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.
| 251. |
PA and PB are two tangents drawn to two circles of radius 3 cm and 5 cm respectively. PA touches the smaller and larger circles at points X and Y respectively. PB touches the smaller and large circle at point U and V respectively. The centres of the smaller and larger circles O and N respectively. If ON = 12 cm, then what is the value (in cm) of PY? |
| A. | 5√35 |
| B. | 7√15 |
| C. | 9√15 |
| D. | 12√5 |
| Answer» B. 7√15 | |
| 252. |
Let ABC and A’B’C’ be two triangles in which AB > A’B’, BC > B’C’ and CA > C’A’. Let D, E and F be the middle points of the sides BC, CA and AB respectively. Let D’, E’ and F’ be the midpoints of the sides of the sides B’C’, C’A’ and A’B’ respectively. Consider the following statements.Statement I:AD > A’D’, BE > B’E’ and CF > C’F’ are always true.Statement II:(AB2 + BC2 + CA2) / (AD2 + BE2 + CF2) = (A’B’2 + B’C’2 + C’A’2) / (A’D’2 + B’E’2 + C’F’2)Which one of the following is correct in respect of the above statements? |
| A. | Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I. |
| B. | Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I. |
| C. | Statement I is true but Statement II is false. |
| D. | Statement I is false but Statement II is true. |
| Answer» E. | |
| 253. |
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. | |
| 254. |
In parallelogram ABCD, the value of x, when ∠A = 40° is: |
| A. | 120° |
| B. | 150° |
| C. | 40° |
| D. | 140° |
| Answer» E. | |
| 255. |
D is a point on the side BC of a ΔABC such that ∠ADC = ∠BAC. If CA = 10 cm and BC = 16 cm, then the length of CD is: |
| A. | 6.5 cm |
| B. | 7 cm |
| C. | 6.25 cm |
| D. | 6 cm |
| Answer» D. 6 cm | |
| 256. |
A line contains: |
| A. | three points |
| B. | one point |
| C. | two points |
| D. | infinitely many points |
| Answer» E. | |
| 257. |
Given ∠POR = 3x° and ∠QOR = 2x° + 10°. If POQ is a straight line, then the value of 3x° + 10° is: |
| A. | 82° |
| B. | 34° |
| C. | 102° |
| D. | 112° |
| Answer» E. | |
| 258. |
In a ΔABC, points D and E are lying on AB and AC, respectively. DE is also parallel to the base BC. O is the intersection of BE and CD. If AD : DB = 4 : 3 find the ratio of DO to DC. |
| A. | 5 : 7 |
| B. | 4 : 11 |
| C. | 5 : 12 |
| D. | 3 : 7 |
| Answer» C. 5 : 12 | |
| 259. |
In a quadrilateral ABCD, ∠B = 90° and AB2 + BC2 + CD2 - AD2 = 0, then what is ∠ACD equal to? |
| A. | 30° |
| B. | 60° |
| C. | 90° |
| D. | 120° |
| Answer» D. 120° | |
| 260. |
If a regular polygon has 9 sides, then each exterior angle is equal to |
| A. | 36° |
| B. | 40° |
| C. | 140° |
| D. | 160° |
| Answer» C. 140° | |
| 261. |
In ∆ABC, AM ⊥ BC and AN is the bisector of ∠A. What is the measure of ∠MAN, if ∠B = 55° and ∠C = 35°? |
| A. | 10° |
| B. | 15° |
| C. | 5° |
| D. | 12° |
| Answer» B. 15° | |
| 262. |
In ΔABC, ∠A = 48°. AB and AC is extended to points D and E respectively, if the bisectors of angle CBD and angle BCE meet at point O, then ∠BOC is equal to: |
| A. | 132° |
| B. | 84° |
| C. | 42° |
| D. | 66° |
| Answer» E. | |
| 263. |
In the figure given below, two equal chords cut at point P. If AB = CD = 10 cm, OC = 13 cm (O is the centre of the circle) and PB = 3 cm, then what is the length of OP? |
| A. | 5 cm |
| B. | 6 cm |
| C. | 2√29 cm |
| D. | 2√37 cm |
| Answer» E. | |
| 264. |
In Δ ABC, D is the midpoint of AC, F is a point on AB such that CF bisects BD at E. If AF = 18 cm, then the length of BF is: |
| A. | 12 cm |
| B. | 8 cm |
| C. | 6 cm |
| D. | 9 cm |
| Answer» E. | |
| 265. |
In the given diagram ABCK is a square an M - B - L (B is between M and L). If KL = 10 cm and MK = 24 cm, then what is the length of \(\overline {AB}\) in cm? |
| A. | \(7\frac{1}{{17}}\) |
| B. | \(9\frac{1}{{17}}\) |
| C. | \(8\frac{1}{{17}}\) |
| D. | \(6\frac{1}{{17}}\) |
| Answer» B. \(9\frac{1}{{17}}\) | |
| 266. |
