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.
| 1051. |
ΔABC is similar to ΔDEF. The area of ΔABC is 100 cm2 and the area of ΔDEF is 49 cm2. If the altitude of ΔABC = 5 cm, then the corresponding altitude of ΔDEF is: |
| A. | 4.5 cm |
| B. | 7 cm |
| C. | 3.5 cm |
| D. | 6 cm |
| Answer» D. 6 cm | |
| 1052. |
In a quadrilateral ABCD, if ∠A = 80°, ∠B = 100°, ∠C = 50°, then ∠D = _____. |
| A. | 130° |
| B. | 100° |
| C. | 110° |
| D. | 120° |
| Answer» B. 100° | |
| 1053. |
In ΔABC, ∠B = 35°, ∠C = 65° and the bisector AD of ∠BAC meets BC at D. Which of the following relation is true? |
| A. | AD > CD > BD |
| B. | AD > BD > CD |
| C. | BD > AD > CD |
| D. | None of the above |
| Answer» D. None of the above | |
| 1054. |
In triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = 9 cm, then what is CF equal to? |
| A. | 2.25 cm |
| B. | 3 cm |
| C. | 4.5 cm |
| D. | 6 cm |
| Answer» B. 3 cm | |
| 1055. |
In Δ ABC, AB = √21 cm, AC = 9 cm and BC = 2√15 cm then ∠B is |
| A. | 120° |
| B. | 60° |
| C. | 90° |
| D. | 45° |
| Answer» D. 45° | |
| 1056. |
If ΔABC ~ ΔQPR, \(\frac{{ar\;\left( {ABC} \right)}}{{ar\;\left( {{\rm{\Delta }}pQR} \right)}} = \frac{9}{4},\) AC = 12 cm, AB = 18 cm and BC = 15 cm, then PR is equal to∶ |
| A. | 20/3 cm |
| B. | 12 cm |
| C. | 8 cm |
| D. | 10 cm |
| Answer» E. | |
| 1057. |
Find the slope of the line which passes through points (1, 2) and (4, 5) |
| A. | \(\frac{4}{5}\) |
| B. | \(\frac{2}{3}\) |
| C. | \(\frac{3}{4}\) |
| D. | 1 |
| Answer» E. | |
| 1058. |
PQR is a right angled triangle in which ∠R = 90°. If RS ⊥ PQ, PR = 3 cm and RQ = 4 cm, then what is the value of RS (in cm)? |
| A. | 12/5 |
| B. | 36/5 |
| C. | 5 |
| D. | 2.5 |
| Answer» B. 36/5 | |
| 1059. |
In the given figure, EF = CE = CA, what is the value (in degrees) of ∠EAC? |
| A. | 58 |
| B. | 64 |
| C. | 72 |
| D. | 32 |
| Answer» C. 72 | |
| 1060. |
ABCD is cyclic quadrilateral. Sides AB and DC, when produced, meet at E, and sides BC and AD, when produced, meet at F. If ∠BFA = 60° ∠AED = 30°, then the measure of ∠ABC is: |
| A. | 65° |
| B. | 75° |
| C. | 70° |
| D. | 80° |
| Answer» C. 70° | |
| 1061. |
Find the area (in sq units) of the triangle formed by lines x - 3y = 0, x – y = 4 and x + y = 4. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 1062. |
P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn from P intersects the circle at point A and B such that PB = 32 cm and PA = 18 cm. The radius of the circle (in cm) is: |
| A. | 12 |
| B. | 10 |
| C. | 13 |
| D. | 8 |
| Answer» C. 13 | |
| 1063. |
ΔGHI is similar to ΔKLM. If the ratio of Perimeter of ΔGHI : Perimeter of ΔKLM = 9 : 4 and length of GH is 27 cm what is the length of the corresponding side KL? |
| A. | 12 cm |
| B. | 9 cm |
| C. | 24 cm |
| D. | 18 cm |
| Answer» B. 9 cm | |
| 1064. |
If ΔDEF is right angled at E, DE = 15 and ∠DFE = 60°, then what is the value of EF? |
| A. | 5√3 |
| B. | 5 |
| C. | 15 |
| D. | 30 |
| Answer» B. 5 | |
| 1065. |
ΔABC is right angled at B. BD is an altitude. AD = 9 cm and DC = 16 cm. What is the value of BD (in cm)? |
| A. | 6 |
| B. | 18 |
| C. | 21 |
| D. | 12 |
| Answer» E. | |
| 1066. |
In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY? (Given that QR = QY) |
| A. | 4√10 |
| B. | 2√10 |
| C. | 6√10 |
| D. | 3√5 |
| Answer» B. 2√10 | |
| 1067. |
In the adjoining figure, if ∠SPQ = 65° and ∠SQP = 70°, then, ∠PRQ = _______. |
| A. | 50° |
| B. | 35° |
| C. | 40° |
| D. | 45° |
| Answer» E. | |
| 1068. |
In a triangle, values of all the angles are integers (in degree measure). Which one of the following cannot be the proportion of their measures? |
