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MCQOPTIONS
This section includes 1900 Mcqs, each offering curated multiple-choice questions to sharpen your 9th Class knowledge and support exam preparation. Choose a topic below to get started.
| 1151. |
In the shown figure, PQRS is a trapezium and\[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{RS}\]. If M is the mid- point of PS such that \[\mathbf{MN}\text{ }\parallel \text{ }\mathbf{RS}\] and \[\mathbf{PQ}\text{ }=\text{ }\mathbf{8}\text{ }\mathbf{cm}\] and \[\mathbf{RS}=\text{ }\mathbf{12cm}\], then MN equals to ______ |
| A. | 6 cm |
| B. | 8 cm |
| C. | 10 cm |
| D. | 8.5 cm |
| E. | None of these |
| Answer» D. 8.5 cm | |
| 1152. |
The intercepts made by 3 parallel lines on a transverse line \[({{l}_{1}})\] are in the ratio 1:1. A second transverse line \[({{l}_{2}})\] making angle of \[30{}^\circ \] with \[{{l}_{1}}\] is drawn. The corresponding intercepts on \[{{l}_{2}}\] are in the ratio |
| A. | 1 : 1 |
| B. | 2 : 1 |
| C. | 1:2 |
| D. | 1 : 3 |
| Answer» B. 2 : 1 | |
| 1153. |
In the shown figure, PQRS is a trapezium where \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{RS}\] and M and N are the mid-points of PR and SQ respectively. If \[\mathbf{PQ}\text{ }=\text{ }\mathbf{7}\text{ }\mathbf{cm}\]and \[\mathbf{RS}\text{ }=\text{ }\mathbf{3cm}\] then the length of MN is ________ |
| A. | 1 cm |
| B. | 2 cm |
| C. | 3 cm |
| D. | 4 cm |
| E. | None of these |
| Answer» C. 3 cm | |
| 1154. |
The sides of a triangle are 5 cm, 6 cm and 7 cm. One more \[\Delta \] is formed by joining the midpoints of the sides. The perimeter of the second \[\Delta \] is |
| A. | 18 cm |
| B. | 12 cm |
| C. | 9 cm |
| D. | 6 cm |
| Answer» D. 6 cm | |
| 1155. |
MNOP is a rhombus in which the diagonal OM is produced to Q. If\[\angle \mathbf{POQ}=\text{ }\mathbf{140}{}^\circ \], then which one is correct? |
| A. | \[x=60{}^\circ \] |
| B. | \[y=50{}^\circ \] |
| C. | \[z=50{}^\circ \] |
| D. | All of the above |
| E. | None of these |
| Answer» D. All of the above | |
| 1156. |
If D is any point on the side BC of \[\Delta ABC\] such that \[\Delta ADB\] and \[\Delta ADC\] are equal in area, then |
| A. | AD is the median |
| B. | AD is the altitude |
| C. | AD is an angle bisector |
| D. | AD is any line |
| Answer» B. AD is the altitude | |
| 1157. |
In the given triangle PQR, another triangle MLN is drawn by joining the mid-points of the sides of \[\Delta \]PQR. Based on this information choose the correct one among the following. |
| A. | \[\angle LMN=\angle QPR\] |
| B. | \[\angle LNM=\text{ }\angle RPQ\] |
| C. | \[\angle MLN=\angle QRP\] |
| D. | All the above |
| E. | None of these |
| Answer» C. \[\angle MLN=\angle QRP\] | |
| 1158. |
If in a triangles XYZ, P, Q are points on XY, YZ respectively such that XP = 2PY, XQ = 2QZ, then the ratio, area of\[\phi \]area of \[x,y,z\], is |
| A. | 4 : 9 |
| B. | 2 : 3 |
| C. | 3 : 2 |
| D. | 9 : 4 |
| Answer» B. 2 : 3 | |
| 1159. |
If PQR is a triangle and M is the mid-point of QR and the perpendiculars from M to PQ and PR are equal, then PQR is _______ |
| A. | an equilateral triangle |
| B. | an isosceles triangle |
