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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.
| 301. |
In figure, E and F are the mid-points of sides AB and AC of a\[\Delta ABC.\]If AB = 5 cm, BC = 5 cm and AC = Q cm, then EF is equal to |
| A. | 3 cm |
| B. | 2.5 cm |
| C. | 4 cm |
| D. | None of these |
| Answer» C. 4 cm | |
| 302. |
If \[ABCD\] is an isosceles trapezium, what is\[\angle C\] equal to? |
| A. | \[\angle B\] |
| B. | \[\angle A\] |
| C. | \[\angle D\] |
| D. | \[{{90}^{o}}\] |
| Answer» D. \[{{90}^{o}}\] | |
| 303. |
If a quadrilateral has two adjacent sides are equal and the opposite sides are unequal, then it is called a |
| A. | Parallelogram |
| B. | Square |
| C. | Rectangle |
| D. | Kite |
| Answer» E. | |
| 304. |
The diagonals of a parallelogram \[ABCD\] intersect at\[O\]. If \[\angle BOC={{90}^{o}}\] and\[\angle BDC={{50}^{o}}\], find\[\angle OAB\]. |
| A. | \[{{10}^{o}}\] |
| B. | \[{{40}^{o}}\] |
| C. | \[{{50}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» C. \[{{50}^{o}}\] | |
| 305. |
In given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that\[CQ=\frac{1}{4}AC\] and 4 PQ produced meet BC at R, then |
| A. | \[CR=\frac{1}{3}CB\] |
| B. | CR= RB |
| C. | \[CR=\frac{1}{2}RB\] |
| D. | None of these |
| Answer» C. \[CR=\frac{1}{2}RB\] | |
| 306. |
In the given figure, if ABCD is a rectangle and P, Q are the mid-points of AD, DC respectively. Then, the ratio of lengths PQ and AC is equal to |
| A. | 1 : 1 |
| B. | 1 : 2 |
| C. | 2 : 1 |
| D. | 3 : 2 |
| Answer» C. 2 : 1 | |
| 307. |
In a parallelogram\[ABCD\], if \[AB=2x+5,\] \[CD=y+1,\] \[AD=y+5\] and\[BC=3x-4\], what is the ratio of \[AB\] and\[BC\]? |
| A. | \[71:21\] |
| B. | \[12:11\] |
| C. | \[31:35\] |
| D. | \[4:7\] |
| Answer» D. \[4:7\] | |
| 308. |
X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in S; CX and BY are joined intersecting in R. Then SXRY is a |
| A. | Rectangle |
| B. | Rhombus |
| C. | Parallelogram |
| D. | Square |
| Answer» D. Square | |
| 309. |
\[ABCD\]is a parallelogram as shown in the figure. If \[AB=2AD\] and \[P\] is the mid-point of\[AB\], find the measure of\[\angle CPD\]. |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{135}^{o}}\] |
| Answer» B. \[{{60}^{o}}\] | |
| 310. |
D and E are the mid-points of the sides AB and AC, respectively of \[\Delta ABC.DE\]is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is |
| A. | \[\angle DAE=\angle EFC\] |
| B. | AE = EF |
| C. | DE = EF |
| D. | \[\angle ADE=\angle ECF\] |
| Answer» D. \[\angle ADE=\angle ECF\] | |
| 311. |
The perimeter of a parallelogram is\[180\,\,cm\]. One side exceeds another by\[10\,\,cm\]. What are the sides of the parallelogram? |
| A. | \[40\,\,cm\] and\[50\,\,cm\] |
| B. | \[45\,\,cm\]each |
| C. | \[50\,\,cm\]each and\[60\,\,cm\] |
| D. | Cannot be determined. |
| Answer» B. \[45\,\,cm\]each | |
| 312. |
ABCD is a parallelogram. If AB is produced to E such that ED bisects BC at O. Then which of the following is correct? |