AB is a tangent to a circle with centre O. If the radius at the circle is 7 cm and the length of AB is 24 cm (A is outside the circle), then what is the length (in cm) of OA? |
| A. | 25 |
| B. | 26 |
| C. | 28 |
| D. | 31 |
| Answer» B. 26 | |
| 267. |
In ΔABC, D and E are the points on sides AC and BC, respectively such that DE || AB. F is a point on CE such that DF ∥ AE. If CE = 6 cm, and CF = 2.5 cm, then BC is equal to: |
| A. | 12 cm |
| B. | 15.6 cm |
| C. | 14 cm |
| D. | 14.4 cm |
| Answer» E. | |
| 268. |
In ΔABC, D is a point on BC such that \(∠ BAD = \dfrac{1}{2} ∠ ADC, ∠ BAC = 84^\circ\) and ∠C = 42°. What is the measure of ∠ADB? |
| A. | 102° |
| B. | 68° |
| C. | 94° |
| D. | 72° |
| Answer» E. | |
| 269. |
I is the incentre of ΔABC of ∠A = 46°, then ∠BIC =? |
| A. | 113° |
| B. | 124° |
| C. | 134° |
| D. | 93° |
| Answer» B. 124° | |
| 270. |
If in a ΔABC, the bisectors of ∠B and ∠C meet at O, inside the triangle. If ∠BOC = 156°, then the measure of ∠A is: |
| A. | 156° |
| B. | 132° |
| C. | 66° |
| D. | 84° |
| Answer» C. 66° | |
| 271. |
In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 cm2. What is the area (in cm2) of triangle FGE? |
| A. | 13 |
| B. | 26 |
| C. | 39 |
| D. | 52 |
| Answer» B. 26 | |
| 272. |
Point A divides segment BC in the ratio 5 : 1. Co-ordinates of B are (6,-4) and C are (0, 8). What are the co-ordinates of point A? |
| A. | (-1, 6) |
| B. | (1, -6) |
| C. | (-1, -6) |
| D. | (1, 6) |
| Answer» E. | |
| 273. |
From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is |
| A. | 225/\(\sqrt{3}\) |
| B. | 500/√3 |
| C. | 275/√3 |
| D. | 250/√3 |
| Answer» C. 275/√3 | |
| 274. |
In given parallelogram ABCD, values of x and y are equal to |
| A. | x = 25°, y = 12.5° |
| B. | x = 12.5°, y = 25° |
| C. | x = 15°, y = 15° |
| D. | x = 30°, y = 15° |
| Answer» D. x = 30°, y = 15° | |
| 275. |
ABCD is a cyclic quadrilateral and AB is the diameter of the circle. If ∠ADC = 140°, then what is the value (in degrees) of ∠BAC? |
| A. | 50 |
| B. | 70 |
| C. | 120 |
| D. | 45 |
| Answer» B. 70 | |
| 276. |
ABCD is a quadrilateral such that ∠D = 90°. A circle with centre O touches the sides AB, BC, CD and DA at P, Q, R and S, respectively. If BC = 40 cm, BP = 28 cm and CD = 25 cm, then what is the radius of the circle ? |
| A. | 5 cm |
| B. | 13 cm |
| C. | 12 cm |
| D. | 8 cm |
| Answer» C. 12 cm | |
| 277. |
In a triangle ABC, 2∠A = 3∠B = 6∠C. Then the smallest angle in the \(\triangle ABC\) is |
| A. | 60° |
| B. | 90° |
| C. | 45° |
| D. | 30° |
| Answer» E. | |
| 278. |
ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of ΔABD? |
| A. | 12 |
| B. | 6 |
| C. | 10 |
| D. | 20 |
| Answer» C. 10 | |
| 279. |
If the angles of the triangle are in the ratio 1 : 2 : 3, then what is the smallest angle? |
| A. | 15° |
| B. | 30° |
| C. | 25° |
| D. | 40° |
| Answer» C. 25° | |
| 280. |
A ladder 5 m long is placed in a room so as to reach a point 4.8 m high on a wall and on turning the ladder over to the opposite side of the wall without moving the base, it reaches a point 1.4 m high. What is the breadth of the room? |
| A. | 5.8 m |
| B. | 6 m |
| C. | 6.2 m |
| D. | 7.2 m |
| Answer» D. 7.2 m | |
| 281. |
Consider the following statements in respect of three straight lines A, B and C on a plane:1. If A and C are parallel and B and C are parallel, then A and B are parallel2. If A is perpendicular to C and B is perpendicular to C, then A and B are parallel3. If the acute angle between A and C is equal to the acute angle between B and C; then A and B are parallelWhich of the above statements are correct? |
| A. | 1, 2 and 3 |
| B. | 1 and 2 only |
| C. | 1 and 3 only |
| D. | 2 and 3 only |
| Answer» C. 1 and 3 only | |
| 282. |
In a circle, AB and CD interest each other at E. If CD = 18 cm and AE = 18 cm, ED = 6 cm, then BE = ? |
| A. | 3 cm |
| B. | 4 cm |
| C. | 8 cm |
| D. | 6 cm |
| Answer» C. 8 cm | |
| 283. |
