Saved Bookmarks
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 301. |
If the length of an enlarged rectangle is 12 cm and the scale factor is `(3)/(2)`, then the length of the original rectangle is __________. |
|
Answer» Correct Answer - 8 cm N/A |
|
| 302. |
Which of the following hasonly 2 lines of symmetry?(a) Equilateral triangle (b) Rhombus(c) Circle (d) Noneof these |
| Answer» Rhombus has only 2 lines of symmetry, and they are two diagonals. | |
| 303. |
Which of the following is false?A. Radius is perpendicular to the tangent at the point of contact.B. Major segment contains the centre of the circleC. The line segment joining any two points on the circumference is called arc.D. None of the above |
| Answer» Correct Answer - C | |
| 304. |
Which of the following is an angle of the major sector?A. `60^(@)`B. `100^(@)`C. `200^(@)`D. `400^(@)` |
| Answer» Correct Answer - C | |
| 305. |
In the following figure, two isosceles right angled triangles, DEF and HGI are on the same base `bar(DH)` and `bar(DH)` is parallel to `bar(FI)`. If DE=GH=9 cm and DH=20 cm, then the area of the quadrilateral FEGI is…………………. A. 99 `cm^(2)`B. `40.5 cm^(2)`C. `81 cm^(2)`D. `180 cm^(2)` |
|
Answer» Correct Answer - A Area of trapezium, `FEGI=1/2(FE + EG) xx FD`. |
|
| 306. |
Which of the following is the angle of a quadrant?A. `60^(@)`B. `90^(@)`C. `180^(@)`D. `360^(@)` |
| Answer» Correct Answer - B | |
| 307. |
An isosceles triangle has ________ line (s) of symmetry. |
| Answer» Correct Answer - one | |
| 308. |
Which of the following can be the angle subtended by a minor arc at the centre?A. `100^(@)`B. `220^(@)`C. `180^(@)`D. `270^(@)` |
| Answer» Correct Answer - A | |
| 309. |
In a mombus PORS,the diagonals intersect at o Given that `/_P=120^(@)` and `OP=3cm` .What is the side of the mombus?A. 4 cmB. 6 cmC. `3 sqrt(3)` cmD. Cannot be determined |
|
Answer» Correct Answer - b (i) In a `30^(@) -60^(@)-90^(@)` triangle , the corresponding side are in the ratio `1: sqrt(3) :2`. (ii) Find the angles of one of the `Delta ("les")` formed by the diagonals in the rhombus. (iii) Use the concept of ratio of sides and ratio of angles and get side .Sides opposite to angles `30^(@)-60^(@)-90^(@)` will be in the ratio `1: sqrt(2) :2`. |
|
| 310. |
In the given rectangle ABCD, the sum of the lengths of two diagonals is equal to 52 cm and E is a point in AB, such that `bar(OE)` is perpendicular to `bar(AB)`. Find the lengths of the sides of the rectangle, if OE=5 cm. A. 24 cm, 10 cmB. 12 cm, 10 cmC. 24 cm, 5 cmD. 12 cm, 15 cm |
|
Answer» Correct Answer - A Find the length of the diagonal. |
|
| 311. |
In the following (not a scale) , if `BC=20cm` and `angleBAD =angle CAD` , then BD = ___________. |
|
Answer» Correct Answer - 8cm N/A |
|
| 312. |
In the given figure, AC is the diameter, AB and AD are equal chords. If `angle AED=110^(@)`, then find `angleBAD`.A. `40^(@)`B. `55^(@)`C. `110^(@)`D. `120^(@)` |
|
Answer» Correct Answer - A `angleBAC=90^(@)` and BC is a diameter. |
|
| 313. |
ABCD is rhombus and `angleBAD=60^(@)`. The measure of `angleCAB` is _______A. `120^(@)`B. `60^(@)`C. `30^(@)`D. `80^(@)` |
|
Answer» Correct Answer - C `30^(@)` Hence, the correct option option is (c ). |
|
| 314. |
In the figure below, ABCD is a square , MDC is an equilateral triangle. Find the value of x. A. `75^(@)`B. `90^(@)`C. `105^(@)`D. `60^(@)` |
|
Answer» Correct Answer - c (i) The diagonal BD bisects `/_B` and `/_ D` . (ii) BCD is an isosceles righ angles triangle using this find `/_ CBD`. (iiI) Given DMC is equilateral, so use this find `/_ MCB`. (iv) Sum of the angles of a triangle is `180^(@)`. Using this find `/_ x`. |
|
| 315. |
