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.
| 201. |
Consider the following statements :1. The minimum number of points of intersection of a square and a circle is 2.2. The maximum number of points of intersection of a square and a circle is 8Which 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 | |
| 202. |
If the triangle ABC and DEF follows the given equation, then these two triangles are similar by which of the following criterion?\(\frac{{AB}}{{DE}} = \frac{{BC}}{{EF}} = \frac{{AC}}{{DF}}\) |
| A. | SAS similarity |
| B. | SSS similarity |
| C. | AAA similarity |
| D. | None of the these |
| Answer» C. AAA similarity | |
| 203. |
Point A divides segment BC in the ratio 1 : 3. The co-ordinates of B are (4, -4) and that of C are (0, 6). What are the co-ordinates of point A? |
| A. | (-3, 1.5) |
| B. | (-1.5, 3) |
| C. | (3, -1.5) |
| D. | (1.5, 3) |
| Answer» D. (1.5, 3) | |
| 204. |
In triangle ABC, AD, BE and CF are medians and G is the centroid of the triangle. If the area of the triangle DGC is 20 cm2, then the area of triangle AGF + the area of triangle BGF is equal to: |
| A. | 40 cm2 |
| B. | 30 cm2 |
| C. | 20 cm2 |
| D. | 25 cm2 |
| Answer» B. 30 cm2 | |
| 205. |
In ΔABC, AD ⊥ BC and BE ⊥ AC. AD and BE intersect each other at F. If BF = AC, then the measure of ∠ABC is: |
| A. | 50° |
| B. | 60° |
| C. | 45° |
| D. | 70° |
| Answer» D. 70° | |
| 206. |
In ΔABC, ∠A = 52°. Its side AB and AC are produced to the points D and E respectively. If the bisectors of the ∠CBD and ∠BCE meet at point O, then ∠BOC is equal to: |
| A. | 106° |
| B. | 64° |
| C. | 16° |
| D. | 32° |
| Answer» C. 16° | |
| 207. |
If the hypotenuse of a right-angled triangle is longer than the bigger side by 4 cm and the bigger side is longer than the smaller side by 4 cm, find out the length of the bigger side of the triangle. |
| A. | 12 cm |
| B. | 16 cm |
| C. | 20 cm |
| D. | 8 cm |
| Answer» C. 20 cm | |
| 208. |
In the figure, G is the centre of the circle and ∠AGB = 150°. Find the value of ∠ACB. |
| A. | 60° |
| B. | 75° |
| C. | 50° |
| D. | 65° |
| Answer» C. 50° | |
| 209. |
In an isosceles triangle ABC, AB = AC and AD is perpendicular to BC at D. If AD = 8 cm and perimeter of ΔABC is 64 cm, then the area of ΔABC is: |
| A. | 130 cm2 |
| B. | 124 cm2 |
| C. | 120 cm2 |
| D. | 125 cm2 |
| Answer» D. 125 cm2 | |
| 210. |
ΔABC ∼ ΔEDF and ar(ΔABC) ∶ ar(ΔDEF) = 1 ∶ 4. If AB = 7 cm, BC = 8 cm and CA = 9 cm, then DF is equal to∶ |
| A. | 14 cm |
| B. | 18 cm |
| C. | 16 cm |
| D. | 8 cm |
| Answer» D. 8 cm | |
| 211. |
If the length of a tangent to a circle is 12 cm and the shortest distance of the point from which it has been drawn, from the circumference of the circle is 8 cm, then the radius of the circle will be ______ |
| A. | 6 cm |
| B. | 5 cm |
| C. | 4 cm |
| D. | 8 cm |
| Answer» C. 4 cm | |
| 212. |
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q, R and S, respectively. If AS = 8 cm, BC = 11 cm, and CR = 5 cm, then the length AB is equal to: |
| A. | 14 cm |
| B. | 13 cm |
| C. | 16 cm |
| D. | 12 cm |
| Answer» B. 13 cm | |
| 213. |
In the given figure, ABC is a triangle in which, AB = 6 cm, AC = 6 cm and altitude AD = 4 cm. If AE is the diameter of the circumcircle, then what is the length (in cm) of BC? |
| A. | 6√5 |
| B. | 2√3 |
| C. | 4√5 |
| D. | √5 |
| Answer» D. √5 | |
| 214. |
ΔABC ~ ΔEDF and ar(ΔABC) : ar(ΔDEF) = 4 : 9. If AB = 6 cm, BC = 8 cm and AC = 10 cm, then DF Is equal to: |
| A. | 15 cm |
| B. | 9 cm |
| C. | 12 cm |
| D. | 18 cm |
| Answer» D. 18 cm | |
| 215. |
From a point, lying outside a circle, how many tangents can be drawn |
| A. | Only one |
| B. | Zero |
| C. | Infinite |
| D. | Only two |
| Answer» E. | |
| 216. |
