | |
| 20. |
In ΔABC, D is a point on AC such that AB = BD = DC, if ∠BAD = 70°, then the measure of ∠B is: |
| A. | 80° |
| B. | 75° |
| C. | 85° |
| D. | 70° |
| Answer» C. 85° | |
| 21. |
AB and CD are two chords of a circle which intersect at a point O inside the circle. It is given that, AB = 10 cm, CO = 1.5 cm and DO = 12.5 cm. What is the ratio between the larger and smaller among AO and BO? |
| A. | 7 : 3 |
| B. | 4 : 1 |
| C. | 3 : 1 |
| D. | 3 : 2 |
| Answer» D. 3 : 2 | |
| 22. |
ABCDE is a regular pentagon. Its sides are extended as shown in the figure. The value of \(\frac {\angle ABC + 2\angle EGD + 3\angle BAJ}{6}\) is: |
| A. | 45° |
| B. | 75° |
| C. | 66° |
| D. | 30° |
| Answer» D. 30° | |
| 23. |
If ∠2 = 2 ∠1, find ∠2 where the two lines are parallel |
| A. | 80° |
| B. | 120° |
| C. | 160° |
| D. | 60° |
| Answer» C. 160° | |
| 24. |
In the above figure, ∠BAE = 30°, ∠ABE = 80°and ∠DBE = 50°. What is the value of ∠BCE? |
| A. | 25° |
| B. | 5° |
| C. | 10° |
| D. | 20° |
| Answer» E. | |
| 25. |
A, B, and C are three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 80° and 120°, respectively. The value of ∠BAC is: |
| A. | 85° |
| B. | 75° |
| C. | 80° |
| D. | 70° |
| Answer» D. 70° | |
| 26. |
In a rhombus ABCD, if AC = 12 cm, BD = 16 cm, then AB = ______. |
| A. | 12 cm |
| B. | 10 cm |
| C. | 15 cm |
| D. | 14 cm |
| Answer» C. 15 cm | |
| 27. |
ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other perpendicularly at O. If AO = a cm, DO = b cm and the area of ΔABC = x cm2, then what is the area (in cm2) of ΔDBC? |
| A. | \(\frac{{bx}}{a}\) |
| B. | \(\frac{a}{b}x\) |
| C. | \(\frac{{ab}}{2}x\) |
| D. | \(\frac{{a + b}}{2}x\) |
| Answer» B. \(\frac{a}{b}x\) | |
| 28. |
A circle has points P, Q, R on a circle in such a way that angle PQR is 60° and angle QRP is 80°. Calculate the angle subtended by an arc QR at the centre. |
| A. | 40° |
| B. | 80° |
| C. | 100° |
| D. | 120° |
| Answer» C. 100° | |
| 29. |
Consider the following statements:Two triangles are said to be congruent, ifThree angles of one triangle are equal to corresponding three angles of the other triangleThree sides of one triangle are equal to the corresponding three sides of the triangleTwo sides and the included angle of one triangle are equal to the corresponding two sides and the included of the other triangleTwo angles and the included side of one triangle are equal to the corresponding two angles and the included sides of other triangleWhich of the above statements are correct? |
| A. | 1, 2 and 3 |
| B. | 1, 3 and 4 |
| C. | 1, 2 and 4 |
| D. | 2, 3 and 4 |
| Answer» E. | |
| 30. |
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 130°. Then ∠BAC is equal to∶ |
| A. | 50° |
| B. | 60° |
| C. | 150° |
| D. | 40° |
| Answer» E. | |
| 31. |
In a trapezium ABCD, DC ∥ AB, AB = 12 cm and DC = 7.2cm. What is the length of the line segment joining the mid-points of its diagonals? |
| A. | 4.8 cm |
| B. | 2.4 cm |
| C. | 3.6 cm |
| D. | 2.6 cm |
| Answer» C. 3.6 cm | |
| 32. |
In the figure given below, ΔABR ~ ΔPQR. If PQ = 3 cm, AB = 6 cm, BR = 8.2 cm and PR = 5.2 cm, then QR and AR are respectively. |
| A. | 8.2 cm, 10.4 cm |
| B. | 4.1 cm, 6 cm |
| C. | 2.6 cm, 5.2 cm |
| D. | 4.1 cm, 10.4 cm |
| Answer» E. | |
| 33. |
A farmer is marking his field to sow seeds if he marks a rectangular area of his field in the ratio of length : width 3 : 1.Write a expression that will give the total area. |
| A. | 3 |
| B. | 3x2 - 3 |
| C. | 3x2 |
| D. | 3x2 + x |
| Answer» D. 3x2 + x | |
| 34. |
In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 62° and ∠ EBD = 60°, then the value of x is: |
| A. | 78° |
| B. | 76° |
| C. | 92° |