| C. | not an equilateral triangle |
| D. | not an isosceles triangle |
| E. | None of these |
| Answer» C. not an equilateral triangle | |
| 1160. |
If in triangles PQR and LMN, \[\angle P=\angle M=60{}^\circ \], \[\text{PQ}\,\,\text{:}\,\,\text{ML}\,\,\text{=}\,\,\text{PR}\,\,\text{:}\,\text{ MN}\] and \[\angle N=55{}^\circ \], then \[\angle \text{Q}\] is |
| A. | \[50{}^\circ \] |
| B. | \[55{}^\circ \] |
| C. | \[65{}^\circ \] |
| D. | \[75{}^\circ \] |
| Answer» D. \[75{}^\circ \] | |
| 1161. |
PQR is a triangle in which\[\angle \mathbf{Q}\text{ }=\text{ }\mathbf{2}\angle \mathbf{R}\]. If a line PS is drawn from vertex P such that it bisects \[\angle \mathbf{QPR}\] and cuts QR at S such that \[\mathbf{PQ}\text{ }=\text{ }\mathbf{RS}\], then \[\angle \mathbf{QPR}\text{ }+\text{ }\angle \mathbf{QRP}\] equals to __________ |
| A. | \[72{}^\circ \] |
| B. | \[136{}^\circ \] |
| C. | \[108{}^\circ \] |
| D. | \[130{}^\circ \] |
| E. | None of these. |
| Answer» D. \[130{}^\circ \] | |
| 1162. |
The four triangle formed by joining the mid- points of the sides of a triangle respectively are |
| A. | similar, not necessarily congruent. |
| B. | congruent. |
| C. | equilateral. |
| D. | isosceles. |
| Answer» C. equilateral. | |
| 1163. |
In a triangle, other than an equilateral triangle, angle opposite to the largest side is _________ |
| A. | lesser than \[\frac{2}{3}\]of a right angle. |
| B. | greater than \[\frac{2}{3}\]of a right angle. |
| C. | always greater than a right angle. |
| D. | lesser than\[\frac{1}{2}\]of a right angle. |
| E. | None of these |
| Answer» C. always greater than a right angle. | |
| 1164. |
The triangle ABC and PQR may not be congruent when |
| A. | \[AB=PQ,\text{ }AC=PR,~\text{ }\,\angle A\,=\,\angle P\] |
| B. | AB = PQ, AC = PR, Altitude AD = Altitude PS |
| C. | \[AB=PQ,\,\,AC=PR,~\text{ }\angle B\,\,=\,\,\angle Q\] |
| D. | \[\angle A\,\,=\,\,\angle P,\,\,\angle B\,=\,\,\angle Q\,\,Altitude\,\,AD=Altitude\,\,PS\] |
| Answer» E. | |
| 1165. |
ABC is a triangle. A line PQ intersects the sides AB and AC in points P and Q such that \[\frac{AP}{PB}=\frac{AQ}{QC}=\frac{m}{n}.\,\,\,m,\,\,n\] being positive integers. The line PQ will pass through the centre of gravity of the triangle if the value of m, n respectively is |
| A. | 2, 3 |
| B. | 1 , 2 |
| C. | 1 , 3 |
| D. | 2, 1 |
| Answer» E. | |
| 1166. |
In the \[\angle ABC,\] BD bisects \[\angle B\], and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y: |
| A. | \[6,\text{ }12\] |
| B. | \[10,\text{ }12\] |
| C. | \[16,\text{ }8\] |
| D. | \[8,\text{ }15\] |
| E. | None of these |
| Answer» D. \[8,\text{ }15\] | |
| 1167. |
In \[\Delta \,ABC\], \[AB=AC\] and AD is the median. Find which of the points lies on AD. (i) Centroid(ii) Incentre(iii) Circumcentre (iv) Orthocentre Correct answer is |
| A. | (i), (ii), (iii) |
| B. | (i), (ii), (iv) |
| C. | (ii) (iii), (iv) |
| D. | (i), (ii) (iii) (iv) |
| Answer» E. | |
| 1168. |
Match List-I with List-II and select the correct answer using the codes given below the lists: List-I (Set of lines)List-II (Intersection points of the set of lines)A. Median lines1. circumcentreB. Altitude lines2. incentreC. Bisectors of angles3. orthocentreD. Perpendicular bisectors of the sides4. centroid |
