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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.
| 251. |
In a quadrilateral ABCD, the line segments bisecting \[\angle C\]and \[\angle D\]meet at E. Then \[\angle A+\angle B\]is equal to _____. |
| A. | \[\angle CED\] |
| B. | \[\frac{1}{2}\angle CED\] |
| C. | \[2\angle CED\] |
| D. | None of these |
| Answer» D. None of these | |
| 252. |
In a square\[ABCD\], the diagonals bisect at\[O\]. What type of a triangle is\[\Delta AOB\]? |
| A. | An equilateral triangle. |
| B. | An isosceles but not a right angled triangle. |
| C. | A right angled but not an isosceles triangle. |
| D. | An isosceles right angled triangle. |
| Answer» C. A right angled but not an isosceles triangle. | |
| 253. |
Two adjacent angles of a parallelogram are in the ratio 2 : 3. The angles are |
| A. | \[{{90}^{o}},\,\,{{180}^{o}}\] |
| B. | \[{{36}^{o}},\,\,{{144}^{o}}\] |
| C. | \[{{72}^{o}},\,\,{{108}^{o}}\] |
| D. | \[{{52}^{o}},\,\,{{104}^{o}}\] |
| Answer» D. \[{{52}^{o}},\,\,{{104}^{o}}\] | |
| 254. |
In the given figure, \[ABCD\] is a trapezium in which\[AB=7\,\,cm,\,\,AD=BC=5\,\,cm\], \[DC=x\,\,cm\] and the distance between \[AB\] and \[DC\] is\[4\,\,cm\]. What is the value of\[x\]? |
| A. | \[13\,\,cm\] |
| B. | \[16\,\,cm\] |
| C. | \[19\,\,cm\] |
| D. | \[12\,\,cm\] |
| Answer» B. \[16\,\,cm\] | |
| 255. |
If the angles of a quadrilateral are \[x+x+{{20}^{o}},x-{{40}^{o}}\]and\[2x.\]Then, the difference between greatest angle and the smallest angle is _____ . |
| A. | \[{{70}^{o}}\] |
| B. | \[{{90}^{o}}\] |
| C. | \[{{80}^{o}}\] |
| D. | None of these |
| Answer» E. | |
| 256. |
In parallelogram\[PQRS\], what are the values of \[\angle QSP\]and\[\angle SPQ\]? |
| A. | \[{{45}^{o}},\,\,{{60}^{o}}\] |
| B. | \[{{60}^{o}},\,\,{{45}^{o}}\] |
| C. | \[{{70}^{o}},\,\,{{35}^{o}}\] |
| D. | \[{{35}^{o}},\,\,{{70}^{o}}\] |
| Answer» C. \[{{70}^{o}},\,\,{{35}^{o}}\] | |
| 257. |
In the given figure, \[\Delta ABC\]and \[\Delta DEF\]are such that\[AB=DE,\,BC=EF,\]and BC//EF. What is ADFC? |
| A. | A square |
| B. | A rectangle |
| C. | A parallelogram |
| D. | A rhombus |
| Answer» D. A rhombus | |
| 258. |
Two opposite angles of a parallelogram are \[{{(3p-4)}^{o}}\]and\[{{(48-p)}^{o}}.\]What is the value of p? |
| A. | 13 |
| B. | 15 |
| C. | 17 |
| D. | 20 |
| Answer» B. 15 | |
| 259. |
\[E\] and \[F\] are the midpoints of the sides \[AB\] and \[AC\] respectively of ; G and H are midpoints of the sides AE and AF respectively of \[\Delta AEF.\]If GH = 1.8 cm, find BC. |
| A. | 0.9 cm |
| B. | 3.6 cm |
| C. | 7.2 cm |
| D. | 5.4 cm |
| Answer» D. 5.4 cm | |
| 260. |
In quadrilateral\[PQRS\]\[,\]\[\angle P+\angle R={{140}^{o}}\] and\[\angle Q:\angle S=5:6\]. Find\[\angle Q\]. |