Let two lines p and q be parallel. Consider two points B and C on the line p and two points D and E on the line q. The line through B and E intersects the line through C and D at A in between the two lines p and q. If AC : AD 4 : 9, then what is the ratio of the area of ΔABC to that of ΔADE? |
| A. | 2 : 3 |
| B. | 4 : 9 |
| C. | 16 : 81 |
| D. | 1 : 2 |
| Answer» D. 1 : 2 | |
| 217. |
In a Δ ABC, DE is parallel to BC, AD = 3 cm, AE = 4 cm and AC = 10 cm, then the value of BD in centimetres is: |
| A. | 4.5 |
| B. | 7.5 |
| C. | 3.5 |
| D. | 5.5 |
| Answer» B. 7.5 | |
| 218. |
If x and y are positive acute angles such that sin(4x - y) = 1 and cos(2x + y) = 1/2, then what is the value of cot (x + 2y)? |
| A. | √3 |
| B. | 1/√3 |
| C. | 1 |
| D. | Cannot be determined |
| Answer» D. Cannot be determined | |
| 219. |
In a circle with centre O, an arc ABC subtends an angle of 140° at the centre of the circle. The chord AB is produced to point P. Then ∠CBP is equal to: |
| A. | 50° |
| B. | 40° |
| C. | 80° |
| D. | 70° |
| Answer» E. | |
| 220. |
In ΔPQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD? |
| A. | (4√86)/3 |
| B. | (2√86)/3 |
| C. | (5√86)/3 |
| D. | (5√86)/2 |
| Answer» B. (2√86)/3 | |
| 221. |
All ______ triangles are similar. |
| A. | Isosceles |
| B. | Equilateral |
| C. | Obtuse angled |
| D. | Right angled |
| Answer» C. Obtuse angled | |
| 222. |
In ΔABC, AC = 24 cm, BC = 10 cm and AB = 26 cm. Then the radius of the inscribed circle will be |
| A. | 26 cm |
| B. | 4 cm |
| C. | 13 cm |
| D. | None of the above |
| Answer» C. 13 cm | |
| 223. |
Point P (-4, 6) is the midpoint of segment AB. Co-ordinates of A and B are (2, y) and (x, -4) respectively. What is the value of x? |
| A. | 10 |
| B. | 6 |
| C. | -6 |
| D. | -10 |
| Answer» E. | |
| 224. |
One fifth of the area of the triangle ABC is cut off by the line DE drawn parallel to BC such that D is on AB and E is one AC. If BC = 10 cm, then what is DE equal to? |
| A. | √5 cm |
| B. | 2√5 cm |
| C. | 3√5 cm |
| D. | 4√5 cm |
| Answer» C. 3√5 cm | |
| 225. |
In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CD = 8 cm, then CB is equal to∶ |
| A. | 18 cm |
| B. | 12 cm |
| C. | 16 cm |
| D. | 15 cm |
| Answer» B. 12 cm | |
| 226. |
In ΔABC, F and E are the points on sides AB and AC, respectively, such that FE||BC and FE divides the triangle in two parts of equal area. If AD ⊥ BC and AD intersects FE at G,Find GD : AG. |
| A. | (√2 + 1) : 1 |
| B. | √2 : 1 |
| C. | 2√2 : 1 |
| D. | (√2 - 1) : 1 |
| Answer» E. | |
| 227. |
________ is the point at which the perpendicular bisectors of the sides meet and the center of the circle that circumscribes the triangle is __________. |
| A. | Incenter, Circumcenter |
| B. | Circumcenter, Circumcenter |
| C. | Circumcenter, Incenter |
| D. | Orthocenter, Circumcenter |
| Answer» C. Circumcenter, Incenter | |
| 228. |
If ΔABC and ΔBDE are two equilateral triangles such that D and E are midpoints of BC and AB respectively, then area (ΔABC) : area (ΔBDE) is : |
| A. | 2 : 1 |
| B. | 4 : 1 |
| C. | 3 : 1 |
| D. | 5 : 1 |
| Answer» C. 3 : 1 | |
| 229. |
A square cardboard with side 3 m is folded through one of its diagonal to make a triangle. The height of the perpendicular drawn to the hypotenuse of the triangle is∶ |
| A. | 3/√2 m |
| B. | 2√3 m |
| C. | 3√2 m |
| D. | 2/√3 m |
| Answer» B. 2√3 m | |
| 230. |
In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109º and ∠ACB = 72º, then the value of ∠ABC is |
| A. | 35º |
| B. | 45º |
| C. | 40º |
| D. | None of the above |
| Answer» B. 45º | |
| 231. |
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140°. Then angle BAC is equal to∶ |
| A. | 38° |
| B. | 40° |
| C. | 50° |
| D. | 60° |
| Answer» D. 60° | |
| 232. |
In the given figure, PQRS is a rectangle and PTU is a triangle. If PQ = 11cm, UR = 8cm, TR = 1cm and QT = 3cm, then what is the length (in cm) of the line joining the mid points of PT and TU? |