| A. | A-3 B-4 C-1 D-2 |
| B. | A-4 B-3 C-2 D-1 |
| C. | A-1 B-2 C-3 D-4 |
| D. | A-2 B-1 C-4 D-3 |
| Answer» C. A-1 B-2 C-3 D-4 | |
| 1169. |
If D, E, F are the midpoints of the sides BC, CA, AB respectively of \[\Delta \,ABC\], then the ratio area \[\Delta \,DEF\]: area \[\Delta \,ABC\] is equal to |
| A. | 0.0430555555555556 |
| B. | 0.04375 |
| C. | 0.0854166666666667 |
| D. | 0.0444444444444444 |
| Answer» E. | |
| 1170. |
In the given figure, if AL is the bisector of \[\Delta \,ABC\], then AB is a |
| A. | 7 cm |
| B. | 10 cm |
| C. | 15 cm |
| D. | 22.50 cm |
| Answer» C. 15 cm | |
| 1171. |
If in a quadrilateral, the diagonals bisect each other, then which one of the following conclusions about the quadrilateral is the most appropriate one? |
| A. | It is a parallelogram |
| B. | It is a square |
| C. | It is a rectangle |
| D. | None of these |
| Answer» B. It is a square | |
| 1172. |
P and Q are the mid points of the sides AB and BC respectively of the triangle ABC, right-angled at B, then |
| A. | \[\text{A}{{\text{Q}}^{\text{2}}}\text{ + C}{{\text{P}}^{\text{2}}}\text{ = A}{{\text{C}}^{\text{2}}}\] |
| B. | \[\text{A}{{\text{Q}}^{\text{2}}}\text{ + C}{{\text{P}}^{\text{2}}}\text{ = }\frac{4}{5}\,\,\text{A}{{\text{C}}^{\text{2}}}\] |
| C. | \[\text{A}{{\text{Q}}^{\text{2}}}-\text{C}{{\text{P}}^{\text{2}}}\text{ = }\frac{4}{5}\,\,\text{A}{{\text{C}}^{\text{2}}}\] |
| D. | \[\text{A}{{\text{Q}}^{\text{2}}}\text{+ C}{{\text{P}}^{\text{2}}}\text{ = }\frac{5}{4}\,\,\text{A}{{\text{C}}^{\text{2}}}\] |
| Answer» E. | |
| 1173. |
ABCD is a quadrilateral with unequal sides, unequal diagonals and unequal angles. E, F, G, H are the middle points of the four sides, then EFGH is a |
| A. | quadrilateral with unequal sides |
| B. | parallelogram |
| C. | rhombus |
| D. | rectangle |
| Answer» C. rhombus | |
| 1174. |
Three sides of a triangle are 6 cm, 12 cm and 13 cm; then |
| A. | all three angles are acute |
| B. | one angle is a right angle and others acute |
| C. | one angle is obtuse and others acute |
| D. | one angle is obtuse, one acute and one right angle |
| Answer» B. one angle is a right angle and others acute | |
| 1175. |
If M is any point in the interior of \[\Delta \,\mathbf{ABC}\]then _______ |
| A. | \[MC+MB>AC+AB\] |
| B. | \[MC+MB=AC+AB\] |
| C. | \[MC+MB=AC+AB\] |
| D. | \[MC+MB\ge AC+AB\] |
| E. | None of these |
| Answer» C. \[MC+MB=AC+AB\] | |
| 1176. |
If one angle of a triangle equals the sum of the other two angles, the triangle must be |
| A. | scalene |
| B. | right angled |
| C. | obtuse angled |
| D. | acute angled |
| Answer» C. obtuse angled | |
| 1177. |
In a quadrilateral PQSR, with a diagonal PS, if QS = SR and \[\angle \,\text{QSP = }\angle \,\text{RSP}\], then consider the following statements: Assertion (A): \[\angle \,\text{QPS = }\angle \,\text{RPS}\]Reason (R): Triangles QPS and RPS are congruent. Of these statements: |
| A. | both A and R are true and R is the correct explanation of A |
| B. | both A and R are true but R is not a correct explanation of A |
