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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.
| 1201. |
ED is chord parallel to the diameter AC of a circle. A point B is on the perimeter of the circle such that angle CBE =\[63{}^\circ \]. The angle DEC is equal to |
| A. | \[63{}^\circ \] |
| B. | \[42{}^\circ \] |
| C. | \[31.5{}^\circ \] |
| D. | \[27{}^\circ \] |
| Answer» E. | |
| 1202. |
A, B, C are three points on a circle such that AB is the chord and CP is perpendicular to OP, where O is the centre and P is any point on AB. The radius r of the circle is given by |
| A. | \[{{r}^{2}}=O{{P}^{2}}+AP\times CP\] |
| B. | \[{{r}^{2}}=O{{P}^{2}}+AP\times PB\] |
| C. | \[{{r}^{2}}=O{{P}^{2}}+PB\times PC\] |
| D. | \[{{r}^{2}}=O{{P}^{2}}+P{{B}^{2}}\] |
| Answer» C. \[{{r}^{2}}=O{{P}^{2}}+PB\times PC\] | |
| 1203. |
The two diagonals of a rhombus are 24 cm and 10 cm long. The length of each side of the rhombus is |
| A. | 17 cm |
| B. | 16 cm |
| C. | 14 cm |
| D. | 13 cm |
| Answer» E. | |
| 1204. |
Which among the following statements is correct? |
| A. | In a triangle PQR, if \[\angle Q<\angle P\] then\[PR\text{ }<\text{ }QR\]. |
| B. | \[\Delta \text{ }ABC\cong \Delta \text{ }PQR\] if \[\angle A\text{ }=\text{ }\angle P,\] and \[AC=\text{ }QR\]. |
| C. | In triangles PQR and STU if \[\angle P\text{ }=\text{ }\angle S,\] \[\angle Q\text{ }=\text{ }\angle T\] and \[PQ\text{ }=\text{ }TU\], then both the triangles are congruent. |
| D. | All the above |
| E. | None of these |
| Answer» B. \[\Delta \text{ }ABC\cong \Delta \text{ }PQR\] if \[\angle A\text{ }=\text{ }\angle P,\] and \[AC=\text{ }QR\]. | |
| 1205. |
In any triangle the centroid divides the median in the ratio |
| A. | 1 : 1 |
| B. | 2 : 1 |
| C. | 3 : 1 |
| D. | 3 : 2 |
| Answer» C. 3 : 1 | |
| 1206. |
In a quadrilateral ABCD, if the diagonals AC,BD intersect at right angles, then |
| A. | \[A{{B}^{2}}+B{{C}^{2}}=D{{C}^{2}}+D{{A}^{2}}\] |
| B. | \[A{{B}^{2}}+C{{D}^{2}}=B{{C}^{2}}+D{{A}^{2}}\] |
| C. | \[A{{B}^{2}}+A{{D}^{2}}=C{{B}^{2}}+C{{D}^{2}}\] |
| D. | \[A{{B}^{2}}+B{{C}^{2}}=2(D{{C}^{2}}+D{{A}^{2}})\] |
| Answer» C. \[A{{B}^{2}}+A{{D}^{2}}=C{{B}^{2}}+C{{D}^{2}}\] | |
| 1207. |
In \[\Delta \,PQR\], if O is the orthocentre and \[\angle \,QOR\,=\,2\,\angle P\] , then \[\angle \,QOR\] is equal to |
| A. | \[90{}^\circ \] |
| B. | \[120{}^\circ \] |
| C. | \[150{}^\circ \] |
| D. | \[160{}^\circ \] |
| Answer» C. \[150{}^\circ \] | |
| 1208. |
In a triangle ABC, a straight line parallel to BC intersects AB and AC at point D and E respectively. If the area of ADE is one-fifth of the area of ABC and BC = 10 cm, then DE equals |
| A. | 2 cm |
| B. | 2/5 cm |
| C. | 4 cm |
| D. | 4/5 cm |
| Answer» C. 4 cm | |
| 1209. |
A trapezium has its non parallel sides congruent, then its opposite angles are |
| A. | congruent |
| B. | supplementary |
| C. | complementary |
| D. | None of these |
| Answer» C. complementary | |
| 1210. |
In \[\Delta \,ABC,D\] is drawn such that \[\Delta \,ABD\] and \[\Delta \,ACD\] are equal in area then, the AD is |
| A. | any segment drawn from A to BC |
| B. | the bisector of \[\angle \,BAC\] |
| C. | A median of \[\Delta \,ABC\] |
| D. | None of these |
| Answer» D. None of these | |
| 1211. |
If the given diagram, BD is the bisector of,if, then which one of the statements is not correct? |
| A. | Triangles ABD and DBE are similar |
| B. | \[Area\text{ }ABD\text{ }:\text{ }Area\text{ }DBE=A{{B}^{2}}:B{{D}^{2}}\] |