| A. | \[{{100}^{o}}\] |
| B. | \[{{120}^{o}}\] |
| C. | \[{{105}^{o}}\] |
| D. | \[{{35}^{o}}\] |
| Answer» B. \[{{120}^{o}}\] | |
| 261. |
\[ABCD\] is a rhombus in which \[AC=16\,\,cm\] and \[BC=10\,\,cm\]. Find the length of the diagonal\[BD\] |
| A. | \[16\,\,cm\] |
| B. | \[8\,\,cm\] |
| C. | \[12\,\,cm\] |
| D. | \[10\,\,cm\] |
| Answer» D. \[10\,\,cm\] | |
| 262. |
If an angle of a parallelogram is four-fifths of its adjacent angle, find the angles of the parallelogram. |
| A. | \[{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}}\] |
| B. | \[{{90}^{o}},\,\,{{90}^{o}},\,\,{{90}^{o}}\] |
| C. | \[{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}}\] |
| D. | \[{{30}^{o}},\,\,{{150}^{o}},\,\,{{30}^{o}},\,\,{{100}^{o}}\] |
| Answer» D. \[{{30}^{o}},\,\,{{150}^{o}},\,\,{{30}^{o}},\,\,{{100}^{o}}\] | |
| 263. |
In quadrilateral\[ABCD\]\[,\] \[\angle A+\angle C={{140}^{o}}\], \[\angle A:\]\[\angle C=1:3\]and\[\angle B:\angle D=5:6\]. Find the measures of\[\angle A,\,\,\angle B,\,\,\angle C\]and\[\angle D\]. |
| A. | \[{{35}^{o}},\,\,{{100}^{o}},\,\,{{105}^{o}},\,\,{{120}^{o}}\] |
| B. | \[{{60}^{o}},\,\,{{45}^{o}},\,\,{{75}^{o}},\,\,{{100}^{o}}\] |
| C. | \[{{20}^{o}},\,\,{{60}^{o}},\,\,{{105}^{o}},\,\,{{135}^{o}}\] |
| D. | \[{{45}^{o}},\,\,{{35}^{o}},\,\,{{90}^{o}},\,\,{{110}^{o}}\] |
| Answer» B. \[{{60}^{o}},\,\,{{45}^{o}},\,\,{{75}^{o}},\,\,{{100}^{o}}\] | |
| 264. |
The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If \[\angle DAC={{32}^{o}}\]and \[\angle AOB={{70}^{o}},\]then,\[\angle DBC\] is equal to ____. |
| A. | \[{{38}^{o}}\] |
| B. | \[{{86}^{o}}\] |
| C. | \[{{24}^{o}}\] |
| D. | \[{{32}^{o}}\] |
| Answer» B. \[{{86}^{o}}\] | |
| 265. |
Two angles of a quadrilateral are \[{{60}^{o}}\] \[\text{are}\] \[{{70}^{o}}\] and other two angles are in the ratio of\[8:15\]. Which of the following are the remaining two angles? |
| A. | \[{{80}^{o}},\,\,{{150}^{o}}\] |
| B. | \[{{90}^{o}},\,\,{{140}^{o}}\] |
| C. | \[{{100}^{o}},\,\,{{130}^{o}}\] |
| D. | \[{{110}^{o}},\,\,{{120}^{o}}\] |
| Answer» B. \[{{90}^{o}},\,\,{{140}^{o}}\] | |
| 266. |
In the parallelogram\[ABCD\], what are the measures of the angles\[x\]and\[y\]? |
| A. | \[{{60}^{o}},\,\,{{30}^{o}}\] |
| B. | \[{{30}^{o}},\,\,{{60}^{o}}\] |
| C. | \[{{45}^{o}},\,\,{{45}^{o}}\] |
| D. | \[{{90}^{o}},\,\,{{90}^{o}}\] |
| Answer» B. \[{{30}^{o}},\,\,{{60}^{o}}\] | |
| 267. |
In\[\Delta DEF\], \[PQ\] is a line segment drawn through mid-points of \[DE\] and\[DF\]respectively. If\[EF=7.6\,\,cm\], find the length of\[PQ\]. |
| A. | \[3.8\,\,cm\] |
| B. | \[4.5\,\,cm\] |
| C. | \[7.2\,\,cm\] |
| D. | \[2.6\,\,cm\] |
| Answer» B. \[4.5\,\,cm\] | |
| 268. |
