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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.
| 751. |
In the triangle, ABC, the internal bisector of angle A meets the side BC at D. If BD = 7.5 cm and BC = 9 cm. Then, calculate the value of AB: AC. |
| A. | 2 : 1 |
| B. | 1 : 2 |
| C. | 5 : 1 |
| D. | 1 : 3 |
| Answer» D. 1 : 3 | |
| 752. |
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 = 6.5 cm, CQ = 4.5 cm and AR = 5.5 cm, then the perimeter (in cm) of the triangle ∆ABC is: |
| A. | 16.5 |
| B. | 66 |
| C. | 33 |
| D. | 22 |
| Answer» D. 22 | |
| 753. |
In the given figure, TB passes through centre O. What is the radius of the circle? |
| A. | (2√5)/3 |
| B. | (3√2)/5 |
| C. | (3√5)/2 |
| D. | (2√3)/5 |
| Answer» D. (2√3)/5 | |
| 754. |
ABC is a triangle. Find the locus of a point P which moves such that area of ΔABC = area of ΔPBC. |
| A. | A line parallel to AC and passing through B |
| B. | A line parallel to BC and passing through A |
| C. | Perpendicular bisector of the side BC |
| D. | Median of the side BC from A |
| Answer» C. Perpendicular bisector of the side BC | |
| 755. |
Negation of ‘All triangles are equilateral triangles’ is |
| A. | All triangles are not equilateral |
| B. | All equilateral triangles are not triangles |
| C. | There exists a triangle which is not an equilateral triangle |
| D. | All of these |
| Answer» D. All of these | |
| 756. |
If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is |
| A. | A straight line |
| B. | A circle |
| C. | Perpendicular bisector of AB |
| D. | An arbitrary curve |
| Answer» C. Perpendicular bisector of AB | |
| 757. |
Given below are two statementsStatement I: Sum of the angles of a triangle is 180°Statement II: The sum of any two sides of a triangle is greater than the third sideIn 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» B. Both Statement I and Statement II are false | |
| 758. |
ABCDA is a con-cyclic quadrilateral of a circle ABCD with radius r and centre at O. If AB is the diameter and CD is parallel and half of AB and if the circle completes one rotation about the centre O, then the locus of the middle point of CD is a circle of radius: |
| A. | 3r/2 |
| B. | 2r/3 |
| C. | 2√3r/3 |
| D. | √3r/2 |
| Answer» E. | |
| 759. |
In the given figure, PQR is an equilateral triangle and diameter PS is the angle bisector of ∠P. What is the value of RT : RQ? |
| A. | 1 : 2 |
| B. | 1 : 1 |
| C. | 2 : 1 |
| D. | 1 : 3 |
| Answer» C. 2 : 1 | |
| 760. |
PA and PB are tangents to a circle with centre O, from a point P outside the circle, and A and B are points on the circle. If ∠APB = 40°, then ∠OAB is equal to: |
| A. | 25° |
| B. | 40° |
| C. | 20° |
| D. | 50° |
| Answer» D. 50° | |
| 761. |
If one of the interior angles of a regular polygon is found to be 9 / 8 times of one of the interior angles of a regular hexagon, then the number of sides of the polygon is? |
| A. | 12 |
| B. | 10 |
| C. | 14 |
| D. | 8 |
| Answer» E. | |
| 762. |
D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD : DB = 2 : 3 and area of ΔADE is 4 sq cm, what is the area (in sq cm) of quadrilateral BDEC. |
| A. | 25 |
| B. | 21 |
| C. | 5 |
| D. | 9 |
| Answer» C. 5 | |
| 763. |
Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that ofABCD and CG is longer than EB, then the ratio of length of EB to that of CG is |
| A. | 3 :8 |
| B. | 2 : 5 |
| C. | 1 : 3 |
| D. | 4 : 0 |
| Answer» D. 4 : 0 | |
| 764. |
In a circle of radius 10 cm, PQ and RS are two parallel chords of lengths 16 cm and 12 cm, respectively. What is the distance between the chords if they are on opposite sides of the centre? |
| A. | 14 cm |
| B. | 2 cm |
| C. | 6 cm |
| D. | 8 cm |
| Answer» B. 2 cm | |
| 765. |
If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA) ∶ (PG - GA)? |