| A. | 1 ∶ 2 ∶ 3 |
| B. | 3 ∶ 4 ∶ 5 |
| C. | 5 ∶ 6 ∶ 7 |
| D. | 6 ∶ 7 ∶ 8 |
| Answer» E. | |
| 1069. |
AB is the diameter of a circle. A point C is situated on the tangent drawn on point A. If AB = 24 cm, and AC = 7 cm then find the length of BC: |
| A. | 50 cm |
| B. | 15 cm |
| C. | 25 cm |
| D. | 26 cm |
| Answer» D. 26 cm | |
| 1070. |
In the given figure, ∠QRN = 40°, ∠PQR = 46° and MN is a tangent at R. What is the value (in degree) of X, Y and Z respectively? |
| A. | 40, 46, 94 |
| B. | 40, 50, 90 |
| C. | 46, 54, 80 |
| D. | 50, 40, 90 |
| Answer» B. 40, 50, 90 | |
| 1071. |
In the given figure, the measure of ∠BAC is: |
| A. | 56° |
| B. | 58° |
| C. | 62° |
| D. | 48° |
| Answer» E. | |
| 1072. |
In the figure given below, the radius of the circle is 6 cm and AT = 4 cm. The length of tangent PT is |
| A. | 6 cm |
| B. | 8 cm |
| C. | 9 cm |
| D. | 10 cm |
| Answer» C. 9 cm | |
| 1073. |
In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP? |
| A. | 3 + √10 : 3 – √10 |
| B. | 3 + √8 : 3 – √8 |
| C. | 3 + √3 : 3 – √3 |
| D. | 3 : √3 |
| Answer» C. 3 + √3 : 3 – √3 | |
| 1074. |
Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon? |
| A. | 3√11 – 7 |
| B. | 5√13 – 8 |
| C. | 4√7 – 11 |
| D. | 6√11 – 9 |
| Answer» B. 5√13 – 8 | |
| 1075. |
On the basis of the adjacent figure, consider the statementsI. ∠1, ∠5, and ∠2, ∠6 are pairs of corresponding angles.II. ∠4 and ∠6 are alternate angles.III. ∠1, ∠2, and ∠8, ∠7 are exterior angles.Which of the following statements are true? |
| A. | I and II |
| B. | II and III |
| C. | I and III |
| D. | I, II and III |
| Answer» E. | |
| 1076. |
In the given figure, PQR is a triangle and quadrilateral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 cm, PA = 5 cm and AD = 3 cm. What is the area (in cm2) of the quadrilateral ABCD? |
| A. | (23√21)/4 |
| B. | (15√21)/4 |
| C. | (17√21)/5 |
| D. | (23√21)/5 |
| Answer» D. (23√21)/5 | |
| 1077. |
In the following figure (not to scale) AB is the common tangent to the circles C1 and C2, where C1, and C2, are touching externally at C, AD and DC are two chords of the circle C1, and BE and EC are the two chords of the circle C2. Find the measure of ∠ADC + ∠BEC? |
| A. | 120° |
| B. | 100° |
| C. | 60° |
| D. | 90° |
| Answer» E. | |
| 1078. |
ΔABC is right angled at B. If ∠A = 30, what is the length of AB (in cm), if AC = 10 cm? |
| A. | 5 |
| B. | 5√3 |
| C. | 10√3 |
| D. | 10 |
| Answer» C. 10√3 | |
| 1079. |
How many solutions does a pair of linear equations will have, if the equations are 4x + 5y – 6 = 0 and 16x + 20y + 20 = 0? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 1080. |
In a circle, chords AD and BC meet at a point E outside the circle. If ∠BAE = 76° and ∠ADC = 102°, then ∠AEC is equal to: |
| A. | 28° |
| B. | 26° |
| C. | 24° |
| D. | 25° |
| Answer» C. 24° | |
| 1081. |
In the given figure, PQ = PS = SR and ∠QPS = 40°, then what is the value of ∠QPR (in degrees)? |
| A. | 45° |
| B. | 60° |
| C. | 75° |
| D. | 50° |
| Answer» D. 50° | |
| 1082. |
In ΔABC, ∠A = 58°. If I is the in-centre of the triangle, then the measure of ∠BIC is∶ |
| A. | 119° |
| B. | 112° |
| C. | 109° |
| D. | 123° |
| Answer» B. 112° | |
| 1083. |
ABC is a triangle right angled at C. Let p be the length of the perpendicular drawn from C on AB. If BC = 6 cm and Ca = 8 cm, then what is the value of p? |
| A. | 5.4 cm |
| B. | 5 cm |
| C. | 4.8 cm |
| D. | 4.2 cm |
| Answer» D. 4.2 cm | |
| 1084. |
ABCD is a rhombus. If ∠BCA = 66°, then ∠CAD = _____. |
| A. | 30° |
| B. | 66° |
| C. | 24° |
| D. | 33° |
| E. | 44° |
