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.
| 51. |
If ∠AOC, ∠COB and ∠BOD together make up 274°, then ∠AOC is ______. |
| A. | 94° |
| B. | 84° |
| C. | 56° |
| D. | 188° |
| Answer» B. 84° | |
| 52. |
AD is the median of the triangle ABC. If P is any point on AD, then which one of the following is correct? |
| A. | Area of triangle PAB is greater than the area of triangle PAC |
| B. | Area of triangle PAB equal to area of triangle PAC |
| C. | Area of triangle PAB is one fourth of the area of triangle PAC |
| D. | Area of triangle PAB is half of the the area of triangle PAC |
| Answer» C. Area of triangle PAB is one fourth of the area of triangle PAC | |
| 53. |
If the diameter of the two circles is 6 units and 10 units and a centre distance of 8 units. Calculate the number of common tangents that can be drawn to both the circle. |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | Infinite |
| Answer» C. 4 | |
| 54. |
In triangle ABC, Ois the orthocentre and angle BOC is 120°. Calculate angle BAC. |
| A. | 30° |
| B. | 40° |
| C. | 60° |
| D. | 80° |
| Answer» D. 80° | |
| 55. |
In a ∆ABC, the bisectors of ∠B and ∠C meet at point O within the triangle. If ∠A is given, then which among the given options is true? |
| A. | ∠BOC = 90° + (∠A/2) |
| B. | ∠BOC = 180° - (∠A/2) |
| C. | ∠BOC = 90° - (∠A/2) |
| D. | ∠BOC = 180° - (∠A) |
| Answer» B. ∠BOC = 180° - (∠A/2) | |
| 56. |
If the two lines px + 6y + 3 = 0 and 2x + qy + 3 = 0 have infinite solutions then find the value of p and q respectively. |
| A. | 2, 6 |
| B. | 6, 2 |
| C. | 2, 2 |
| D. | 6, 6 |
| Answer» B. 6, 2 | |
| 57. |
AB||CD and EF is the transversal meeting AB and CD at P and Q, respectively. If ∠APE = 6x and ∠PQD = 4x, then ∠APQ =______. |
| A. | 108° |
| B. | 72° |
| C. | 94° |
| D. | 56° |
| Answer» C. 94° | |
| 58. |
In the figure, chords AB and CD of a circle intersect externally at P. If AB = 4 cm, CD = 11 cm and PD = 15 cm, then the length of PB is: |
| A. | 10 cm |
| B. | 12 cm |
| C. | 8 cm |
| D. | 14 cm |
| Answer» B. 12 cm | |
| 59. |
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 142°. ∠BAC is equal to∶ |
| A. | 60° |
| B. | 40° |
| C. | 52° |
| D. | 50° |
| Answer» D. 50° | |
| 60. |
PT is a tangent at the point R on a circle with centre O. SQ is a diameter, which when produced meets the tangent PT at P. If ∠SPT = 32°, then what will be the measure of ∠QRP? |
| A. | 58° |
| B. | 30° |
| C. | 32° |
| D. | 29° |
| Answer» E. | |
| 61. |
If ΔABC is a right angled triangle with ∠ABC = 90º, and AC = 10 cm, BC = 8 cm, then length of AB is: |
| A. | 12 cm |
| B. | 6 cm |
| C. | 2 cm |
| D. | 18 cm |
| Answer» C. 2 cm | |
| 62. |
In ΔABC, AD is a median and P is a point on AD such that AP : PD = 3 : 4. Then ar(ΔBPD) : ar(ΔABC) is equal to: |
| A. | 1 : 3 |
| B. | 2 : 5 |
| C. | 4 : 7 |
| D. | 2 : 7 |
| Answer» E. | |
| 63. |
In a stadium an athlete is running on a circular path with uniform speed during a practice session. The angle covered by him during one second is found to be 10° by coach observing him from the centre of the circular track. What would be the measure of angle (in degree) described by the athlete by an observer standing on the circle? |
| A. | it depends on the exact position of the observer on the circle |
| B. | 20 |
| C. | 10 |
| D. | 5 |
| Answer» E. | |
| 64. |
ΔABC is similar to ΔPQR. If ratio of perimeters of ΔABC : ΔPQR is 3 : 5 and if PQ = 15 cm, then what is the length (in cm) of AB? |
| A. | 9 |
| B. | 10 |
| C. | 12 |
| D. | 8 |
| Answer» B. 10 | |
| 65. |
From a point P outside the circle with centre O, two tangents PA and PB are drawn to meet the circle at A and B respectively. If ∠APB = 70°, then ∠OAB is equal to∶ |
| A. | 35° |
| B. | 65° |
| C. | 45° |
| D. | 55° |
| Answer» B. 65° | |
| 66. |
In the given figure, O is the centre of the circle and ∠QOR = 50°, then what is the value of ∠RPQ? |