| A. | 4 ∶ 1 |
| B. | 3 ∶ 1 |
| C. | 2 ∶ 1 |
| D. | 3 ∶ 2 |
| Answer» C. 2 ∶ 1 | |
| 766. |
For the figure given below, find the value (in degrees) of 2∠A + ∠B. |
| A. | 180° |
| B. | 202.5° |
| C. | 250° |
| D. | 279° |
| Answer» C. 250° | |
| 767. |
In ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC = __________. |
| A. | 120° |
| B. | 100° |
| C. | 110° |
| D. | 105° |
| Answer» B. 100° | |
| 768. |
If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the largest angle.A. 36° B. 96° C. 84° D. 60° |
| A. | A |
| B. | C |
| C. | D |
| D. | B |
| Answer» E. | |
| 769. |
A rhombus is formed by joining midpoints of the sides of a rectangle in suitable order. If the area of the rhombus is 2 square units, then the area of the rectangle is |
| A. | 2√2 square units |
| B. | 4 square units |
| C. | 4√2 square units |
| D. | 8 square units |
| Answer» C. 4√2 square units | |
| 770. |
A closed polygon has six sides and one of its angles is 30° greater than each of the other five equal angles. What is the value of the equal angles? |
| A. | 55° |
| B. | 115° |
| C. | 150° |
| D. | 175° |
| Answer» C. 150° | |
| 771. |
Consider the two equiangular triangles ABC and DEF having medians as AL and DM respectively as shown in figure below. |
| A. | \(\frac{{BC}}{{EF}} = \frac{{DM}}{{AL}}\) |
| B. | \(\frac{{BC}}{{EF}} = \frac{{AL}}{{DM}}\) |
| C. | \(\frac{{EF}}{{BC}} = \frac{{AL}}{{DM}}\) |
| D. | All options are correct |
| Answer» C. \(\frac{{EF}}{{BC}} = \frac{{AL}}{{DM}}\) | |
| 772. |
In ΔABC, the perpendiculars are drawn from A, B and C to meet the opposite sides at D, E and F, respectively AD, BE and CF intersect at point p. If ∠EPD = 116° and the bisectors of ∠A and ∠B meet at Q, then the measure of ∠AQB is: |
| A. | 96° |
| B. | 64° |
| C. | 124° |
| D. | 122° |
| Answer» E. | |
| 773. |
If one angle of a parallelogram is 21° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is: |
| A. | 113° |
| B. | 159° |
| C. | 103° |
| D. | 112° |
| Answer» B. 159° | |
| 774. |
A unique circle can always be drawn through x number of given non – collinear points, then x must be∶ |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 1 |
| Answer» C. 4 | |
| 775. |
A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 8 cm and PB = 21 cm, then the radius of the circle is: |
| A. | 10 cm |
| B. | 12 cm |
| C. | 11 cm |
| D. | 15 cm |
| Answer» D. 15 cm | |
| 776. |
For the circle shown below, find the length (in cm) of the largest chord of the circle. |
| A. | 8 |
| B. | 12 |
| C. | 16 |
| D. | 18 |
| Answer» D. 18 | |
| 777. |
A circle passing through points Q and R of triangle PQR, cut the sides PQ and PR at point X and Y respectively. If PQ = PR, then what is the value (in degrees) of ∠PRQ + ∠QXY? |
| A. | 120 |
| B. | 150 |
| C. | 240 |
| D. | 180 |
| Answer» E. | |
| 778. |
If (3, 2), (6, 3), (x. y) and (6, 5) are the vertices of a parallelogram, the (x, y) is: |
| A. | (5, 6) |
| B. | (9, 6) |
| C. | (9, 8) |
| D. | (8, 7) |
| Answer» C. (9, 8) | |
| 779. |
PQRST is a regular pentagon. If PR and QT intersects each other at X, then what is the value (in degrees) of ∠TXR? |
| A. | 98 |
| B. | 90 |
| C. | 72 |
| D. | 108 |
| Answer» E. | |
| 780. |
One angle of a triangle is 55 If the other two angles are in the ratio 9 : 16, find the angles?A. 65 and 115B. 90 and 160C. 55 and 165D. 45 and 80 |
| A. | B |
| B. | C |
| C. | A |
| D. | D |
| Answer» E. | |
| 781. |
If O be the incentre of a triangle ABC and ∠BOC = 110°, then value of ∠BAC will be |
| A. | 40° |
| B. | 55° |
| C. | 110° |
| D. | 20° |
| Answer» B. 55° | |
| 782. |
A circle is inscribed in an equilateral triangle of side 20 cm, touching its sides. What is the area of the circle? |
| A. | 50π cm2 |
| B. | 50π/3 cm2 |
| C. | 100π/3 cm2 |
| D. | 100π cm2 |