In quadrilateral \[ABCD\], \[\angle B={{90}^{o}},\,\,\angle C-\angle D\]\[={{60}^{o}}\]and\[\angle A-\angle C-\angle D={{10}^{o}}\]. Find\[\angle A\], \[\angle C\]and\[\angle D\]. |
| A. | \[{{140}^{o}},\,\,{{95}^{o}},\,\,{{35}^{o}}\] |
| B. | \[{{95}^{o}},\,\,{{70}^{o}},\,\,{{65}^{o}}\] |
| C. | \[{{25}^{o}},\,\,{{45}^{o}},\,\,{{105}^{o}}\] |
| D. | \[{{150}^{o}},\,\,{{20}^{o}},\,\,{{35}^{o}}\] |
| Answer» B. \[{{95}^{o}},\,\,{{70}^{o}},\,\,{{65}^{o}}\] | |
| 269. |
\[JUMP\] is a square with\[\angle JUP={{45}^{o}}\]. Find\[\angle PUM\]. |
| A. | \[{{45}^{o}}\] |
| B. | \[{{90}^{o}}\] |
| C. | \[{{35}^{o}}\] |
| D. | \[{{15}^{o}}\] |
| Answer» B. \[{{90}^{o}}\] | |
| 270. |
In a quadrilateral three angles are in the ratio \[3:3:1\] and the fourth angle is\[{{80}^{o}}\]. Find the measure of the other angles. |
| A. | \[{{120}^{o}},\,\,{{120}^{o}},\,\,{{40}^{o}}\] |
| B. | \[{{100}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] |
| C. | \[{{110}^{o}},\,\,{{110}^{o}},\,\,{{60}^{o}}\] |
| D. | \[{{90}^{o}},\,\,{{90}^{o}},\,\,{{30}^{o}}\] |
| Answer» B. \[{{100}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] | |
| 271. |
In a quadrilateral ABCD, diagonals bisect each other at right angles. If\[AB=BC=AD=6\,\,cm\], find the length of\[CD\]. |
| A. | \[3\,\,cm\] |
| B. | \[6\,\,cm\] |
| C. | \[6\sqrt{2}cm\] |
| D. | \[12\,\,cm\] |
| Answer» C. \[6\sqrt{2}cm\] | |
| 272. |
In \[\Delta ABC\]\[,\] \[\angle A={{50}^{o}}\]\[,\]\[\angle B={{60}^{o}}\]and\[\angle c={{70}^{o}}\]. Find the measures of the angles of the triangle formed by joining the mid-points of the sides of\[\Delta ABC\]. |
| A. | \[{{90}^{o}}\] |
| B. | \[{{120}^{o}}\] |
| C. | \[{{180}^{o}}\] |
| D. | \[{{0}^{o}}\] |
| Answer» E. | |
| 273. |
If \[PQRS\] is a parallelogram, find the value of\[\angle Q-\angle S\]. |
| A. | \[{{90}^{o}}\] |
| B. | \[{{120}^{o}}\] |
| C. | \[{{180}^{o}}\] |
| D. | \[{{0}^{o}}\] |
| Answer» E. | |
| 274. |
Two adjacent angles of rhombus are \[3x-{{40}^{o}}\] and\[2x+{{20}^{o}}\]. Find the measurement of the greater angle. |
| A. | \[{{160}^{o}}\] |
| B. | \[{{100}^{o}}\] |
| C. | \[{{80}^{o}}\] |
| D. | \[{{120}^{o}}\] |
| Answer» C. \[{{80}^{o}}\] | |
| 275. |
In a\[\Delta ABC,P,Q\]and R are the mid-points of sides BC, CA and AB respectively. If AC =21 cm, BC=29cmandAB=30cm.The perimeter of the quadrilateral ARPQ \ is _____. |
| A. | 91 cm |
| B. | 60 cm |
| C. | 51 cm |
| D. | 70cm |
| Answer» D. 70cm | |
| 276. |
The diameter of the circumcircle is the diagonal of a rectangle which is \[10\,\,cm\] and breadth of the rectangle is\[6\,\,cm\]. Find its length. |
| A. | \[6\,\,cm\] |
| B. | \[5\,\,cm\] |
| C. | \[8\,\,cm\] |
| D. | \[7\,\,cm\] |
| Answer» D. \[7\,\,cm\] | |
| 277. |
Which of the following pairs of angles are opposite angles of a cyclic quadrilateral? |