| A. | AB = OE |
| B. | AB = BE |
| C. | OE = OC |
| D. | None of these |
| Answer» C. OE = OC | |
| 313. |
One of the diagonals of a rhombus is equal to its side. Find the angles of the rhombus. |
| A. | \[{{60}^{o}}\]and\[{{80}^{o}}\] |
| B. | \[{{60}^{o}}\]and\[{{120}^{o}}\] |
| C. | \[{{120}^{o}}\]and\[{{240}^{o}}\] |
| D. | \[{{100}^{o}}\]and\[{{120}^{o}}\] |
| Answer» C. \[{{120}^{o}}\]and\[{{240}^{o}}\] | |
| 314. |
ABCD is a rhombus with\[\angle ABC={{56}^{o}},\]then \[\angle ACD\]is equal to |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{56}^{o}}\] |
| D. | \[{{62}^{o}}\] |
| Answer» E. | |
| 315. |
In quadrilateral\[ABCD\], if the diagonals \[AC\] and \[BD\] are equal and perpendicular to each other, what is\[ABCD\]? |
| A. | A square |
| B. | A parallelogram |
| C. | A rhombus |
| D. | A trapezium |
| Answer» B. A parallelogram | |
| 316. |
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if |
| A. | PQRS is a rectangle |
| B. | PQRS is a parallelogram |
| C. | Diagonals of PQRS are equal |
| D. | Diagonals of PQRS are at right angles |
| Answer» E. | |
| 317. |
In parallelogram\[ABCD,\] \[AB=12\,\,cm\]. The altitudes corresponding to the sides \[AB\] and \[AD\] are respectively \[9\,\,cm\] and\[11\,\,cm\]. Find\[AD\]. |
| A. | \[\frac{108}{11}cm\] |
| B. | \[\frac{108}{10}cm\] |
| C. | \[\frac{99}{10}cm\] |
| D. | \[\frac{108}{17}cm\] |
| Answer» B. \[\frac{108}{10}cm\] | |
| 318. |
\[ABCD\] and \[MNOP\] are quadrilaterals as shown in the figure. Which of these is correct? |
| A. | \[p+q+r+s=w+x+y+z\] |
| B. | \[p+q+r+s<w+x+y+z\] |
| C. | \[p+q+r+s>w+x+y+z\] |
| D. | \[p+q+x+y=r+s+w+z\] |
| Answer» B. \[p+q+r+s<w+x+y+z\] | |
| 319. |
If diagonals of a quadrilateral bisect each other at right angles, then it is a |
| A. | Parallelogram |
| B. | Rectangle |
| C. | Rhombus |
| D. | Trapezium |
| Answer» D. Trapezium | |
| 320. |
The bisectors of angles of a parallelogram forms |
| A. | Trapezium |
| B. | Rectangle |
| C. | Rhombus |
| D. | Kite |
| Answer» C. Rhombus | |
| 321. |
In the parallelogram\[ABCD\], \[AP\] and \[BP\] are bisectors of\[\angle A\]and\[\angle B\]which meet at\[P\]. What is \[2\angle APB\] equivalent to? |
| A. | \[\angle A+\angle B\] |
| B. | \[\angle A+\angle C\] |
| C. | \[\angle B+\angle D\] |
| D. | \[\angle A-\angle D\] |
| Answer» B. \[\angle A+\angle C\] | |
| 322. |
ABCD is a cyclic quadrilateral and AD is a diameter. If \[\angle \mathbf{DAC}=\mathbf{6}{{\mathbf{5}}^{{}^\circ }}\] then value of \[\angle \mathbf{ABC}\] is |
| A. | \[{{55}^{{}^\circ }}\] |
| B. | \[{{35}^{{}^\circ }}\] |
| C. | \[{{155}^{{}^\circ }}\] |
| D. | \[{{125}^{{}^\circ }}\] |
| Answer» D. \[{{125}^{{}^\circ }}\] | |
| 323. |
ABCD is a cyclic quadrilateral and O is the centre of the circle. If \[\angle \mathbf{COD}=\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\]and \[\angle \mathbf{BAC}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\], then the value of \[\angle \mathbf{BCD}\] is equal to |