| A. | 15° |
| B. | 25° |
| C. | 20° |
| D. | 30° |
| Answer» C. 20° | |
| 67. |
ABCD is a cyclic quadrilateral in which AB = 15 cm, BC = 12 cm and CD = 10 cm. If AC bisects BD, then what is the measure of AD? |
| A. | 15 cm |
| B. | 13.5 cm |
| C. | 18 cm |
| D. | 20 cm |
| Answer» D. 20 cm | |
| 68. |
Consider the following statements:1. There exists a regular polygon whose exterior angle is 70°.2. Let n ≥ 5. Then the exterior angle of any regular polygons of n sides is acute.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» C. Both 1 and 2 | |
| 69. |
In ΔABC, the sides AB, AC are produced and the bisectors of exterior angles of ∠ABC and ∠ACB intersect at D. If ∠BAC = 50°, then ∠BDC is equal to |
| A. | 115° |
| B. | 65° |
| C. | 55° |
| D. | 40° |
| Answer» C. 55° | |
| 70. |
If a polygon has 6 sides then the exterior angle of the polygon is: |
| A. | 60° |
| B. | 90° |
| C. | 70° |
| D. | 80° |
| Answer» B. 90° | |
| 71. |
In the figure given above, AF is a tangent to the circle at E, ∠CDE = 80° and \(m\left( {\overline {BC} } \right) = m\left( {\overline {BE} } \right)\). What is the measure of ∠BEA? |
| A. | 30° |
| B. | 45° |
| C. | 40° |
| D. | 35° |
| Answer» D. 35° | |
| 72. |
PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR? |
| A. | 30 |
| B. | 45 |
| C. | 60 |
| D. | 90 |
| Answer» E. | |
| 73. |
One side of rhombus is 13 cm and one of its diagonals is 24 cm. What is the area of the rhombus? |
| A. | 156 cm2 |
| B. | 120 cm2 |
| C. | 130 cm2 |
| D. | 312 cm2 |
| Answer» C. 130 cm2 | |
| 74. |
O is the circumcenter of the isosceles ΔABC. Given that AB = AC = 5 cm and BC = 6 cm. The radius of the circle is |
| A. | 3.015 cm |
| B. | 3.205 cm |
| C. | 3.025 cm |
| D. | 3.125 cm |
| Answer» E. | |
| 75. |
In the given figure, ∠QRU = 72°, ∠TRS = 15° and ∠PSR = 95°, then what is the value (in degrees) of ∠PQR? |
| A. | 95 |
| B. | 85 |
| C. | 75 |
| D. | 90 |
| Answer» C. 75 | |
| 76. |
In ΔABC, AD is a median and P is a point on AD such that AP ∶ PD is 3 ∶ 4,then ar (ΔAPB) ∶ ar(ΔABC) is equal to∶ |
| A. | 3 ∶ 4 |
| B. | 3 ∶ 14 |
| C. | 3 ∶ 7 |
| D. | 2 ∶ 7 |
| Answer» C. 3 ∶ 7 | |
| 77. |
In the figure given below, ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD = 9 cm and DC = 4 cm, then what is the length of BD? |
| A. | 13/36 cm |
| B. | 36/13 cm |
| C. | 13/2 cm |
| D. | 6 cm |
| Answer» E. | |
| 78. |
Analyse the figure shown below in which DE ∥ BC and the other dimensions are as follows: AD = 3 cm, BD = 4 cm, AE = 4.4 cm and DE = 6 cm. Calculate the length (in cm) of BC. |
| A. | 6 |
| B. | 8 |
| C. | 12 |
| D. | 14 |
| Answer» E. | |
| 79. |
How many tangents can be drawn to the two circles, whose radii are equal to 4 cm and 5 cm respectively and the distance between the two centres is 5 cm. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 80. |
In what ratio is the segment joining point (3, -3) and point (-5, 2) divided by the y-axis? |
| A. | 5 : 3 |
| B. | 3 : 2 |
| C. | 3 : 5 |
| D. | 2 : 3 |
| Answer» D. 2 : 3 | |
| 81. |
In ΔABC, the medians AD, BE and CF meet at O. What is the ratio of the area of ΔABD to the area of ΔAOE? |
| A. | 2 : 1 |
| B. | 3 : 2 |
| C. | 5 : 2 |
| D. | 3 : 1 |
| Answer» E. | |
| 82. |
In a circle, O is centre of the circle. Chords AB and CD intersect at P. If ∠AOD = 32° and ∠COB = 26° , then the measure of ∠APD lies between: |
| A. | 30° and 34° |
| B. | 26° and 30° |
| C. | 18° and 22° |
| D. | 22°and 26° |
| Answer» C. 18° and 22° | |
| 83. |
Measure of an exterior angle of a regular polygon is 72°. What is the sum of measures of all the interior angles of it? |
| A. | 360° |
| B. | 480° |
| C. | 352° |
| D. | 540° |
| Answer» E. | |
| 84. |
In a triangle the length of the sides, AB is 3 cm and BC is 5 cm what is the length of AC, if the angle formed at B is 600. |