| A. | \[{{131}^{o}},\,\,{{28}^{o}}\] |
| B. | \[{{95}^{o}},\,\,{{55}^{o}}\] |
| C. | \[{{123}^{o}},\,\,{{57}^{o}}\] |
| D. | \[{{64}^{o}},\,\,{{52}^{o}}\] |
| Answer» D. \[{{64}^{o}},\,\,{{52}^{o}}\] | |
| 278. |
Find the measure of each angle of a parallelogram, if one of its angles is \[{{30}^{o}}\] less than twice the smallest angle. |
| A. | \[{{70}^{o}},\,\,{{110}^{o}},\,\,{{70}^{o}},\,\,{{110}^{o}}\] |
| B. | \[{{70}^{o}},\,\,{{110}^{o}},\,\,{{80}^{o}},\,\,{{110}^{o}}\] |
| C. | \[{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}}\] |
| D. | \[{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] |
| Answer» B. \[{{70}^{o}},\,\,{{110}^{o}},\,\,{{80}^{o}},\,\,{{110}^{o}}\] | |
| 279. |
\[ABCD\] is a rectangle with\[\angle ABD={{40}^{o}}\]. Find\[\angle DBC\]. |
| A. | \[{{45}^{o}}\] |
| B. | \[{{30}^{o}}\] |
| C. | \[{{50}^{o}}\] |
| D. | \[{{35}^{o}}\] |
| Answer» D. \[{{35}^{o}}\] | |
| 280. |
In the given figure, \[p,\,\,q\] and \[r\] are three parallel lines. \[l\] and \[m\] are two transversals, such that \[DE=1.5\,\,cm\]\[,\] \[EF=3\,\,cm\]. Find \[BC\] if\[AB=2.5\,\,cm\]. |
| A. | \[4\,\,cm\] |
| B. | \[5.5\,\,cm\] |
| C. | \[5\,\,cm\] |
| D. | \[6\,\,cm\] |
| Answer» D. \[6\,\,cm\] | |
| 281. |
In quadrilateral\[ABCD,\]\[\angle A={{38}^{o}}\], \[\angle C=3\angle A\]and\[\angle D=4\angle A\]. Find the value of\[\angle B\]. |
| A. | \[{{56}^{o}}\] |
| B. | \[{{304}^{o}}\] |
| C. | \[{{52}^{o}}\] |
| D. | \[{{114}^{o}}\] |
| Answer» B. \[{{304}^{o}}\] | |
| 282. |
Which of the following is not a property of a rhombus? |
| A. | All four sides are equal. |
| B. | Diagonals bisect each other. |
| C. | Diagonals bisect opposite angles. |
| D. | One angle between the diagonals is\[{{60}^{o}}\] |
| Answer» D. One angle between the diagonals is\[{{60}^{o}}\] | |
| 283. |
\[ABCD\] is a rhombus such that one of its diagonals is equal to its side. Find the measure of the angles of rhombus\[ABCD\]. |
| A. | \[{{45}^{o}},\,\,{{135}^{o}},\,\,{{45}^{o}},\,\,{{135}^{o}}\] |
| B. | \[{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] |
| C. | \[{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}}\] |
| D. | \[{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}}\] |
| Answer» D. \[{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}}\] | |
| 284. |
In a quadrilateral, the angles, \[A,\,\,B,\,\,C\] and \[D\] are in the ratio\[1:2:3:4\]. What is the measure of the largest angle of the quadrilateral? |
| A. | \[{{135}^{o}}\] |
| B. | \[{{144}^{o}}\] |
| C. | \[{{154}^{o}}\] |
| D. | \[{{108}^{o}}\] |
| Answer» C. \[{{154}^{o}}\] | |
| 285. |
\[PQRS\]is a quadrilateral. \[PR\] and \[QS\] intersect each other at\[O\], In which of the following cases is PQRS a parallelogram? |