| A. | 2.5 |
| B. | 3 |
| C. | 4.5 |
| D. | 5 |
| Answer» B. 3 | |
| 233. |
In triangle ABC, point M is on side AB and point N is on side AC such that BMNC becomes a trapezium. The ratio of side MN and side BC is 7 : 9. Calculate the ratio of the area of triangle AMN and the area of trapezium BMNC. |
| A. | 7 : 9 |
| B. | 49 : 32 |
| C. | 32 : 49 |
| D. | 49 : 81 |
| Answer» C. 32 : 49 | |
| 234. |
AB is a diameter of a circle with centre O. CB is tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is: |
| A. | 2√5 cm |
| B. | 6√6 cm |
| C. | 6√5 cm |
| D. | 2√6 cm |
| Answer» D. 2√6 cm | |
| 235. |
An angle is 10° more than one third of its complement. Find the greater angle. |
| A. | 30° |
| B. | 60° |
| C. | 45° |
| D. | 75° |
| Answer» C. 45° | |
| 236. |
In ∆ABC, if ∠A = 90°, which is the largest side? |
| A. | BC |
| B. | AB |
| C. | AC |
| D. | CA |
| Answer» B. AB | |
| 237. |
If a regular polygon has 10 sides, then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees? |
| A. | 120 |
| B. | 132 |
| C. | 140 |
| D. | 108 |
| Answer» E. | |
| 238. |
Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is |
| A. | 3√2 |
| B. | 3 |
| C. | 4 |
| D. | √3 |
| Answer» C. 4 | |
| 239. |
In the following figure, AB ∥ CD, ∠OAB = 120º and ∠OCD = 140º. Then the value of x is |
| A. | 60º |
| B. | 70º |
| C. | 100º |
| D. | None of the above |
| Answer» D. None of the above | |
| 240. |
A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at the points P, Q and R respectively. If BP = 5.4 cm, CQ = 7.3 cm and AR = 6.1 cm, then the perimeter (in cm) of the ΔABC is: |
| A. | 36 |
| B. | 37.6 |
| C. | 37 |
| D. | 37.25 |
| Answer» C. 37 | |
| 241. |
If in triangle ΔABC = 2 cm, BC = 4 cm, and AC = 5 and in triangle ΔPQR PQ = 12 cm, QR = 24 cm, and PR = 30 cm then triangle are: |
| A. | Isosceles |
| B. | Right angled triangle |
| C. | Similar |
| D. | Equilateral |
| Answer» D. Equilateral | |
| 242. |
In the given figure, SX = OX = OR. If QX = 3 cm and PQ = 9 cm, that what is the value (in cm) of OS? |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 243. |
Let PQRS be a parallelogram whose diagonals PR and QS intersect at O. If ΔQRS is an equilateral triangle having a side of length 10 cm, then what is the length of the diagonal PR? |
| A. | 5√3 cm |
| B. | 10√3 cm |
| C. | 15√3 cm |
| D. | 20√3 cm |
| Answer» C. 15√3 cm | |
| 244. |
Δ ABC is similar to Δ DEF. The perimeters of Δ ABC and Δ DEF are 40 cm and 30 cm respectively. What is the ratio of (BC + CA) to (EF + FD) equal to? |
| A. | 5 ∶ 4 |
| B. | 4 ∶ 3 |
| C. | 3 ∶ 2 |
| D. | 2 ∶ 1 |
| Answer» C. 3 ∶ 2 | |
| 245. |
In a ΔABC, the bisectors of ∠B and ∠C meet at O within the triangle. If ∠A = 110°, then the measure of ∠BOC is: |
| A. | 145° |
| B. | 84° |
| C. | 110° |
| D. | 55° |
| Answer» B. 84° | |
| 246. |
In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 30°, then what is the value (in degrees) of ∠PBC? |
| A. | 30 |
| B. | 36 |
| C. | 45 |
| D. | 60 |
| Answer» B. 36 | |
| 247. |
An angle is 2° more than its complement. What is the measure of the angle? |
| A. | 50° |
| B. | 60° |
| C. | 90° |
| D. | 46° |
| Answer» E. | |
| 248. |
Find the value of k if the points (k, 3), (6, - 2), (- 3, 4) align. |
| A. | 3 |
| B. | - 2 |
| C. | - 3/2 |
| D. | None of these |
| Answer» D. None of these | |
| 249. |
A ΔABC, D and E are the points on sides AB and AC, respectively, such that DE || BC. If DE : BC is 3 : 5, then (Area of ΔADE): (Area of quadrilateral DECB) is: |
| A. | 5 : 8 |
| B. | 3 : 4 |
| C. | 9 : 16 |
| D. | 9 : 25 |
| Answer» D. 9 : 25 | |
| 250. |
In figure, if ∠ABC = 65° and ∠ACB = 35° then ∠BDC is |
| A. | 100° |
| B. | 80° |
| C. | 25° |
| D. | 55° |
| Answer» C. 25° | |