| C. | \[AB\times BE=B{{D}^{2}}\] |
| D. | \[AB\times DE=AD\times BE\] |
| Answer» E. | |
| 1212. |
If the area of two similar triangles are equal, then they are |
| A. | equilateral |
| B. | isosceles |
| C. | congruent |
| D. | not congruent |
| Answer» D. not congruent | |
| 1213. |
Two sides of a triangle are of lengths 6.2 cm and 3.5 cm. The length of the third side of the triangle cannot be ________ |
| A. | 9.2cm |
| B. | 8.5cm |
| C. | 2.8cm |
| D. | 2.6cm |
| E. | None of these |
| Answer» E. None of these | |
| 1214. |
Two triangles ABC and PQR are similar, if BC : CA : AB = 1 : 2 : 3, then \[\frac{\text{QR}}{\text{PR}}\] is |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{1}{\sqrt{2}}\] | |
| 1215. |
ABODE is a regular pentagon. If AD is joined, then |
| A. | ABCD is a parallelogram. |
| B. | ABCD is a rhombus. |
| C. | ABCD is a cyclic trapezium. |
| D. | ABCD is not cyclic quadrilateral. |
| Answer» D. ABCD is not cyclic quadrilateral. | |
| 1216. |
If O is the orthocentre of the \[\Delta \,ABC\], then |
| A. | \[\angle \,BOC=2\,\,\angle \,BAC\] |
| B. | \[\angle \,BOC\,\,and\,\,\angle \,BAC\] are supplementary |
| C. | \[\angle \,BOC\,=\,\angle \,BAC\] |
| D. | None of these |
| Answer» C. \[\angle \,BOC\,=\,\angle \,BAC\] | |
| 1217. |
The parallel sides of a trapezium are x and y in length. The length of the line segement joining the mid points of the non parallel sides is |
| A. | \[\frac{x+y}{2}\] |
| B. | \[x+y\] |
| C. | \[\frac{2x+3y}{2}\] |
| D. | \[\frac{xy}{2}\] |
| Answer» B. \[x+y\] | |
| 1218. |
Each angle of a regular polygon of n sides contains |
| A. | 4n right angles |
| B. | \[\frac{2(n+1)}{n}\] right angles |
| C. | \[\frac{2(n-1)}{n}\]right angles |
| D. | \[\frac{2(n-2)}{n}\] right angles |
| Answer» E. | |
| 1219. |
Given inside a circle, whose radius is equal to 13 cm, is a point M at a distance 5 cm from the centre of the circle. A chord AB = 25 cm is drawn through M. The lengths of the segments into which the chord AB is divided by the point M in CM are |
| A. | 12, 13 |
| B. | 14, 11 |
| C. | 15, 10 |
| D. | 16, 9 |
| Answer» E. | |
| 1220. |
Two non-intersecting circles, one lying inside another, are of radii a and b (a > b). The minimum distance between their circumference is c. The distance between their centres is |
| A. | a - b |
| B. | a - b + c |
| C. | a + b - c |
| D. | a - b - c |
| Answer» E. | |
| 1221. |
In the given figure, \[\angle \,\text{B}\,\text{=}\angle \,\text{C}\,=\,65{}^\circ \] and \[\angle \,D\,=\,30{}^\circ \]. Then. |
| A. | BC < CA < CD |
| B. | BC > CA > CD |
| C. | BC < CA, CA > CD |
| D. | BC > CA, CA < CD |
| Answer» B. BC > CA > CD | |
| 1222. |
One angle of a cyclic trapezium is double the other. What is the measure of the larger angle? |
| A. | \[60{}^\circ \] |
| B. | \[80{}^\circ \] |
| C. | \[75{}^\circ \] |
| D. | \[120{}^\circ \] |
| Answer» E. | |
| 1223. |
In the following figure, \[AE\bot BC,\,\,D\] is the mid-point of BC, then \[x\] is equal to |
| A. | \[\frac{1}{\alpha }\left[ {{b}^{2}}-{{d}^{2}}-\frac{{{a}^{2}}}{4} \right]\] |
| B. | \[\frac{h+d}{3}\] |
| C. | \[\frac{c+d-h}{2}\] |
| D. | \[\frac{{{a}^{2}}+{{b}^{2}}+{{d}^{2}}-{{c}^{2}}}{4}\] |
| Answer» B. \[\frac{h+d}{3}\] | |
| 1224. |
If \[l,m,n\] are three parallel lines and the transversals \[{{t}_{1}}\] and \[{{t}_{2}}\] cut the lines \[l,m,n\] at the points A, B, C and P, Q, R as shown in the figure, then |
| A. | \[\frac{AB}{BC}=\frac{PQ}{QR}\] |