| A. | \[\angle P={{100}^{o}},\,\,\angle Q={{80}^{o}},\,\,\angle R={{100}^{o}}\] |
| B. | \[\angle P={{85}^{o}},\,\,\angle Q={{85}^{o}},\,\,\angle R={{95}^{o}}\] |
| C. | \[PQ=7\,\,cm,\,\,QR=7\,\,cm,\,\,RS=8\,\,cm,\]\[OS=5.2\,\,cm\] |
| D. | \[OP=6.5\,\,cm,\,\,OQ=6.5\,\,cm,\,\,OR=5.2\,\,cm,\] \[OS=5.2\,\,cm\] |
| Answer» B. \[\angle P={{85}^{o}},\,\,\angle Q={{85}^{o}},\,\,\angle R={{95}^{o}}\] | |
| 286. |
If the angles of a quadrilateral are in the ratio 1: 2 : 3 ; 4. Then, the measure of angles in descending order are |
| A. | \[{{36}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\] and \[{{144}^{o}}\] |
| B. | \[{{144}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\]and\[{{36}^{o}}\] |
| C. | \[{{36}^{o}},\,\,{{72}^{o}},\,\,{{108}^{o}}\]and\[{{144}^{o}}\] |
| D. | None of these |
| Answer» C. \[{{36}^{o}},\,\,{{72}^{o}},\,\,{{108}^{o}}\]and\[{{144}^{o}}\] | |
| 287. |
In a parallelogram find the sum of the bisected angles of two adjacent angles. |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» E. | |
| 288. |
\[APB\] and \[CQD\] are parallel lines and a transversal \[PQ\] cuts them at \[P\] and\[Q\]. Which of the following is formed by the bisectors of angles \[APQ,\,\,BPQ,\,\,CQP\] and\[PQD\]? |
| A. | A rectangle |
| B. | A rhombus |
| C. | A square |
| D. | Any other parallelogram |
| Answer» B. A rhombus | |
| 289. |
Which of the following is not true for a parallelogram? |
| A. | Opposite sides are equal. |
| B. | Opposite angles are equal. |
| C. | Opposite angles are bisected by the diagonals. |
| D. | Diagonals bisect each other. |
| Answer» D. Diagonals bisect each other. | |
| 290. |
In a parallelogram\[ABCD\], \[AB=4\,\,cm\] and\[BC=7\,\,cm\]. Each of its diagonals is less than which of the following? |
| A. | \[3\,\,cm\] |
| B. | \[4\,\,cm\] |
| C. | \[7\,\,cm\] |
| D. | \[11\,\,cm\] |
| Answer» E. | |
| 291. |
By using a given figure of quadrilateral ABCD, match the following: Column-I Column-II (p) (P) If ABCD is a parallelogram, then sum of the angles x, y and z is (1) \[{{25}^{o}}\] (q) (Q) If ABCD is a rhombus, where \[\angle D={{130}^{o}},\]then the value of \[x\]is (2) \[{{180}^{o}}\] (r) (R) If ABCD is a rhombus, the value of w is (3) \[{{50}^{o}}\] (s) (S) If ABCD is a parallelogram, where\[x+y={{130}^{o}}\] then the value of B is (4) \[{{90}^{o}}\] |
| A. | \[(p)\to (1),(q)\to (2),(r)\to (3),(s)\to (4)\] |
| B. | \[(p)\to (2),(q)\to (1),(r)\to (4),(s)\to (3)\] |
| C. | \[(p)\to (3),(q)\to (1),(r)\to (2),(s)\to (4)\] |
| D. | \[(p)\to (4),(q)\to (3),(r)\to (1),(s)\to (2)\] |
| Answer» D. \[(p)\to (4),(q)\to (3),(r)\to (1),(s)\to (2)\] | |
| 292. |
If the lengths of two diagonals of a rhombus are \[12\,\,cm\] and\[16\,\,cm\], find the length of each side of the rhombus. |
| A. | \[10\,\,cm\] |