| A. | \[{{70}^{{}^\circ }}\] |
| B. | \[{{90}^{{}^\circ }}\] |
| C. | \[{{60}^{{}^\circ }}\] |
| D. | \[{{80}^{{}^\circ }}\] |
| Answer» D. \[{{80}^{{}^\circ }}\] | |
| 324. |
ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If \[\angle \mathbf{ABC}=\mathbf{7}{{\mathbf{5}}^{{}^\circ }}\], then the measure of the \[\angle \mathbf{BCD}\] is |
| A. | \[{{162}^{{}^\circ }}\] |
| B. | \[{{18}^{{}^\circ }}\] |
| C. | \[{{108}^{{}^\circ }}\] |
| D. | \[{{75}^{{}^\circ }}\] |
| Answer» E. | |
| 325. |
In the adjoining figure, AP and BP are angle bisectors of \[\angle \mathbf{A}\] and \[\angle B\] which meets At P in the parallelogram ABCD. Then\[\mathbf{2}\angle \mathbf{APB=?}\] |
| A. | \[\angle C+\angle D\] |
| B. | \[\angle A+\angle C\] |
| C. | \[\angle B+\angle D\] |
| D. | \[2\angle C\] |
| Answer» B. \[\angle A+\angle C\] | |
| 326. |
In a rhombus ABCD,, its diagonal intersect at O then \[\angle \mathbf{AOB}\] is |
| A. | \[{{180}^{{}^\circ }}\] |
| B. | \[{{0}^{{}^\circ }}\] |
| C. | \[{{90}^{{}^\circ }}\] |
| D. | \[{{60}^{{}^\circ }}\] |
| Answer» D. \[{{60}^{{}^\circ }}\] | |
| 327. |
The length of each side of a rhombus is 10 cm and of its diagonals 1$ of 16cm. The length of the other diagonal is |
| A. | 13 cm |
| B. | 12 cm |
| C. | \[2\sqrt{39}\] cm |
| D. | 6 cm |
| Answer» C. \[2\sqrt{39}\] cm | |
| 328. |
The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of side of the rhombus is |
| A. | 10 cm |
| B. | 12 cm |
| C. | 9 cm |
| D. | 8 cm |
| Answer» B. 12 cm | |
| 329. |
The diagonals AC and BD of a parallelogram ABCD intersect each other at the O such that \[\angle \mathbf{DAC}=\mathbf{4}{{\mathbf{0}}^{{}^\circ }}\]and \[\angle \mathbf{AOB}=\mathbf{8}{{\mathbf{0}}^{{}^\circ }}\], Then \[\angle \mathbf{DBC}=\]? |
| A. | \[{{40}^{{}^\circ }}\] |
| B. | \[{{35}^{{}^\circ }}\] |
| C. | \[{{45}^{{}^\circ }}\] |
| D. | \[{{50}^{{}^\circ }}\] |
| Answer» B. \[{{35}^{{}^\circ }}\] | |
| 330. |
In a quadrilateral ABCD, If AO and BO are the bisectors of \[\angle \mathbf{A}\] and \[\angle B\] respectively \[\angle \mathbf{C}=\mathbf{3}{{\mathbf{0}}^{{}^\circ }}\]and\[\angle \mathbf{D}=\mathbf{7}{{\mathbf{0}}^{{}^\circ }}\]. Then, \[\angle \mathbf{AOB}=\]? |
| A. | \[{{40}^{{}^\circ }}\] |
| B. | \[{{50}^{{}^\circ }}\] |
| C. | \[{{80}^{{}^\circ }}\] |
| D. | \[{{100}^{{}^\circ }}\] |
| Answer» C. \[{{80}^{{}^\circ }}\] | |
| 331. |
The length of the diagonal BD of the parallelogram \[\Delta \mathbf{BCD}\] is 12 cm. If P and Q are the centroid of the \[\Delta \mathbf{ABC}\] and \[\Delta \mathbf{ADC}\] respectively then the length of the line segment PQ is |
| A. | 4 cm |
| B. | 4 cm |
| C. | 9 cm |
| D. | 12 cm |
| Answer» C. 9 cm | |
| 332. |
In given figure, ABCD is a rhombus. If \[\angle OAB={{35}^{{}^\circ }}\], Then the value of x is |
| A. | \[{{25}^{{}^\circ }}\] |
| B. | \[{{35}^{{}^\circ }}\] |
| C. | \[{{55}^{{}^\circ }}\] |
| D. | \[{{70}^{{}^\circ }}\] |
| Answer» D. \[{{70}^{{}^\circ }}\] | |
| 333. |