| Answer» C. 24° | |
| 1085. |
In ΔABC, D and E are the midpoints of sides BC and AC, respectively. AD and BE intersect at G at right angle. If AD = 18 cm and BE = 12 cm, then the length of DC (in cm) is: |
| A. | 10 |
| B. | 6 |
| C. | 9 |
| D. | 8 |
| Answer» B. 6 | |
| 1086. |
In the adjoining figure, ∠ADE = ∠B, AE = 8 cm, EB = 7 cm, BC = 9 cm, AD = 10 cm and DC = 2 cm, then the length DE is - |
| A. | 2.1 cm |
| B. | 6 cm |
| C. | 6.75 cm |
| D. | 7.8 cm |
| Answer» C. 6.75 cm | |
| 1087. |
In the given figure, PAQ is the tangent of the circle at point A and ABCD is a cyclic quadrilateral.If ∠CAQ = 70°, then ∠ABC is |
| A. | 70° |
| B. | 80° |
| C. | 110° |
| D. | 90° |
| Answer» D. 90° | |
| 1088. |
In what ratio does the point T(x, 0) divide the segment joining the points S(-4, -1) and U(1, 4)? |
| A. | 1 : 4 |
| B. | 4 : 1 |
| C. | 1 : 2 |
| D. | 2 : 1 |
| Answer» B. 4 : 1 | |
| 1089. |
In a circle, two equal and parallel chords are 6 cm apart and they lie on the opposite sides of the centre of the circle, whose radius is 5 cm. The length of each chord (in cm), is: |
| A. | 10 |
| B. | 12 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 1090. |
At what point does the line 5x + 3y = 15 cuts the y-axis? |
| A. | (0, 5) |
| B. | (0, -5) |
| C. | (3, 0) |
| D. | (-3, 0) |
| Answer» B. (0, -5) | |
| 1091. |
Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC, If the ratio of areas of triangle APQ : triangle ABC is 25 : 36. Then the ratio of AP : PB is ___. |
| A. | 5 : 6 |
| B. | 1 : 5 |
| C. | 6 : 5 |
| D. | 5 : 1 |
| Answer» E. | |
| 1092. |
PA and PB are two tangents to a circle with centre O, from a point P outside the circle. A and B are points on the circle. If ∠OAB = 35°, then ∠APB is equal to∶ |
| A. | 35° |
| B. | 70° |
| C. | 25° |
| D. | 20° |
| Answer» C. 25° | |
| 1093. |
If angle A of the triangle ABC is 30° and the circumradius of the triangle is 10 cm, then what is the length of side BC? |
| A. | 5 cm |
| B. | 10 cm |
| C. | 5√3 cm |
| D. | 10√3 cm |
| Answer» C. 5√3 cm | |
| 1094. |
If \(R_n (n \in N)\) is a rectangle of length \(I_n = \dfrac{1}{n}\), breadth \(b_n = \dfrac{1}{n+1}\), then the sum of areas of \(R_1, R_2, ...., R_{100}\) is: |
| A. | \(\dfrac{99}{100}\) |
| B. | \(\dfrac{101}{100}\) |
| C. | \(\dfrac{100}{101}\) |
| D. | \(\dfrac{100}{99}\) |
| Answer» D. \(\dfrac{100}{99}\) | |
| 1095. |
In ΔABC, P is a point on BC such the BP : PC = 4 : 3 and Q is the midpoint of BP. Then ar(ΔABQ) : Ar(ΔABC) is equal to: |
| A. | 1 : 5 |
| B. | 4 : 7 |
| C. | 2 : 7 |
| D. | 3 : 7 |
| Answer» D. 3 : 7 | |
| 1096. |
In ΔABC, AD bisects ∠A and intersects BC at D. If BC = a, AC = b and AB = c, then BD = ? |
| A. | ab/(b + c) |
| B. | bc/(c + a) |
| C. | ac/(b + c) |
| D. | ca/(a + b) |
| Answer» D. ca/(a + b) | |
| 1097. |
In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of the two circle. If RQ is a tangent to the circle, then what is the length (in cm) of RQ? |
| A. | 3√3 |
| B. | 2√6 |
| C. | 4√2 |
| D. | 6√2 |
| Answer» D. 6√2 | |
| 1098. |
AD and BE are medians and M is the centroid of ΔABC. AD = 18 and BE = 15 and AD is perpendicular bisector of side BC. Find the area of ΔABC. |
| A. | 132 |
| B. | 128 |
| C. | 144 |
| D. | 136 |
| Answer» D. 136 | |
| 1099. |
In ΔABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is: |
| A. | 124° |
| B. | 68° |
| C. | 54° |
| D. | 148° |
| Answer» B. 68° | |
| 1100. |
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 cm, CQ = 7 cm and AR = 6 cm, then the perimeter (in cm) of the ΔABC is: |
| A. | 37.25 |
| B. | 35 |
| C. | 37.5 |
| D. | 36 |
| Answer» E. | |