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.
| 901. |
In figure ∠XYZ = 64° and XY is produced to point P. If ray YQ bisect ∠ZYP, then the value of ∠XYQ is - |
| A. | 122° |
| B. | 105° |
| C. | 116° |
| D. | 302° |
| Answer» B. 105° | |
| 902. |
In a triangle PQR, PX bisects QR. PX is the angle bisector of angle P. If PQ = 12 cm and QX = 3 cm, then what is the area (in cm2) of triangle PQR? |
| A. | 12√3 |
| B. | 8√15 |
| C. | 18√2 |
| D. | 9√15 |
| Answer» E. | |
| 903. |
A square is inscribed in a quarter circle in such a way that two of its vertices on the radius are equidistant from the centre and one vertice lie on the circumference. If the side of square is √(5/2) cm, then what is the radius (in cm) of the circle? |
| A. | √5 |
| B. | √3 |
| C. | √2 |
| D. | √7 |
| Answer» B. √3 | |
| 904. |
In the given figure, \(\overline {PQ} \parallel \overline {LM} \), if ∠PAB = 45°, ∠BCL = 62°, then how much is ∠CBA ? |
| A. | 97° |
| B. | 107° |
| C. | 117° |
| D. | 127° |
| Answer» C. 117° | |
| 905. |
In right angle ΔABC, AB = c cm, AC = b cm and CB = a cm. If ∠ A = 2∠B, then which of the following is true? |
| A. | a2 = b2 – bc |
| B. | a2 = b2 – ac |
| C. | a2 = b2 + bc |
| D. | a2 = b2 + ac |
| Answer» D. a2 = b2 + ac | |
| 906. |
PA and PB are two tangents from a point P outside the circle with center O at the point A and B on it. If ∠APB = 130°, then ∠OAB is equal to: |
| A. | 45° |
| B. | 65° |
| C. | 35° |
| D. | 50° |
| Answer» C. 35° | |
| 907. |
A geometric representation, showing the relationship between a whole and its part, is— |
| A. | histogram |
| B. | pie chart |
| C. | bar graph |
| D. | pictograph |
| Answer» C. bar graph | |
| 908. |
In the following figure, O is the centre of the circle and D, E and F are the mid points of AB, BO and OA respectively. If ∠DEF = 30°, thea find ∠ACB. |
| A. | 120° |
| B. | 30° |
| C. | 60° |
| D. | 90° |
| Answer» D. 90° | |
| 909. |
In the given figure, AB, AC and EF are tangents to a circle. If AC = 15 cm and DE = 3 cm, then the length of AE is: |
| A. | 12 cm |
| B. | 24 cm |
| C. | 18 cm |
| D. | 9 cm |
| Answer» B. 24 cm | |
| 910. |
If the length of a chord AB is equal to the radius OA of a circle, then ∠AOB = ______, |
| A. | 75° |
| B. | 30° |
| C. | 90° |
| D. | 60° |
| Answer» E. | |
| 911. |
ΔABC is similar to ΔPQR. Length of AB is 36 cm and length of the corresponding side PQ is 16 cm. If area of ΔABC is 1296 sq cm, what is the area of ΔPQR? |
| A. | 128 sq cm |
| B. | 512 sq cm |
| C. | 64 sq cm |
| D. | 256 sq cm |
| Answer» E. | |
| 912. |
In ΔABC, D and E are the points on sides AB and BC respectively such that DE∥ AC. If AD ∶ DB = 5 ∶ 3, then what is the ration of the area of ΔBDE to that of the trapezium ACED? |
| A. | 1 ∶ 6 |
| B. | 4 ∶ 25 |
| C. | 9 ∶ 55 |
| D. | 9 ∶ 64 |
| Answer» D. 9 ∶ 64 | |
| 913. |
In the circle below, chord \(\overline {AB}\) is extended to meet the tangent \(\overline {DE}\) at D. If \(\overline {AB}\) = 9 cm and \(\overline {BD}\) = 3 cm, find the length of \(\overline {DE}\). |
| A. | 5 cm |
| B. | 4 cm |
| C. | \(\sqrt {27} cm\) |
| D. | 6 cm |
| Answer» E. | |
| 914. |
In ΔPQR, QT ⊥ PR and S is a point on QR such that ∠PSQ = p°. If ∠TQR = 46° and ∠SPR = 32°, then the value of p is∶ |
| A. | 72° |
| B. | 82° |
| C. | 76° |
| D. | 78° |
| Answer» D. 78° | |
| 915. |
If the sides of a triangle are in the ratio 3 ∶ \(1\frac{1}{4}\) ∶ \(3\frac{1}{4}\), then the triangle is- |
| A. | Right-angled triangle |
| B. | Obtuse-angled triangle |
| C. | Acute-angled triangle |
| D. | Isosceles triangle |
| Answer» B. Obtuse-angled triangle | |
| 916. |