In the adjoining figure ABCD is a parallelogram and E, F are the centroids of \[\Delta \mathbf{ABD}\] and \[\Delta \mathbf{BCD}\] respectively, then EF equals: |
| A. | AE |
| B. | BE |
| C. | CE |
| D. | DE |
| Answer» B. BE | |
| 334. |
In the adjoining figure, the value of x and y are: |
| A. | \[{{5}^{{}^\circ }},{{4}^{{}^\circ }}\] |
| B. | \[{{3}^{{}^\circ }},{{4}^{{}^\circ }}\] |
| C. | \[{{2}^{{}^\circ }},{{1}^{{}^\circ }}\] |
| D. | None of these |
| Answer» B. \[{{3}^{{}^\circ }},{{4}^{{}^\circ }}\] | |
| 335. |
A quadrilateral is a parallelogram if: |
| A. | A pair of opposite sides is equal |
| B. | A pair of opposite sides is equal and parallel |
| C. | A pair of opposite sides is parallel |
| D. | None of these |
| Answer» C. A pair of opposite sides is parallel | |
| 336. |
In a rectangle ABCD, P, Q are the mid-points of BC and AD respectively and R is any point on PQ, then \[\Delta \mathbf{ARB}\] equals: |
| A. | \[\frac{1}{2}\left( [\,\,\,\,]\,ABCD \right)\] |
| B. | \[\frac{1}{3}\left( [\,\,\,]\,ABCD \right)\] |
| C. | \[\frac{1}{4}\left( [\,\,\,]\,ABCD \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 337. |
PQRA is a rectangle, \[\mathbf{AP}=\mathbf{24}\]cm. \[\mathbf{PQ}=\mathbf{8}\]cm. \[\Delta \mathbf{ABC}\] is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and \[\mathbf{QC}=\mathbf{18}\]cm. Then the length of the line joining the mid points of the sides AB and BC is |
| A. | \[4\sqrt{2}\]cm. |
| B. | 5 cm |
| C. | 6 cm. |
| D. | 10 cm. |
| Answer» C. 6 cm. | |
| 338. |
The sides BA and DC of quadrilateral ABCD are produced as shown la figure. Them which of the following statements is correct? |
| A. | \[2{{x}^{{}^\circ }}+{{y}^{{}^\circ }}={{a}^{{}^\circ }}+{{b}^{{}^\circ }}\] |
| B. | \[{{x}^{{}^\circ }}+\frac{1}{2}{{y}^{{}^\circ }}=\frac{{{a}^{{}^\circ }}+{{b}^{{}^\circ }}}{2}\] |
| C. | \[{{x}^{{}^\circ }}+{{y}^{{}^\circ }}={{a}^{{}^\circ }}+{{b}^{{}^\circ }}\] |
| D. | \[{{x}^{{}^\circ }}+{{a}^{{}^\circ }}={{y}^{{}^\circ }}+{{b}^{{}^\circ }}\] |
| Answer» D. \[{{x}^{{}^\circ }}+{{a}^{{}^\circ }}={{y}^{{}^\circ }}+{{b}^{{}^\circ }}\] | |
| 339. |
ABCD is a trapezium in which \[\mathbf{AB}\parallel \mathbf{CD}\] and \[AB=3CD\]Its diagonals intersect other at O then the ratio of the areas of the triangles AOB and COD is: |
| A. | 1 : 2 |
| B. | 2 : 1 |
| C. | 9 : 1 |
| D. | 1 : 4 |
| Answer» D. 1 : 4 | |
| 340. |
If PQRS be a rhombus, PR is its smallest diagonal and \[\angle \mathbf{PQR}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\], find length of a side of the rhombus when \[\mathbf{PR}=\mathbf{6}\]cm. |
| A. | 6 cm |
| B. | 3 cm |
| C. | \[6\sqrt{2}\]cm |
| D. | \[3\sqrt{3}\]cm |
| Answer» B. 3 cm | |
| 341. |
In a quadrilateral ABCD, the bisectors of \[\angle \mathbf{A}\] and \[\angle B\] meet at O. If \[\angle C={{80}^{{}^\circ }}\]and \[\angle \mathbf{D}=\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\], then measure of \[\angle \mathbf{AOB}\] is |
| A. | \[{{40}^{{}^\circ }}\] |
| B. | \[{{60}^{{}^\circ }}\] |
