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.
| 151. |
I is the in centre of ΔABC. If BIC = 108°, then ∠A = ? |
| A. | 81° |
| B. | 72° |
| C. | 54° |
| D. | 36° |
| Answer» E. | |
| 152. |
If the sum of the interior angles of a regular polygon is 1260°, then how many sides does it have? |
| A. | 10 |
| B. | 12 |
| C. | 15 |
| D. | 9 |
| Answer» E. | |
| 153. |
A circle touches all the sides of a quadrilateral PQRS, whose sides, PQ = 2 cm, QR = 3 cm and RS = 4 cm. What is the length of PS? |
| A. | 3 cm |
| B. | 2 cm |
| C. | 1 cm |
| D. | 4 cm |
| Answer» B. 2 cm | |
| 154. |
In ΔADC, E and B are the points on the sides AD and AC respectively such that ∠ABE = ∠ADC. If AE = 6 cm, BC = 2 cm, BE = 3 cm and CD = 5 cm, then (AB + DE) is equal to∶ |
| A. | 46/3 cm |
| B. | 14 cm |
| C. | 16 cm |
| D. | 49/3 cm |
| Answer» B. 14 cm | |
| 155. |
A line through the vertex A of a parallelogram ABCD meets DC in P and BC produced in Q. If P is the mid-point of DC, then which of the following is/are correct?1. Area of ΔPDA is equal to that of ΔPCQ2. Area of ΔQAB is equal to twice that of ΔPCQSelect the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 156. |
Let ΔABD be on the same base AB and between the same parallels AB and CD.Then the relation between areas of ΔABC and ΔABD will be: |
| A. | Area (ΔABC) = Area (ΔABD) |
| B. | Area (ΔABD) = 1/2 × Area(ΔABC) |
| C. | Area (ΔABD) = 1/3 × Area(ΔABC) |
| D. | Area (ΔABD) = 1/4 × Area(ΔABC) |
| Answer» B. Area (ΔABD) = 1/2 × Area(ΔABC) | |
| 157. |
In what ratio does the point T(x, 0) divide the segment joining the points S(6, -3) and U(-3, 9)? |
| A. | 1 : 3 |
| B. | 2 : 1 |
| C. | 1 : 4 |
| D. | 2 : 3 |
| Answer» B. 2 : 1 | |
| 158. |
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is: |
| A. | 54° |
| B. | 18° |
| C. | 30° |
| D. | 36° |
| Answer» E. | |
| 159. |
If two distinct circles in a plane are intersecting each other, then they intersect in : |
| A. | exactly one point |
| B. | infinitely many points |
| C. | at the most two points |
| D. | exactly two points |
| Answer» E. | |
| 160. |
A ladder 10 m long is leaning against a vertical wall. lt makes an angle of 60° with the ground. How faris the foot of the ladder from the wall? |
| A. | 5 m |
| B. | 8.66 m |
| C. | 17.32 m |
| D. | 15 m |
| Answer» B. 8.66 m | |
| 161. |
ΔABC is inscribed in a circle with centre O. AO is produced to meet the circle at K and AD⊥ BC. If ∠B = 80° and ∠C = 64°, then the measure of ∠DAK is: |
| A. | 16° |
| B. | 12° |
| C. | 20° |
| D. | 10° |
| Answer» B. 12° | |
| 162. |
If the two circles touch each other internally, then only _______ common tangent can be drawn to them. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 163. |
If the angle between two radii of a circle be 130º, then the angle between the tangents at the end of these radii (in degree) is: |
| A. | 50º |
| B. | 90º |
| C. | 40º |
| D. | 70º |
| Answer» B. 90º | |
| 164. |
Distance between the points (3, 6) and (0, 0) is - |
| A. | \(\sqrt 46\) units |
| B. | 5 units |
| C. | \(\sqrt 35\) units |
| D. | \(3\sqrt 5\) units |
| Answer» E. | |
| 165. |
In a circle with center O, AB is a diameter. Points C, D and E are on the circle on one side of AB such that ABEDC is a pentagon. The sum of angles ACD and BED is. |
| A. | 240° |
| B. | 270° |
| C. | 180° |
| D. | 225° |
| Answer» C. 180° | |
| 166. |
Centre of two concentric circles is O. The area of two circles is 616 cm2 and 154 cm2 respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches small circle at B and intersects larger circle at C. What is the length (in cm) of AC? |