| B. | \[14\,\,cm\] |
| C. | \[16\,\,cm\] |
| D. | \[8\,\,cm\] |
| Answer» B. \[14\,\,cm\] | |
| 293. |
If the sides BA and DC of quadrilateral ABCD are produced as shown in the given figure, then |
| A. | \[x+y=a+b\] |
| B. | \[x-y=a-b\] |
| C. | \[\frac{x-y}{2}=a-b\] |
| D. | \[2(x+y)=a+b\] |
| Answer» B. \[x-y=a-b\] | |
| 294. |
What is the number of measurements required to construct a quadrilateral? |
| A. | \[5\] |
| B. | \[4\] |
| C. | \[3\] |
| D. | \[2\] |
| Answer» B. \[4\] | |
| 295. |
Fill in the blanks. (a) If consecutive sides of a parallelogram are equal then it is necessarily a P . (b) The figure formed by joining the mid-points of consecutive sides of a quadrilateral is Q . (c) If the diagonals of a parallelogram are equal and perpendicular to each other, it is a R . |
| A. | P Q R Square Parallelogram Rhombus |
| B. | P Q R Kite Rhombus Square |
| C. | P Q R Rhombus Rectangle Rectangle |
| D. | P Q R Rhombus Parallelogram Square |
| Answer» E. | |
| 296. |
If \[PQ\] and \[RS\] are two perpendicular diameters of a circle, what is\[PRQS\]? |
| A. | A rectangle |
| B. | A trapezium |
| C. | A square |
| D. | A rhombus but not a square |
| Answer» D. A rhombus but not a square | |
| 297. |
Read the statements carefully and state ?T? for true and 'F' for false. (i) Diagonals of a parallelogram are perpendicular to each other. (ii) All four angles of a quadrilateral can be obtuse angles. (iii) If all sides of a quadrilateral are equal, then it is a rhombus. |
| A. | (i) (ii) (iii) T F F |
| B. | (i) (ii) (iii) F F T |
| C. | |
| D. | (i) (ii) (iii) F F F |
| Answer» D. (i) (ii) (iii) F F F | |
| 298. |
If angles \[P,\,\,Q,\,\,R\] and \[S\] of the quadrilateral\[PQRS\], taken in order, are in the ratio\[3:7:6:4\], what is\[PQRS\]? |
| A. | A rhombus |
| B. | A parallelogram |
| C. | A trapezium |
| D. | A kite |
| Answer» D. A kite | |
| 299. |
Study the statements carefully. Statement 1: If a sum of a pair of opposite angles of a quadrilateral is\[{{180}^{o}}\], the quadrilateral is cyclic. Statement 2: A line drawn through mid-point of a side of a triangle, parallel to another side equal to third side. Which of the following options holds? |
| A. | Both Statement-1 and Statement-2 are true. |
| B. | Statement-1 is true but Statement-2 is false. |
| C. | Statement-1 is false but Statement-2 is true. |
| D. | Both Statement-1 and Statement-2 are false. |
| Answer» C. Statement-1 is false but Statement-2 is true. | |
| 300. |
When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral\[PQRS\], taken in order, a rhombus? |
| A. | \[PQRS\] is a rhombus. |
| B. | \[PQRS\]is a parallelogram. |
| C. | Diagonals of \[PQRS\] are perpendicular. |
| D. | Diagonals of \[PQRS\] are equal. |
| Answer» E. | |