| B. | \[\frac{AB}{QR}=\frac{BC}{PQ}\] |
| C. | \[\frac{AP}{BQ}=\frac{BQ}{CR}\] |
| D. | \[\frac{AB}{PQ}=\frac{AP}{BQ}\] |
| Answer» B. \[\frac{AB}{QR}=\frac{BC}{PQ}\] | |
| 1225. |
In the given diagram CE is parallel to AD and the measures of two angles at B and C have been indicated. Then \[\angle \,\text{DAB}\] is equal to |
| A. | \[30{}^\circ \] |
| B. | \[35{}^\circ \] |
| C. | \[40{}^\circ \] |
| D. | Cannot be determined |
| Answer» D. Cannot be determined | |
| 1226. |
If the straight lines AB and XY intersect at the point O and \[\angle \,\text{AOX}\,=\,\,8\,\,\angle \,\text{XOB}\], then the four angles formed at 0 are |
| A. | \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }90{}^\circ ,\text{ }210{}^\circ \] |
| B. | \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }150{}^\circ ,\text{ }150{}^\circ \] |
| C. | \[45{}^\circ ,\text{ }135{}^\circ ,\text{ }90{}^\circ ,\text{ }90{}^\circ \] |
| D. | \[45{}^\circ ,\text{ }45{}^\circ ,\text{ }135{}^\circ ,\text{ }135{}^\circ \] |
| Answer» E. | |
| 1227. |
In the given figure, \[\angle \,\text{QPB}\] is |
| A. | \[60{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[30{}^\circ \] |
| D. | \[15{}^\circ \] |
| Answer» D. \[15{}^\circ \] | |
| 1228. |
In the given figure, \[\angle \,\text{MON}\,=\,\,8\text{0}{}^\circ ,\,\,\angle \,\text{MQO}\,\text{=}\,\text{20}{}^\circ \], then the measure of \[\angle \,\text{MOP}\] is |
| A. | \[40{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[50{}^\circ \] |
| D. | \[55{}^\circ \] |
| Answer» B. \[45{}^\circ \] | |
| 1229. |
In the given figure (PQ is diameter), x is equal to |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[70{}^\circ \] |
| D. | \[60{}^\circ \] |
| Answer» E. | |
| 1230. |
Tangents at the end points of the diameter of a circle intersect at angle Q. Q is equal to |
| A. | \[90{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[0{}^\circ \] |
| D. | \[30{}^\circ \] |
| Answer» D. \[30{}^\circ \] | |
| 1231. |
In a \[\Delta \,\mathbf{ABC}\], if \[\angle \mathbf{A}\text{ }-\text{ }\angle \mathbf{B}\text{ }=\mathbf{35}{}^\circ \] and \[\angle \mathbf{C}\text{ }-\angle \mathbf{B}\text{ }=\mathbf{34}{}^\circ \], then |
| A. | \[\angle A=71{}^\circ \] |
| B. | \[\angle B=72{}^\circ \] |
| C. | \[\angle A+\angle B=109{}^\circ \] |
| D. | \[\angle A+\angle C=142{}^\circ \] |
| E. | None of these |
| Answer» D. \[\angle A+\angle C=142{}^\circ \] | |
| 1232. |
If two altitudes of a triangle are equal in length, then the triangle is |
| A. | right angled |
| B. | equilateral |
| C. | isosceles |
| D. | scalene |
| Answer» D. scalene | |
| 1233. |
From an external point, K tangents can be drawn to a circle, then K is equal to |
| A. | 0 |
| B. | 2 |
| C. | 1 |
| D. | infinity |
| Answer» C. 1 | |
| 1234. |
Consider a cube ABCD - PQRS, if 0 is the angle between diagonal BS and the plane PQRS, then the value of tan 0 is equal to |
| A. | \[1\] |
| B. | \[\sqrt{2}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\sqrt{3}\] |
| Answer» D. \[\sqrt{3}\] | |
| 1235. |
If ABCDE is a regular pentagon, then the angle BDE is equal to |
| A. | \[90{}^\circ \] |
| B. | \[72{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[54{}^\circ \] |
| Answer» C. \[60{}^\circ \] | |
| 1236. |
In the given figure OA, OB are opposite rays and \[\angle \,\text{AOC}\,+\angle \,\text{BOD}\,\text{=}\,\text{90}{}^\circ \], then \[\angle \,\text{COD}\] is |
| A. | \[90{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[45{}^\circ \] |