The following sentences are the steps involved in construction of the incircle for the triangle XYZ in which `/_Y =90^(@), XZ=6` cm and `YZ =4` cm. Arrange them in sequential order from the first to the last. (A) Mark the foot of the perpendicular from I onto YZ as D. (B) Construct the triangle XYZ with `/_ Y =90^(@),XZ=6` cm and `YZ =4 cm`. (C ) Draw a circle with I as the centre and ID as radius. This is the required incircle. (D) Draw the bisectors of `/_ X, /_ Y` and `/_Z` and mark their point of concurrence as I.A. BDCAB. DBACC. DBCAD. BDAC |
|
Answer» Correct Answer - D (B),(C ) ,(A) and (D) are the sequencital order |
|
| 316. |
In the above figure, `bar(AF) || bar(ED),bar(CG) ||bar(AB)` and `bar(AE) ||bar(HD)` If `/_ FPD =40^(@)`, then `/_ AED =`A. `40^(@)`B. `80^(@)`C. `120^(@)`D. `140^(@)` |
|
Answer» Correct Answer - D (i) `(/_FPD` and `/_PDE` are alternate angles and are equal. (ii) `/_ PDE` and `/_ AED` are interior angles on the same side of transversal and their sum is `180^(@)`. |
|
| 317. |
Ar and BS are the tangents to the circle, with centre O, touching at P and Q respectively and PQ is the chord. If `angle OQP=24^@, then angle RPQ=` __________. A. `100^@`B. `115^@`C. `150^@`D. `90^@` |
|
Answer» Correct Answer - B Radius is perpendicular to the tangent at the point of contact. |
|
| 318. |
In trapezium KLMN ,KL and MN are parallel sides. A line is drawn, from the point A on LN, parallel to MN meeting LM at `B. KN :LM` is equal to _________.A. `KL: NM`B. `(KL+KA):(NM+MB)`C. `(KA-AN):(LB-BM)`D. `KL^2:MN^2` |
|
Answer» Correct Answer - C Apply BPT and use componodo -divisible after drawing the complete figure . |
|
| 319. |
In the following figure, ABCD is square and AED is an equilateral triangle. Find the value of a.A. `30^@`B. `45^@`C. `60^@`D. `75^@` |
|
Answer» Correct Answer - D Diagonal of a square bisects the angles at the vertices. `angle FDC 30^@ and angle FCD =45 ^@`. |
|
| 320. |
In `trianglePQR`, M and N are points on PQ and PR, respectively, such that `bar(MN) || bar(QR)`, If PM =`x`, PR `=x+9, PQ=x+13` and `PN=x-2`, then find `x`.A. 10B. 11C. 13D. 15 |
|
Answer» Correct Answer - C i) Use BPT. ii) By BPT, `(PM)/(PQ) = (PN)/(PR)` |
|
| 321. |
In the following figure, ABC is an equilateral triangle. DE is parallel to BC and equal to half the lengths of BC. If AD+ EC+ CB=24 cm, then What is the perimeter of triangle ADE? A. 12 cmB. 16 cmC. 18 cmD. Cannot be determined. |
|
Answer» Correct Answer - C In `triangleABC, (AD)/(AB) = (AE)/(AC) = (DE)/(BC)`. |
|
| 322. |
In the following, PQRS is a rhombus, SQ and PR are the diagonals of the rhombus intersecting at O. If angle `OPQ = 35^(@)`, then find the value of angle ORS + angle OQP. A. `90^(@)`B. `180^(@)`C. `135^(@)`D. `45^(@)` |
|
Answer» Correct Answer - A In a rhombus, diagonals bisect at `90^(@)`. |
|
| 323. |
In a quadrilateral PQRS, `bar(PQ)||bar(RS)` and PR=QS. PQRS is a /an_____A. squareB. rectangleC. rhombusD. isosceles trapezium. |
|
Answer» Correct Answer - D Given quadrilateral is an isosceles trapezium. Hence, the correct option is (d). |
|
| 324. |
The measure of one of the angles of an isosceles triangle is `94^(@)`. Which of the following is definitely the measure of one of the other angles of the given triangle ?A. `94^(@)`B. `86^(@)`C. `43^(@)`D. `46^(@)` |
|
Answer» Correct Answer - C The sum of the measure of the angles of a triangle `=180^(@)` One of the angles is `94^(@)` ( given ) ltvrgt `implies `The sum of the measure of the other two angles `=180^(@)-94^(@)=86^(@)` . `:.` The measure of each of the equal angles is `=(86^(@))/(2)=43^(@)`. Hence, the correct option is ( c). |
|
| 325. |
In the given figure, if l||m, then what type of a triangle is ABC ? A. ScaleneB. IsoscelesC. Right angledD. Both (b) and (c ) |
|