| A. | 4 cm |
| B. | 19 cm |
| C. | 3 cm |
| D. | √19 cm |
| Answer» E. | |
| 85. |
In the given figure, O is the incenter of the triangle ABC. If AO/OE = 5/4 and CO/OD = 3/2, then what is the value of BO/OF? |
| A. | 19/14 |
| B. | 38/17 |
| C. | 38/7 |
| D. | 19/7 |
| Answer» D. 19/7 | |
| 86. |
A triangle PQR is right angled at Q. E and F are mid points of QR and PR respectively. What will be the ratio of the area of the quadrilateral PQEF to the area of triangle PQR. |
| A. | \(\frac{3}{4}\) |
| B. | \(\frac{4}{3}\) |
| C. | \(\frac{2}{3}\) |
| D. | \(\frac{3}{2}\) |
| Answer» B. \(\frac{4}{3}\) | |
| 87. |
In ΔABC, D is a point on BC such that, ∠BAC = 87° and ∠C = 42°. What is the measure of ∠ABD? |
| A. | 94° |
| B. | 68° |
| C. | 51° |
| D. | 102° |
| Answer» D. 102° | |
| 88. |
ABC is a triangle right angled at C as shown in the figure below. Which one of the following is correct? |
| A. | AQ2 + AB2 = BP2 + PQ2 |
| B. | AQ2 + PQ2 = AB2 + BP2 |
| C. | AQ2 + BP2 = AB2 + PQ2 |
| D. | AQ2 + AP2 = BK2 + KQ2 |
| Answer» D. AQ2 + AP2 = BK2 + KQ2 | |
| 89. |
ABC is a triangle in which ∠ABC = 90°. BD is perpendicular to AC. Which of the following is TRUE?I. Triangle BAD is similar to triangle CBD.II. Triangle BAD is similar to triangle CAB.III. Triangle CBD is similar to triangle CAB. |
| A. | Only I |
| B. | Only II and III |
| C. | Only I and IIII |
| D. | All I, II and III |
| Answer» E. | |
| 90. |
If in ΔABC, D and E are the points on AB and BC respectively such that DE∥AC, and AD : AB = 3 : 8, then (area of ΔBDE) : (area of quadrilateral DECA) = ? |
| A. | 9 : 64 |
| B. | 9 : 55 |
| C. | 8 : 13 |
| D. | 25 : 39 |
| Answer» E. | |
| 91. |
If the length of the three sides of a triangle are AB = 5 cm, BC = 12 cm and AC = 13 cm respectively, then calculate the length (in cm) of the median of side AC of the given triangle. |
| A. | 5 |
| B. | 6 |
| C. | 6.5 |
| D. | 7 |
| Answer» D. 7 | |
| 92. |
Circum - Centre of ΔPQR is O. If ∠QPR = 55° and ∠QRP = 75°, what is the value (in degrees) of ∠OPR? |
| A. | 45 |
| B. | 40 |
| C. | 65 |
| D. | 70 |
| Answer» C. 65 | |
| 93. |
A regular hexagon is inscribed in a circle. Find the ratio of area of circle to the area of that portion which is not covered by the hexagon? |
| A. | 2π/(2π – 3√3) |
| B. | π/(π – 3√3) |
| C. | 2π/√3 |
| D. | π/√3 |
| Answer» B. π/(π – 3√3) | |
| 94. |
If four angles of a quadrilateral are (6x - 18), (80 - 4x), (4x + 14), (12x - 58), then find the value of the smallest angle of the quadrilateral. |
| A. | 4° |
| B. | 10° |
| C. | 18° |
| D. | 20° |
| Answer» B. 10° | |
| 95. |
Euclid’s Postulate III is: |
| A. | All right angles are equal to one another |
| B. | A terminal line can be produced indefinitely |
| C. | A straight line may be drawn from any point to any other point |
| D. | A circle can be drawn with any centre any radius |
| Answer» E. | |
| 96. |
ABC is a triangle inscribed in a circle with center O and if ∠OAB = 30 and ∠OCB = 40 , then ∠ABC = ____. |
| A. | 40° |
| B. | 60° |
| C. | 70° |
| D. | 30° |
| Answer» D. 30° | |
| 97. |
In the given figure, O is the center of circle, ∠PQR = 100° and ∠STR = 105°. What is the value of (in degrees) of ∠OSP? |
| A. | 95 |
| B. | 45 |
| C. | 75 |
| D. | 65 |
| Answer» E. | |
| 98. |
Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant that intersects the circle at Q and R such that PQ = 12 cm and PR = 19.2 cm. The length of AB (in cm) is: |
| A. | 14.4 |
| B. | 15.2 |
| C. | 14.2 |
| D. | 15.8 |
| Answer» B. 15.2 | |
| 99. |
ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3 BD. What is the ratio of AD2 to AB2? |
| A. | 7 ∶ 9 |
| B. | 1 ∶ 3 |
| C. | 5 ∶ 7 |
| D. | 1 ∶ 2 |
| Answer» B. 1 ∶ 3 | |
| 100. |
In the given figure AB = AC and ∠ACD = 105°, then ∠BAC is equal to |
| A. | 60° |
| B. | 105° |
| C. | 30° |
| D. | 75° |
| Answer» D. 75° | |