| D. | \[30{}^\circ \] |
| Answer» B. \[60{}^\circ \] | |
| 1237. |
In the given figure, O is the centre of the circle and\[\ge \], then |
| A. | \[m+n=90{}^\circ \] |
| B. | \[m+n=180{}^\circ \] |
| C. | \[m+n=120{}^\circ \] |
| D. | \[m+n=150{}^\circ \] |
| Answer» B. \[m+n=180{}^\circ \] | |
| 1238. |
Two isosceles triangles have equal vertical angles and their areas are in the ratio of 9 : 16. Then their heights are in the ratio of |
| A. | 9 : 16 |
| B. | 16 : 9 |
| C. | 4 : 3 |
| D. | 3 : 4 |
| Answer» E. | |
| 1239. |
In \[\Delta \,\text{ABC}\], O is the orthocentre and \[\angle \,\text{BOC}\,\text{=}\,\,2\angle \,\text{A}\] then the measure of \[\angle \,\text{BOC}\] is equal to |
| A. | \[120{}^\circ \] |
| B. | \[100{}^\circ \] |
| C. | \[80{}^\circ \] |
| D. | \[60{}^\circ \] |
| Answer» B. \[100{}^\circ \] | |
| 1240. |
In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is |
| A. | \[40{}^\circ \] |
| B. | \[42{}^\circ \] |
| C. | \[44{}^\circ \] |
| D. | \[45{}^\circ \] |
| Answer» E. | |
| 1241. |
In the shown figure, if \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{BC}\] and \[\mathbf{AP}=\mathbf{5}.\mathbf{4}\text{ }\mathbf{cm}\],\[\text{ }\mathbf{AQ}=\left( \mathbf{x}+\mathbf{1} \right)\,\,\mathbf{cm},\]\[\mathbf{AB}=\mathbf{8}.\mathbf{1}cm\] cm and \[QC=(x-1)\]cm, then AC equals to _______ |
| A. | 12 cm |
| B. | 6 cm |
| C. | 3 cm |
| D. | 4 cm |
| E. | None of these |
| Answer» C. 3 cm | |
| 1242. |
If two medians of a triangle are equal in length, then the triangle is |
| A. | right angled but not isosceles |
| B. | isosceles but not right angle |
| C. | right angled isosceles |
| D. | equilateral |
| Answer» C. right angled isosceles | |
| 1243. |
The point O lies inside a triangle \[\text{PQR}\] such that \[\Delta \,\text{OPQ}\], \[\Delta \,\text{OQR}\]and \[\text{AORP}\] are equal in area. Then the point O is called as |
| A. | incentre |
| B. | centroid |
| C. | circumcentre |
| D. | orthocenter |
| Answer» C. circumcentre | |
| 1244. |
If \[\angle \,P\] and \[\angle \,Q\] are complementary in a triangle PQR, then the measure of \[\angle \,R\] is |
| A. | \[45{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[75{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» E. | |
| 1245. |
Two secants PAB and PCD are drawn to a circle from an outside point P. Then, which of the following is true? |
| A. | PA . PB = PC + CD |
| B. | PA. PB = PC . PD |
| C. | PA + PB = PC + PD |
| D. | PA - PB= PC. CD |
| Answer» C. PA + PB = PC + PD | |
| 1246. |
In the figure, \[\angle \,B\] is equal to |
| A. | \[85{}^\circ \] |
| B. | \[95{}^\circ \] |
| C. | \[70{}^\circ \] |
| D. | \[115{}^\circ \] |
| Answer» C. \[70{}^\circ \] | |
| 1247. |
The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» B. \[45{}^\circ \] | |
| 1248. |
If E and F are any two points lying on the sides DC and AD, respectively of a parallelogram ABCD, then |
| A. | BF + CF = AE + BE |
| B. | AE = BF |
| C. | Ar(AEB) = Ar(BFC) |
| D. | Ar(ADE) = Ar(BEC) |
| Answer» D. Ar(ADE) = Ar(BEC) | |
| 1249. |
ABC is a triangle and AD is median. If E is any point on AD, then |
| A. | Ar(ABE) = Ar(ACE) |
| B. | BE = CE |
| C. | AB + BE = AC + CE |
| D. | \[AE=\frac{(BE+CE)}{2}\] |
| Answer» B. BE = CE | |
| 1250. |
If two medians of a triangle are equal, the triangh is |
| A. | right angled |
| B. | isosceles |
| C. | equilateral |
| D. | scalene |
| Answer» C. equilateral | |