| C. | A is true, but R is false |
| D. | A is false, but R is true |
| Answer» B. both A and R are true but R is not a correct explanation of A | |
| 1178. |
\[\Delta \,ABC\] is congruent of \[\Delta \,DEF\], if |
| A. | \[AB=4=DE,\,AC=6=DF,\,\,\angle A=\angle D\,\] |
| B. | \[AB=4=DE,\,AC=6=DF,\,\,\angle B=\angle E\,\] |
| C. | \[AB=6=DE,\,AC=4=DF,\,\,\angle C=\angle F\,\] |
| D. | \[AB=4=DE,\,AC=6=DF,\,\,\angle C=\angle F\,\] |
| Answer» C. \[AB=6=DE,\,AC=4=DF,\,\,\angle C=\angle F\,\] | |
| 1179. |
In a right-angled triangle \[ABC,\,\,\angle BCA=90{}^\circ \]. CD is perpendicular from C to AB. By using the concept of area or areas of triangles, which one of the following relationships holds good? |
| A. | \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}-\frac{1}{C{{A}^{2}}}\] |
| B. | \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}+\frac{1}{C{{A}^{2}}}\] |
| C. | \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}-\frac{1}{C{{A}^{2}}}\] |
| D. | \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}+\frac{1}{C{{A}^{2}}}\] |
| Answer» E. | |
| 1180. |
The perimeter of a triangle is |
| A. | greater than the sum of its altitudes |
| B. | less than the sum of its altitudes |
| C. | equal to the sum of its altitudes |
| D. | none of these |
| Answer» B. less than the sum of its altitudes | |
| 1181. |
AB and CD are parallel straight lines. EG intersects the lines AB and CD at F and G respectively If \[\angle \,AFE=60{}^\circ \] and the straight line HI bisects \[\angle \,EGD\], then \[\angle DGI\] is |
| A. | \[60{}^\circ \] |
| B. | \[120{}^\circ \] |
| C. | \[130{}^\circ \] |
| D. | \[140{}^\circ \] |
| Answer» C. \[130{}^\circ \] | |
| 1182. |
BD is a median of a triangle ABC. F is a point on AB such that CF intersects BD at E and BE = ED. If BF = 5 cm. BA is equal to |
| A. | 10 |
| B. | 12 |
| C. | 15 |
| D. | 17 |
| Answer» D. 17 | |
| 1183. |
Given AB, CD and EF straight lines intersecting at the point O. If \[a=c |
| A. | EF bisects \[\angle \,BOD\] |
| B. | CD bisects \[\angle \,AOF\] |
| C. | AB bisects \[\angle \,COD\] |
| D. | CD bisects \[\angle \,EOB\] |
| Answer» B. CD bisects \[\angle \,AOF\] | |
| 1184. |
In the shown figure, the bisector of angle P is bisecting the opposite side QR. If \[\mathbf{PQ}\text{ }=\text{ }\mathbf{3}\text{ }\mathbf{cm}\] then the value of PR is _________ |
| A. | 3cm |
| B. | 4cm |
| C. | 6cm |
| D. | 1.5cm |
| E. | None of these |
| Answer» B. 4cm | |
| 1185. |
If two angles of a triangle are acute angles, the third angle |
| A. | is less than the sum of the two angles |
| B. | is an acute angle |
| C. | is the largest angle of the triangle |
| D. | may be an obtuse angle |
| Answer» E. | |
| 1186. |
One angle of a seven-sided polygon is 114. And each of the other six angles is \[x{}^\circ \]. The value of \[x\] is |
| A. | \[114{}^\circ \] |
| B. | \[121{}^\circ \] |
| C. | \[131{}^\circ \] |
| D. | \[151{}^\circ \] |
| Answer» D. \[151{}^\circ \] | |
| 1187. |
If the sum of all interior angles of a convex polygon is 1440., then the number of sides of the polygon is |
| A. | 8 |
| B. | 10 |
| C. | 11 |
| D. | 12 |
| Answer» E. | |
| 1188. |