In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 3 : 2 and HF is 8 cm, then the length of DF is |
| A. | 12 cm |
| B. | 20 cm |
| C. | 14 cm |
| D. | 16 cm |
| Answer» C. 14 cm | |
| 917. |
In the given figure, if ∠ABC = 90°, and ∠A = 30°, then ∠ACD = ? |
| A. | 120° |
| B. | 110° |
| C. | 130° |
| D. | 100° |
| Answer» B. 110° | |
| 918. |
PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the in-radius of triangle PQR? |
| A. | 5/√3 |
| B. | 10√3 |
| C. | 10/√3 |
| D. | 5√2 |
| Answer» B. 10√3 | |
| 919. |
ABC is an equilateral triangle. O is the point of intersection of altitudes AL, BM and CN. If OA = 16 cm, then what is the semi-perimeter (in cm) of the triangle ABC? |
| A. | 8√3 |
| B. | 12√3 |
| C. | 16√3 |
| D. | 24√3 |
| Answer» E. | |
| 920. |
A rectangle ABCD is inscribed in a circle with centre O. Its diagonal CA is produced to a point E, outside the circle. ED is a tangent to the circle at D. If AC = 2BC, then what is the measure of ∠DEC? |
| A. | 30° |
| B. | 60° |
| C. | 40° |
| D. | 45° |
| Answer» B. 60° | |
| 921. |
Consider the following two triangles as shown in the figure below.Choose the correct statement for the above situation. |
| A. | ∆BAC ~ ∆NMP |
| B. | ∆BAC ~ ∆MNP |
| C. | ∆CAB ~ ∆NMP |
| D. | ∆BAC ~ ∆PMN |
| Answer» C. ∆CAB ~ ∆NMP | |
| 922. |
In the given figure, ∠DBC = 65°, ∠BAC = 35° and AB = BC, then the measure of ∠ECD is equal to: |
| A. | 65° |
| B. | 50° |
| C. | 45° |
| D. | 55° |
| Answer» D. 55° | |
| 923. |
In the given figure ΔABC, if θ = 80°, the measure of each of the other two angles will be: |
| A. | 50° |
| B. | 80° |
| C. | 40° |
| D. | 60° |
| Answer» B. 80° | |
| 924. |
In the given figure, if ∠KLN = 58°, then ∠KMN = ? |
| A. | 58° |
| B. | 32° |
| C. | 26° |
| D. | 42° |
| Answer» B. 32° | |
| 925. |
In the given figure, ABC is a right angle triangle. ∠ABC = 90° and ∠ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle? |
| A. | 4 |
| B. | 6 |
| C. | 4.5 |
| D. | 7.5 |
| Answer» C. 4.5 | |
| 926. |
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 = 30°, then ∠OAB is equal to: |
| A. | 40° |
| B. | 15° |
| C. | 50° |
| D. | 25° |
| Answer» C. 50° | |
| 927. |
In ΔABC, P is a point on BC such that BP : PC = 2 : 3 and Q is the midpoint of BP. Then ar(ΔABQ) : ar(ΔABC) is equal to: |
| A. | 1 : 4 |
| B. | 2 : 5 |
| C. | 1 : 5 |
| D. | 2 : 3 |
| Answer» D. 2 : 3 | |
| 928. |
A tangent touches the circle at _______. |
| A. | one point |
| B. | the centre point |
| C. | 2 points |
| D. | infinitely many points |
| Answer» B. the centre point | |
| 929. |
If medians of a triangle have lengths 18 cm, 24 cm and 30 cm, then what is the area (in cm2) of the triangle? |
| A. | 24√6 |
| B. | 244 |
| C. | 288 |
| D. | 360 |
| Answer» D. 360 | |
| 930. |
In the given figure, if RS = 3√3 cm and RPS is an equilateral triangle, then find the value of QR |
| A. | 6√3 cm |
| B. | 6 cm |
| C. | 12√3 cm |
| D. | 24 cm |
| Answer» C. 12√3 cm | |
| 931. |
In the given figure, AB || CD, ∠ABO = 100°, and ∠OCD = 110°, then ∠BOC = ___. |
| A. | 80° |
| B. | 60° |
| C. | 70° |
| D. | 30° |
| Answer» E. | |
| 932. |
In a triangle PQR, ∠PQR = 90°, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle? |
| A. | 9 |
| B. | 4 |
| C. | 8 |
| D. | 6 |
| Answer» C. 8 | |
| 933. |
Δ LMN is right angled at M. If m∠N = 45°. What is the length of MN (in cm), if NL = 8 cm? |
| A. | 8√2 |
| B. | 4/√2 |
| C. | 4√2 |
| D. | 4 |
| Answer» D. 4 | |
| 934. |
It is given that ΔABC ~ ΔEDF and Area ΔABC : Area ΔEDF = 64 : 25. If AB = 16 cm, BC = 18 cm, CA = 20 cm. What is the value of EF (in cm)? |
| A. | 15 |
| B. | 12.5 |