In the figure, O is the centre of a circle of radius 29 cm, OP ⊥ AB, OQ ⊥ CD and AB is parallel CD. If AB = 40 cm and CD = 42 cm, then the length of PQ is: |
| A. | 41 cm |
| B. | 20 cm |
| C. | 32 cm |
| D. | 21 cm |
| Answer» B. 20 cm | |
| 284. |
In a circle centered at O, a tangent AP is drawn from an external point. If OA = 13 cm and OP = 5cm, then the length of tangent AP is: |
| A. | 10 cm |
| B. | 8 cm |
| C. | 18 cm |
| D. | 12 cm |
| Answer» E. | |
| 285. |
In the given figure, PQRS is a square of side 20 cm and SR is extended to point T. If the length of QT is 25 cm, then what is the distance (in cm) between the centres O1 and O2 of the two circle? |
| A. | 5√10 |
| B. | 4√10 |
| C. | 8√5 |
| D. | 16√2 |
| Answer» B. 4√10 | |
| 286. |
In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 46° and ∠EBD = 60°, then the value of x is: |
| A. | 76° |
| B. | 72° |
| C. | 78° |
| D. | 68° |
| Answer» B. 72° | |
| 287. |
In a triangle, all of its four special points are coincident. The triangle is |
| A. | right-angled triangle |
| B. | equilateral triangle |
| C. | isosceles triangle |
| D. | None of the above |
| Answer» C. isosceles triangle | |
| 288. |
In the given figure, from the point P two tangents PA and PB are drawn to a circle with centre O and radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord AB is 5 cm, then what is the value (in degrees) of ∠COD? |
| A. | 90 |
| B. | 120 |
| C. | 150 |
| D. | 135 |
| Answer» C. 150 | |
| 289. |
Consider the following statements with reference to the given figure:1. The sum of the areas of ΔAOD and ΔBOC is equal to the sum of the areas of ΔAOB and ΔDOC.2. ∠AOD = ∠BOC3. AB + BC + CD + DA > AC + BDWhich 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» C. 1 and 3 only | |
| 290. |
If the angles, in degrees, of a triangle, are x, 3x + 20 and 6x, the triangle must be |
| A. | Acute |
| B. | Right |
| C. | Isosceles |
| D. | Obtuse |
| Answer» E. | |
| 291. |
If centroid of the points (3, 5), (6, y) and (-3, 4) is (x, y), then find the values of x and y. |
| A. | \(x=2,\;y=\frac9 2\) |
| B. | \(x=\frac9 2,\;y=3\) |
| C. | x = 2, y = 3 |
| D. | x = 3, y = 2 |
| Answer» B. \(x=\frac9 2,\;y=3\) | |
| 292. |
PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. Which of the following is TRUE?I. Triangle PST is similar to Triangle PQR.II. ST = 1/2(QR)III. ST is parallel to QR. |
| A. | Only I and II |
| B. | Only II and III |
| C. | Only I and III |
| D. | All I, II and III |
| Answer» E. | |
| 293. |
PQRS is a cyclic quadrilateral. If ∠P is four times ∠R and ∠S is three ∠Q, then the sum of ∠Q and ∠R is: |
| A. | 73° |
| B. | 77° |
| C. | 81° |
| D. | 86° |
| Answer» D. 86° | |
| 294. |
In a circle, AB is the diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle. If PD = 15.3 cm, CD = 11.9 cm and AP = 30.6 cm, then the radius of the circle is: |
| A. | 7.5 cm |
| B. | 9 cm |
| C. | 8.5 cm |
| D. | 8 cm |
| Answer» D. 8 cm | |
| 295. |
In the given figure XYZ is a secant and ZT is a tangent. What is the value of X. |
| A. | 7 |
| B. | 5 |
| C. | 9 |
| D. | 8 |
| Answer» C. 9 | |
| 296. |
In a ΔABC, 2∠ABC = 9∠ACB and 2∠BAC = 7∠ACB. If AB = 8 cm, AC = 17 cm, then the length of BC is: |
| A. | 15 cm |
| B. | 8 cm |
| C. | 9 cm |
| D. | 25 cm |
| Answer» B. 8 cm | |
| 297. |
If ΔABC is right angled at B, AB = 30 and ∠ACB = 60°, then what is the value of AC? |
| A. | 20 |
| B. | 20√3 |
| C. | 40 |
| D. | 60 |
| Answer» C. 40 | |
| 298. |
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD? |
| A. | 25, 9 |
| B. | 24, 12 |
| C. | 24, 10 |
| D. | 25, 10 |
| Answer» D. 25, 10 | |
| 299. |
At what point does the line 3x + 2y = - 12 intercept the Y - axis? |
| A. | (0, 6) |
| B. | (0, - 6) |
| C. | (- 4, 0) |
| D. | (4, 0) |
| Answer» C. (- 4, 0) | |
| 300. |
ABC is an isosceles triangle such that AB = AC = 30 cm and BC = 48 cm. AD is a median to base BC. What is the length (in cm) of AD? |
| A. | 18 |
| B. | 20 |
| C. | 24 |
| D. | 32 |
| Answer» B. 20 | |