Answer» Correct Answer - D Given , `l||m`, `angleBCA=angleDEC=45^(@)` ( corresponding angles ) `angleCBA=angleEDB=45^(@)` ( corresponding angles ) `angleBCA+angleCBA+angleBAC=180^(@)` `implies 45^(@)+45^(@)+angleBAC=180^(@)` `implies angleBAC=90^(@)` `:.` In `DeltaABC, angleA=90^(@), angleB=angleC=45^(@)`. `implies DeltaABC` is a right - angled isosoceles triangle . Hence, the correct option is (d). |
|
| 326. |
Which of the following statement is true ?A. Every trapezium is a parallelogramB. Every square is a rhombus.C. Every rectangle is a squareD. Every parallelogram is a rectangle . |
|
Answer» Correct Answer - B Every square is a rhombus . It is true statement. Hence, the correct option is (b) |
|
| 327. |
In the given figure (not to scale), `bar(AB)||bar(QP)||bar(SD)|` and also `bar(QR)| |bar(DP)`. Find x |
|
Answer» (a) QSDP is a parallelogram. (b) Find `/_QSC`, as vertically opposite angles are equal. (c ) `/_ QSD` and `/_ SDP` are supplementary as they are the angles on the same side of the transversal. Use this to find `/_SDP`. (d) `/_SDP` and x are corresponding angles. |
|
| 328. |
The sides of `Delta ABC` measure 5 cm, 12 cm and 13 cm. What type of a triagnel is ABC ? |
|
Answer» Since no two sides are equal , ABC is a scalence triangle. Further, `5^(2)+12^(2)=13^(2)`. Since, the square on the longest side is equal to the sum of the squares on the other two sdes, ABC is a right angles triangle. |
|
| 329. |
In the given figure (not to scale), ABC is an isosceles triangle in which AB=AC. AEDC is a parallelogram. If `angleCDF=70^(@)` and `angleBFE=180^(@)`, then find `angleFBA`. A. `30^(@)`B. `40^(@)`C. `50^(@)`D. `80^(@)` |
|
Answer» i) In a parallelogram, any pair of adjacent angles are supplementary. ii) `angleEFG=angleFGC=angleAGB` and `angleACB` `=angleABC=angleCDE. (therefore angle bar(AC) || bar(DE))` iii) Use the above data and find `angleBAC`, and then `angleABC`. |
|
| 330. |
Find the number of diagonals of a 10-sided polygon. |
|
Answer» Here, n=10 `therefore` Number of diagonals `=(10(10-3))/2=35` |
|
| 331. |
Find the sum of the interior angles of a polygon of 8 sides. |
|
Answer» Here, n=8 `therefore` Sum of interior angles `=[(2)(8)-4]90^(@)=1080^(@)`. |
|
| 332. |
In a `DeltaABC`, if the exterior angle of C is `135^(@)`, then `angleA+angleB=`_______ |
| Answer» Correct Answer - `135^(@)` | |
| 333. |
In the figure above, ABC is a triangle in which BC=10 cm and AC=13 cm. If AD is the perpendicular bisector of BC, then find the length of AD.A. 12B. 13C. 10D. 5 |
| Answer» Correct Answer - A | |
| 334. |
Construct the incircle of a given triangle ABC. The following sentences are the steps involved in the above construction. Arrange them in sequencial order from first to left. (A) Draw perpendicular `overline(IM)` from I onto `overline(BC)`. (B) Taking I as centre and IM as the radius , draw a circle. (C) Draw a DABC with the given measurements. (D) Draw bisects of two to the angles. say `angle B and angle C` to intersect at I. (D) Draw bisects of two of the angles, say `angle B and angle C` to intersect at I.A. DCABB. CDABC. CADBD. DACB |
|
Answer» Correct Answer - B CDAB is the required sequential order. |
|
| 335. |
In `DeltaABC, AB=5 cm and BC=4 cm`. Find the range of value that CA can take. |
|
Answer» In a triangle, the sum of two sides is greater than the third side and the difference of two sides is less than the third sides. `CA lt AB+ BC and CA gt AB-BC` `implies CA lt 9 cm and CA gt 1 cm` `implies 1 cm lt CA lt 9cm ` |
|
| 336. |
In `DeltaABC, AC=BC and angleBAC=50^(@).` Find `angleBCA`. |
|
Answer» Given : AC=BC In a triangle, angles opposite to equal sides are equal. `:. angleABC=angleCAB=50^(@)` `angleABC+angleBCA+angleCAB=180^(@)` `50^(@)+angleBCA+50^(@)=180^(@)` `implies angleBCA=80^(@)` |
|
| 337. |