| Answer» D. 100π cm2 | |
| 783. |
(-5, 5) ; (x, 10) ; (10, 6) ; (-2, 1) are the co-ordinates of the vertices of a parallelogram. Find x. |
| A. | -4 |
| B. | -2 |
| C. | 7 |
| D. | 5 |
| Answer» D. 5 | |
| 784. |
If the equations x - 2y = 3 and 2x + by = 6 represent the same line, then the value of b is |
| A. | 4 |
| B. | -4 |
| C. | -2 |
| D. | None of these |
| Answer» C. -2 | |
| 785. |
In what ratio is the segment joining (-1, 3) and (2, -4) divided by the Y axis? |
| A. | 2 : 1 |
| B. | 1 : 4 |
| C. | 1 : 2 |
| D. | 4 : 1 |
| Answer» D. 4 : 1 | |
| 786. |
In E is a point inside the quadrilateral ABCD where DE and CE is the angle bisector of ∠D and ∠C respectively. If ∠B is 82° and ∠DEC is 80°, then find the ∠A. |
| A. | 84° |
| B. | 78° |
| C. | 81° |
| D. | 75° |
| Answer» C. 81° | |
| 787. |
If a regular polygon has 16 sides, then what is the measure (in degrees) of its each interior angle? |
| A. | 155 |
| B. | \(159 \frac{1}{2}\) |
| C. | \(157 \frac{1}{2}\) |
| D. | 154 |
| Answer» D. 154 | |
| 788. |
In the circle above, chord \(\overline {AB} \) is extended to meet the tangent \(\overline {DE}\) at D. If \(\overline {AB} \; = \;5\;cm\) and \(\overline {DE} \; = \;6\;cm,\) find the length of \(\overline {BD} \). |
| A. | 6 cm |
| B. | √30 cm |
| C. | 4 cm |
| D. | 5 cm |
| Answer» D. 5 cm | |
| 789. |
In the given figure, the arms of two angles are parallel, If ∠DEF = 34°, then ∠ABC = ______. |
| A. | 27° |
| B. | 17° |
| C. | 34° |
| D. | 68° |
| Answer» D. 68° | |
| 790. |
A circle can have ______ parallel tangents at the most. |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | Infinite |
| Answer» D. Infinite | |
| 791. |
In Δ ABC, ∠C = 70°. The bisectors of ∠A and < B meet BC and AC in points D and E, respectively. AD and BE intersect each other at P. What is the measure of ∠DPB? |
| A. | 55° |
| B. | 65° |
| C. | 35° |
| D. | 45° |
| Answer» B. 65° | |
| 792. |
If two complementary angles are in the ratio of 2 : 3, find the ratio of the square of the smaller angle to the square of the greater angle. |
| A. | 3 : 2 |
| B. | 9 : 11 |
| C. | 4 : 5 |
| D. | 4 : 9 |
| Answer» E. | |
| 793. |
A line touches a circle of radius 6 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel, then the distance between them is: |
| A. | 6 cm |
| B. | 10 cm |
| C. | 8 cm |
| D. | 12 cm |
| Answer» E. | |
| 794. |
If ΔLMN and ΔUVW are similar triangles, the value of side S is: |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 9 |
| Answer» D. 9 | |
| 795. |
If ∠A = 60º, then ∠BOC = ______. |
| A. | 100° |
| B. | 120° |
| C. | 80° |
| D. | 60° |
| Answer» C. 80° | |
| 796. |
In triangles ABC and DEF, ∠C = ∠F, AC = DF, and BC = EF. If AB = 2x - 1 and DE = 5x - 4, then the value of x is |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 1 |
| Answer» E. | |
| 797. |
In the triangle given below, D and E are mid points of AF and AG respectively, F and G are mid points of AB and AC respectively. If DE = 2.4 cm, then BC is equal to∶ |
| A. | 9.6 cm |
| B. | 7.2 cm |
| C. | 4.8 cm |
| D. | 3.6 cm |
| Answer» B. 7.2 cm | |
| 798. |
If each interior angle of a regular polygon is \({\left( {128\frac{4}{7}} \right)^0}\), then what is the sum of the number of its diagonals and the number of its sides? |
| A. | 17 |
| B. | 19 |
| C. | 21 |
| D. | 15 |
| Answer» D. 15 | |
| 799. |
Let S be the parallelogram obtained by joining the mid-points of the parallelogram T. Consider the following statements :1. The ratio of the area of T to that of S is 2 : 1.2. The perimeter of S is half of the sum of diagonals of T.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» B. 2 only | |
| 800. |
In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is: |
| A. | 3 |
| B. | 4.5 |
| C. | 5 |
| D. | 4 |
| Answer» D. 4 | |