| A. | 12√3 |
| B. | 14√3 |
| C. | 10√6 |
| D. | 18√2 |
| Answer» C. 10√6 | |
| 167. |
If one of the angles of a triangle is 64°, then the angle between the bisectors of the other two interior angles is: |
| A. | 100° |
| B. | 122° |
| C. | 96° |
| D. | 112° |
| Answer» C. 96° | |
| 168. |
Circles having equal radii are called: |
| A. | Chord of the circle |
| B. | Similar circles |
| C. | Congruent circles |
| D. | Centre of the circle |
| Answer» D. Centre of the circle | |
| 169. |
If the difference of the two supplementary angles is 48°, then the large angle is: |
| A. | 122° |
| B. | 108° |
| C. | 114° |
| D. | 110° |
| Answer» D. 110° | |
| 170. |
In a triangle ABC, D is a point on BC such that \(\frac {AB}{AC} = \frac {BD}{DC}.\) If ∠B = 68° and ∠C = 52°, then the measure of ∠BAD is equal to: |
| A. | 40° |
| B. | 30° |
| C. | 60° |
| D. | 50° |
| Answer» C. 60° | |
| 171. |
A spherical balloon of radius 1 m subtends an angle of 60° at the eye of an observer. If the angle of elevation of its centre is 45°, what is the height of the centre of the balloon? Assume that the eye of observer is at ground level. |
| A. | 100 cm |
| B. | 100√2 cm |
| C. | 100√3/3 cm |
| D. | 100√3 cm |
| Answer» C. 100√3/3 cm | |
| 172. |
In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and ∠OBA = 60°, If ∠DOC = 60°, then what is the length of BC? |
| A. | 7 cm |
| B. | \(3\sqrt 7\) cm |
| C. | 3.5 cm |
| D. | \(5\sqrt 7\) cm |
| Answer» B. \(3\sqrt 7\) cm | |
| 173. |
If the angle subtended by the radius of a circle (OC) and the side BC of the triangle ABC at vertex B is 40° then calculate the value of ∠BAC. |
| A. | 35° |
| B. | 45° |
| C. | 50° |
| D. | 65° |
| Answer» D. 65° | |
| 174. |
In ΔABC, D is a point on BC. If \(\frac{AB}{AC}=\frac {BD}{DC}, \) ∠B = 75° and ∠C = 45°, then ∠BAD is equal to: |
| A. | 60° |
| B. | 50° |
| C. | 30° |
| D. | 45° |
| Answer» D. 45° | |
| 175. |
PQR is an isosceles triangle such that PQ = QR = 10 cm and ΔPQR = 90°. What is the length of the perpendicular drawn from Q on PR? |
| A. | 5√2 cm |
| B. | 7√2 cm |
| C. | 4√2 cm |
| D. | 6√2 cm |
| Answer» B. 7√2 cm | |
| 176. |
In a circle of radius 17 cm, if a chord is at a distance of 8 cm from the centre of the circle, then the length of the chord is: |
| A. | 24 cm |
| B. | 28 cm |
| C. | 30 cm |
| D. | 20 cm |
| Answer» D. 20 cm | |
| 177. |
It is given the area of a triangle is A. The value of its perimeter, inradius, circumradius and the average of the lengths of the medians are P. r. R and d respectively. The ratio A : P is equal to |
| A. | r : 1 |
| B. | (R + r)2 : d |
| C. | r : 2 |
| D. | (R - r)2 : r |
| Answer» D. (R - r)2 : r | |
| 178. |
In ΔABC, ∠A + ∠B = 135º and ∠C + 2∠B = 180º. Then which one of the following relations is true? |
| A. | CA > AB |
| B. | CA = AB |
| C. | CA < AB |
| D. | None of the above |
| Answer» C. CA < AB | |
| 179. |
Name the point that lies in the fourth quadrant of a graph? |
| A. | (8, 5) |
| B. | (8, -5) |
| C. | (4, 5) |
| D. | (8, 4) |
| Answer» C. (4, 5) | |
| 180. |
P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle? |
| A. | 1.5 |
| B. | 2 |
| C. | 2.5 |
| D. | 3 |
| Answer» D. 3 | |
| 181. |
In the circle below, chord \(\overline {AB}\) is extended to meet the tangent \(\overline {DE}\) at D. If \(\overline {AB}\) = 24 cm \(\overline {DE}\) = 9 cm, what is the length of \(\overline {BD}\)? |
| A. | 4√6 cm |
| B. | 3 cm |