The ratio of the product of the sides of an equilateral triangle to its perimeter is equal to the ratio of the product of the sides of another equilateral triangle to its perimeter. Then the triangles are |
|
Answer» Let the sides of the triangles be x and y. Given `(x^(3))/(3x)=(y^(3))/(3y)` `x^(2)=y` `x=y` `:.` Both the triangles are congruent. `:.` They are similar. |
|
| 338. |
In the figure above, the angles a,b,c,d and e are consecutive integers in degrees, a=__________A. `70^(@)`B. `74^(@)`C. Either (a) or (b)D. Neither (a) nor (b) |
|
Answer» Correct Answer - C `a^(@),b^(@),c^(@),d^(@), and e^(@)` can be in ascending order or in descending order. `:. B=a+1, c=a+2,d=a+3, and e=a+4 ro b=a-1, c=a-2, d=a-3, and e=a-4` `:. a+b+c+d+e+=5a+10 or 5a-10` Sum of the angles around a point is `360^(@)`. `:. a^(@)+b^(@)+c^(@)+d^(@)+e^(@)=360^(@)` `:. (5a+10)^(@)=360^(@) or (5a-10)^(@)=360^(@)` `:. a^(@)=70^(@) or 74^(@)` Hence, the correct option is ( c). |
|
| 339. |
There are three angles. The second angle is one-third of the compliment of the first angle. The third angle is half of the supplement of the first angle. The third angle is 6 times the second angle. Find the first angle.A. `45^(@)`B. `60^(@)`C. `75^(@)`D. `90^(@)` |
|
Answer» Correct Answer - B Let the first angle, the second angle, and the third angle be f, s and t, respectively. `s=((90^(@)-f)/(3))=(30^(@)-(f)/(3))` `t=((180^(@)-f)/(2))=(90^(@)-(f)(2))` t=6s `:. (90^(@)-(f)/(2))=6(30^(@)-(f)/(3))` `implies (90^(@)-(f)/(2))=(180^(@)-2f)` `f=60^(@)` Hence, the correct option is (b) |
|
| 340. |
In the following figure, O is the center of the circle. If `angleMPN = 55^(@)`, then find the value of `angleMON+angleOMN +1/2angleMNO`. A. `145^(@)`B. `162 (1/2)^(@)`C. `158(1/2)^(@)`D. `180^(@)` |
|
Answer» Correct Answer - B Angle subtended by an arc at the center is double the angle subtended by it on the remaining part of the circle. |
|
| 341. |
Which of the following pairs of angles are supplementary ?A. `(0, 180^(@))`B. `(90^(@), 90^(@))`C. `(120^(@),60^(@))`D. All the above |
|
Answer» Correct Answer - D If the sum of two angle is `180^(@)`, then the two angles are supplementary. |
|
| 342. |
If the arms of an angle on the paper are increased, the angle increases. |
|
Answer» The correct answer is False. |
|
| 343. |
In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle? |
|
Answer» XY + YZ = 17 cm … (1) XZ + YW = 26 cm … (2) (2) ⇒ XZ = 13, YW = 13 (∵ In rectangle diagonals are equal). (1) ⇒ XY = 5, YZ = 12 XY + YZ = 17 ⇒ Using Pythagoras theorem 52 + 122 = 25 + 144 = 169 = 132 ∴ In ΔXYZ = 132 = 52 + 122 it is verified ∴ The length is 12 cm and the breadth is 5 cm. |
|
| 344. |
Fill in the blank,The number of capital letters of the English alphabets having only vertical line of symmetry is________. |
|
Answer» The number of capital letters of the English alphabets having only vertical line of symmetry is 7 (A,M,U,V,W,Y,T). |
|
| 345. |
Fill int the b;lank,The number of digits having no line of symmetry is_________. |
|
Answer» The number of digits having no line of symmetry is 7 (1,2,4,5,6,7,9). |
|
| 346. |
The number of lines of symmetry in a 30o - 60o - 90o set square is (A) 0 (B) 1 (C) 2 (D) 3 |
|
Answer» The correct answer is (A) 0 |
|
| 347. |
The number of lines of symmetry in a ruler is (A) 0 (B) 1 (C) 2 (D) 4 |
|
Answer» The correct answer is (C) 2 |
|
| 348. |
The number of lines of symmetry in a divider is (A) 0 (B) 1 (C) 2 (D) 3 |
|
Answer» The correct answer is (B) 1 |
|
| 349. |
The number of lines of symmetry in compasses is (A) 0 (B) 1 (C) 2 (D) 3 |
|
Answer» The correct answer is (A) 0 |
|
| 350. |
In this Figure, which is not the correct way of naming an angle?(a) ∠Y(b) ∠ZXY(c) ∠ZYX(d) ∠XYZ |
|
Answer» The correct option is (b) ∠ZXY. |
|