| C. | 11.25 |
| D. | 10 |
| Answer» C. 11.25 | |
| 935. |
In a ΔABC, DE is parallel to BC where D and E are the points on AB and AC, respectively and AD = 4 cm, DB = 8 cm, AE = 3 cm. Length of EC is: |
| A. | 5 cm |
| B. | 6 cm |
| C. | 9 cm |
| D. | 7 cm |
| Answer» C. 9 cm | |
| 936. |
Consider the following diagram:An equilateral triangle is inscribed in a circle of radius 1 unit. The area of the shaded region, in square unit, is |
| A. | \(\frac{\pi }{3} - \frac{{\sqrt 3 }}{4}\) |
| B. | \(\frac{\pi }{3} - \frac{1}{2}\) |
| C. | \(\frac{\pi }{3} - \frac{3}{4}\) |
| D. | \(\frac{\pi }{3} - 1\;\) |
| Answer» B. \(\frac{\pi }{3} - \frac{1}{2}\) | |
| 937. |
ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and ∠ADC = 155°, then what is the measure of ∠BAC? |
| A. | 35° |
| B. | 55° |
| C. | 65° |
| D. | 45° |
| Answer» D. 45° | |
| 938. |
In the given figure, O is the centre of the circle and DCE = 45°. If CD = 10√2cm, then what is the length (in cm) of AC. CB = BD |
| A. | 14 |
| B. | 15.5 |
| C. | 18.5 |
| D. | 20 |
| Answer» D. 20 | |
| 939. |
ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true? |
| A. | BP = PC |
| B. | BP > PC |
| C. | BP < PC |
| D. | BP = PC/2 |
| Answer» B. BP > PC | |
| 940. |
If P(9a – 2, –b) divides line segment joining the points A(3a + 1, –3) and B(8a, 5) in the ratio 3 ∶ 1, then the values of a and b are - |
| A. | a = 1, b = 3 |
| B. | a = -1, b = 3 |
| C. | a = -1, b = -3 |
| D. | a = 1, b = -3 |
| Answer» E. | |
| 941. |
Consider the circle as shown in the figure and choose the CORRECT option for this case. |
| A. | QC ∥ PB |
| B. | QC is never parallel to PB |
| C. | QC = 1/2 × PB |
| D. | QC ∥ PB, QC = 1/2 × PB |
| Answer» B. QC is never parallel to PB | |
| 942. |
From a point P which is at a distance of 10 cm from the centre O of a circle of radius 6 cm, a pair of tangents PQ and PR to the circle at point Q and R, respectively, are drawn. The area of the quadrilateral PQOR is equal to |
| A. | 30 sq.cm |
| B. | 40 sq.cm |
| C. | 24 sq.cm |
| D. | 48 sq.cm |
| Answer» E. | |
| 943. |
In ΔABC, AB = 8 cm. ∠A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA? |
| A. | 12 cm |
| B. | 12.5 cm |
| C. | 10.5 cm |
| D. | 10 cm |
| Answer» E. | |
| 944. |
If the interior angle of a regular polygon is 108°, then it is a |
| A. | Octagon |
| B. | Hexagon |
| C. | Pentagon |
| D. | Tetragon |
| Answer» D. Tetragon | |
| 945. |
Find the area of triangle (in sq units) enclosed by y = 0, x + 6 = 0 and 2x - 3y = 6. |
| A. | 9 |
| B. | 16 |
| C. | 20 |
| D. | 27 |
| Answer» E. | |
| 946. |
A circle is inscribed in quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and ∠B = 90°. If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle? |
| A. | 18π |
| B. | 20π |
| C. | 15π |
| D. | 12π |
| Answer» B. 20π | |
| 947. |
In a circle with centre O, an arc ABC subtends an angle of 110° at the centre of the circle. The chord AB is produced to a point P. Then ∠CBP is equal to: |
| A. | 70° |
| B. | 55° |
| C. | 60° |
| D. | 65° |
| Answer» C. 60° | |
| 948. |
In ΔPQR, O is the in-center and ∠R = 42 °. Find the measure of ∠QOP. |
| A. | 121° |
| B. | 138° |
| C. | 111° |
| D. | 132° |
| Answer» D. 132° | |
| 949. |
If the two sides of an acute angled triangle is 8 cm and 15 cm and the length of the third side is x, then |
| A. | 13 < x < 17 |
| B. | 7 < x < 1 |
| C. | √161 < x < 17 |
| D. | 7 < x < 23 |
| Answer» D. 7 < x < 23 | |
| 950. |
In the given figure, XYZ is an equilateral triangle, ∠XAY = 40°, ∠XBZ = 30° then ∠AXB is equal to∶ |
| A. | 110° |
| B. | 60° |
| C. | 80° |
| D. | 90° |
| Answer» B. 60° | |