| C. | \[{{80}^{{}^\circ }}\] |
| D. | \[{{100}^{{}^\circ }}\] |
| Answer» E. | |
| 342. |
The probability of guessing the correct answer to a question is \[\frac{x}{2}.\]If the probability of not guessing the correct answer to this question is \[\frac{2}{3},\] then \[x=\_\_\_\_.\] |
| A. | 2 |
| B. | 3 |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{3}\] |
| Answer» D. \[\frac{1}{3}\] | |
| 343. |
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a '10' of a black suit. |
| A. | \[\frac{1}{13}\] |
| B. | \[\frac{1}{26}\] |
| C. | \[\frac{5}{23}\] |
| D. | \[\frac{1}{52}\] |
| Answer» C. \[\frac{5}{23}\] | |
| 344. |
A die is thrown once. The probability of 1 getting a number greater than 6 is ____. |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | 0 |
| Answer» E. | |
| 345. |
Direction: for question number 14 ? 17. If A and B be two mutually exclusive events in a sample space such that. \[\operatorname{P}(A)\,=\frac{2}{5}\]and \[\operatorname{P}(B)\,=\frac{1}{2}\] then Find \[\operatorname{P}\left( A\,\cup B \right)\]: |
| A. | \[\frac{7}{16}\] |
| B. | \[\frac{9}{16}\] |
| C. | \[\frac{9}{10}\] |
| D. | \[\frac{1}{2}\] |
| E. | None of these |
| Answer» D. \[\frac{1}{2}\] | |
| 346. |
The given table shows the ages (in years) of 360 patients, getting medical treatment in a hospital. Age n years) 10-20 20-30 30-40 40-50 50-60 60-70 No. of patients 90 50 60 80 50 30 One of the patients is selected at random. The probability that his age is (a) 30 years or more but less than 40 years is ____. (b) 10 years or more is ___. |
| A. | (a) (b) \[\frac{1}{6}\] \[\frac{2}{9}\] |
| B. | (a) (b) \[\frac{1}{6}\] 0 |
| C. | (a) (b) \[\frac{2}{9}\] 1 |
| D. | (a) (b) \[\frac{1}{6}\] 1 |
| Answer» E. | |
| 347. |
Determine the probability of getting an even number when a die is rolled. |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{36}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{3}\] |
| Answer» D. \[\frac{1}{3}\] | |
| 348. |
When two dice are thrown, what is the probability of getting a number always greater than 4 on the second dice? |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{36}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{1}{36}\] | |
| 349. |
A die is rolled 120 times and the outcomes are recorded in the given table. Outcome 1 Even number less than 6 Odd number greater-than 1 6 Frequency 30 35 30 25 Determine the probability of getting an odd number greater than 1 in a trial. |
| A. | 0.167 |
| B. | 0.125 |
| C. | 0.29 |
| D. | 0.25 |
| Answer» E. | |
| 350. |
400 students of class IX of a school appeared for a test of 100 marks in the subject of mathematics and the data about the marks secured is presented in the table. Marks secured 0-25 26-50 51-75 Above 75 Number of student 50 220 100 30 If the result card of a student is picked up at random, what is the probability that the student has secured more than 50 marks? |
| A. | 0.523 |
| B. | 0.532 |
| C. | 0.325 |
| D. | 0.352 |
| Answer» D. 0.352 | |