| C. | 5 cm |
| D. | 4 cm |
| Answer» C. 5 cm | |
| 182. |
In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is |
| A. | 5 cm |
| B. | 12 cm |
| C. | 15 cm |
| D. | 10 cm |
| Answer» E. | |
| 183. |
If two complimentary angles are in the ratio of 11 : 7, find the smaller angle.A. 35° B. 55° C. 65° D. 25° |
| A. | C |
| B. | D |
| C. | A |
| D. | B |
| Answer» D. B | |
| 184. |
In the figure given below, ∠A = 80° and ∠ABC = 60°, BD and CD bisects angles B and C respectively. What are the values of x and y respectively? |
| A. | 10 and 130 |
| B. | 10 and 125 |
| C. | 20 and 130 |
| D. | 20 and 125 |
| Answer» D. 20 and 125 | |
| 185. |
Perimeter of rectangle of sides a & b is given by |
| A. | 2(a + b) |
| B. | 4(a + b) |
| C. | a × b |
| D. | a + b |
| Answer» B. 4(a + b) | |
| 186. |
Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is: |
| A. | 20 |
| B. | 17 |
| C. | 16 |
| D. | 19 |
| Answer» E. | |
| 187. |
In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm, the length of the chord BC is |
| A. | 10 cm |
| B. | 9 cm |
| C. | 8 cm |
| D. | 9.6 cm |
| Answer» E. | |
| 188. |
How many diagonals can be drawn by joining the vertices of an octagon? |
| A. | 20 |
| B. | 24 |
| C. | 28 |
| D. | 64 |
| Answer» B. 24 | |
| 189. |
In the given figure BD perpendicular to AC then what be the measure of angle AEB? |
| A. | 60° |
| B. | 80° |
| C. | 45° |
| D. | 100° |
| Answer» C. 45° | |
| 190. |
In a circle with centre O, AB is 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° | |
| 191. |
If ABCD is a Cyclic Quadrilateral, then the value of cos2A – cos2B – cos2C + cos2D is: |
| A. | -1 |
| B. | 1 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 192. |
In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle? |
| A. | 32/√3 |
| B. | 24√3 |
| C. | 64/√3 |
| D. | 64√2 |
| Answer» C. 64/√3 | |
| 193. |
In the figure, PA is a tangent from an external point P to the circle with centre O. If ∠POB = 110°, then the measure of ∠APO is: |
| A. | 40° |
| B. | 20° |
| C. | 25° |
| D. | 30° |
| Answer» C. 25° | |
| 194. |
If point A (x, y) is equidistant from the point B (3, -4) and C (-2, 0) then - |
| A. | 4x - 8y = 16 |
| B. | 4x - 13 = 2y |
| C. | 10x - 8y = 21 |
| D. | 10x + 8y = 16 |
| Answer» D. 10x + 8y = 16 | |
| 195. |
In the given figure, if AB = 10 cm, CD = 7 cm, SD = 4 cm and AS = 5 cm, then BC = ? |
| A. | 9 cm |
| B. | 8 cm |
| C. | 7.5 cm |
| D. | 6 cm |
| Answer» C. 7.5 cm | |
| 196. |
In the given figure, AP is perpendicular to BC, and AQ is the bisector of angle BAC. What will be the measure of angle PQA? |
| A. | 30° |
| B. | 60° |
| C. | 50° |
| D. | 75° |
| Answer» E. | |
| 197. |
Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct?(1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y(2) ∠POC + ∠QCO = 90°Select the correct answer using the code given below. |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 198. |
Ina triangle one angle is twice the other and their sum is the third angle. The angles are: |
| A. | 30°, 60°, 90° |
| B. | 20°, 40°, 60° |
| C. | 40°, 80°, 120° |
| D. | None of these |
| Answer» B. 20°, 40°, 60° | |
| 199. |
In ΔPQR, ∠R = 54°, the perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 46°, then what is the value (in degrees) of ∠PQR? |
| A. | 25 |
| B. | 40 |
| C. | 50 |
| D. | 60 |
| Answer» C. 50 | |
| 200. |
In ΔABC, ∠BCA = 90°, AC = 24 cm and BC = 10 cm. What is the radius (in cm) of the circum-circle of ΔABC? |
| A. | 12.5 |
| B. | 13 |
| C. | 25 |
| D. | 26 |
| Answer» C. 25 | |