A, B, C, D are four points in a straight line. Distance from A to B is 10, B to C is 5, C to D is 4 and A to D is 1. Which one of the following is the correct sequence of the points? |
| A. | \[A-B-C-D\] |
| B. | \[A-C-B-D\] |
| C. | \[A-D-C-B\] |
| D. | \[A-C-D-B\] |
| Answer» D. \[A-C-D-B\] | |
| 1189. |
If X, Y, Z, P are points on a line, X, Y have coordinates -7,11 with respect to an origin 0 on the line and XZ = ZY = PY = 9, ZP = 18, then which one of the following is the correct sequence ? |
| A. | \[X-Z-P-Y\] |
| B. | \[Y-Z-X-P\] |
| C. | \[P-Z-X-Y\] |
| D. | \[P-Y-Z-X\] |
| Answer» E. | |
| 1190. |
A circle has two equal chords AB and AC. Chord AD cuts BC in E. If AC = 12 cm. and AE = 8 cm., then AD is equal to |
| A. | 27 |
| B. | 24 |
| C. | 21 |
| D. | 18 |
| Answer» E. | |
| 1191. |
The sides of a triangle are in the ratio 4 : 6 : 7 Then |
| A. | The triangle is obtuse-angled |
| B. | The triangle is acute-angled |
| C. | The triangle is right-angled |
| D. | The triangle is impossible |
| Answer» C. The triangle is right-angled | |
| 1192. |
In the trapezium PQRS, PQ is parallel to RS and the diagonals intersect at O. If OP . SR=m(OR . PQ), then the value of m is |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[1\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 1193. |
The direct common tangents of two congruent circles are |
| A. | equal |
| B. | parallel |
| C. | parallel and equal |
| D. | parallel and unequal |
| Answer» D. parallel and unequal | |
| 1194. |
In a parallelogram PQRS, PQ = 4.5 cm, PR = 6 cm, QS = 7.8 cm and the diagonals PR and QS intersect each other at 0, then to draw a parallelogram we have to draw first |
| A. | APQR |
| B. | AROS |
| C. | AQOR |
| D. | APRS |
| Answer» C. AQOR | |
| 1195. |
For a regular polygon the sum of the interior angles is twice the sum of the exterior angles, then the number of sides of the regular polygon is |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 1196. |
S is a point on the side QR of a triangle PQR such that PS bisects\[\text{ }\angle QPR\] then _________ |
| A. | \[QS=SR\] |
| B. | \[PR<RS\] |
| C. | \[PQ>QS\] |
| D. | Both B and C are true |
| E. | None of these |
| Answer» D. Both B and C are true | |
| 1197. |
The straight lines which join the middle points of opposite sides of a quadrilateral |
| A. | Are parallel to one another |
| B. | Bisect one another |
| C. | Trisect one another |
| D. | None of these |
| Answer» C. Trisect one another | |
| 1198. |
Two equal circles in the same plane can have at the most the following numbers of common tangents |
| A. | 3 |
| B. | 2 |
| C. | 4 |
| D. | 1 |
| Answer» D. 1 | |
| 1199. |
If P is (-3, 4) and My Mx (P) shows the reflectior of the point P in the x-axis and then the reflectior of the image in the y-axis, then My Mx (P) is |
| A. | (3, 4) |
| B. | (-3, -4) |
| C. | (-3, 4) |
| D. | (3, -4) |
| Answer» E. | |
| 1200. |
Three circles have the centres at A, B, C and each circle touches the other two externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, then the radii of three circles respectively are |
| A. | 2, 3, 4 |
| B. | 3, 4, 5 |
| C. | 2, 4, 5 |
| D. | 2, 3, 5 |
| Answer» B. 3, 4, 5 | |