| D. | 68° |
| Answer» D. 68° | |
| 35. |
If the angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7, then the largest angle is: |
| A. | 40 |
| B. | 100 |
| C. | 145 |
| D. | 140 |
| Answer» E. | |
| 36. |
In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP? |
| A. | 4√5 |
| B. | 4√4 |
| C. | 6√3 |
| D. | 4√6 |
| Answer» B. 4√4 | |
| 37. |
In a rhombus, the lengths of diagonals are 16 cm and 12 cm. The side of the rhombus is |
| A. | 7 cm |
| B. | 8 cm |
| C. | 9 cm |
| D. | 10 cm |
| Answer» E. | |
| 38. |
Asha and Suman's mud forts have heights 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other? |
| A. | 25 |
| B. | 16 |
| C. | 24 |
| D. | 7 |
| Answer» B. 16 | |
| 39. |
AB is a diameter of a circle with centre O, and P is point on the circle. If ∠POA = 130°, then ∠BPO is equal to: |
| A. | 55° |
| B. | 65° |
| C. | 45° |
| D. | 60° |
| Answer» C. 45° | |
| 40. |
Given below are two statements : Statement I : If you know the length of two sides of a right-angled triangle then the length of the third side can not be found.Statement II : The internal angles of a triangle add up to 180°.In the light of the above statements. choose the correct answer from the options given below: |
| A. | Both Statement I and Statement II are true |
| B. | Both Statement I and Statement II are false |
| C. | Statement I is correct but Statement II is false |
| D. | Statement I is incorrect but Statement II is true |
| Answer» E. | |
| 41. |
In ΔABC, AD bisects ∠A which meets BC at D. If BC = a, AC = b and AB = c, then DC = ? |
| A. | ac/(a + b) |
| B. | ac/(a + c) |
| C. | ab/(b + c) |
| D. | bc/(a + c) |
| Answer» D. bc/(a + c) | |
| 42. |
In a triangle ABC, the length of in-radius and circum-radius is 2 units and 6 units respectively. Find the distance (in units) between the in-center and circumcenter. |
| A. | √3 |
| B. | 2√3 |
| C. | 3√3 |
| D. | 4√3 |
| Answer» C. 3√3 | |
| 43. |
ABCD passes through the centres of the three circles as shown in the figure. AB = 2 cm and CD = 1 cm. If the area of middle circle is the average of the areas of the other two circles, then what is the length (in cm) of BC? |
| A. | (√6) - 1 |
| B. | (√6) + 1 |
| C. | (√6) - 3 |
| D. | (√6) + 3 |
| Answer» B. (√6) + 1 | |
| 44. |
In a ΔABC, ∠ABC = 2 ∠CAB, If the side BC is extended to D and ∠ACD = 126°, then ∠CAB is: |
| A. | 36° |
| B. | 42° |
| C. | 63° |
| D. | 84° |
| Answer» C. 63° | |
| 45. |
In ΔABC, AB = 7 cm, AC = 13 cm and BC = 2√30 cm then B is |
| A. | 120° |
| B. | 60° |
| C. | 90° |
| D. | 45° |
| Answer» D. 45° | |
| 46. |
In the given figure, PQ = 30, RS = 24 and OM = 12, then what is the value of ON? |
| A. | 9 |
| B. | 12 |
| C. | 15 |
| D. | 18 |
| Answer» D. 18 | |
| 47. |
ΔABC is right angled at B. BD is an altitude. If DC = 5 cm and AD = 40 cm, what is the value of BC (in cm)? |
| A. | 12 |
| B. | 18 |
| C. | 15 |
| D. | 16 |
| Answer» D. 16 | |
| 48. |
In the given figure, ABCD is a cyclic quadrilateral. Then the ordered pair (x, y) is |
| A. | (15°, 25°) |
| B. | (10°, 15°) |
| C. | (15°, 35°) |
| D. | (40°, 35°) |
| Answer» B. (10°, 15°) | |
| 49. |
ABCD is a trapezium. Sides AB and CD are parallel to each other. AB = 6 cm, CD = 18 cm, BC = 8 cm and AD = 12 cm. A line parallel to AB divides the trapezium in two parts of equal perimeter. This line cuts BC at E and AD at F. If BE/EC = AF/FD, than what is the value of BE/EC? |
| A. | 1/2 |
| B. | 2 |
| C. | 4 |
| D. | 1/4 |
| Answer» D. 1/4 | |
| 50. |
Choose the CORRECT option if the two sides of a triangle are of length 4 cm and 10 cm and the length of its third side is a cm. |
| A. | a < 6 |
| B. | a > 6 |
| C. | a > 5 |
| D. | 5 |
| Answer» C. a > 5 | |