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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
C is a triangle in which 4B -24C. D is a point on BC such that AD bisects 4BACand AD-CD. Prove that ZBAC 728. AB |
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| 2. |
13. AABC is an equilateral triangle. AD bisects ZBAC. Show that AABDAACDnand a cncOngruent? If so |
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Answer» it is too hard for me to understand can you answer in simple language I study in class 7 |
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| 3. |
Δ'ABC and Δ DBCare two isosceles triangles onthe same base BC and vertices A and D are on thesame side of BC (see Fig. 7.39). IfAD is extendedto intersect BC at P, show that1.(ii) Δ ΑΒΡ Δ ACP(iii) AP bisects LA as well as < D.(iv) AP is the perpendicular bisector of BC.Fig. 7.39 |
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Answer» thanks |
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| 4. |
he internal height of the cylinder is 7m and the internal radius is 3.5 m. Calculate:The total area of the internal surface, excluding the base,(i)(ii)14The internal volume of the container in m3. |
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Answer» (i) Total area of the internal surface of the container excluding the base =Area of the internal curved surface of the cylinder + Area of the internal surface of the hemisphere = {2π × 3.5 × 7 × (3.5)^2} m^2= 2π × 3.5 (7 + 3.5) m^2= 231 m^2 (ii). The internal volume of the container = Volume of the cylinder + volume of the hemisphere = {π × (3.5)^2× 7 + (2/3)π × (3.5)^3} m^3= (1078/3) m^3= 359.3 m^3 |
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| 5. |
32. The sides PQ, PRof a triangle PQR are equal, and S, T are points on PR, PQ such thatZPSQ and PTR are right angles. Prove that the triangles PTR and PSQ are congruentIf QS and RT intersect at X, prove that the triangles PTX and PSX are congruent. |
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| 6. |
19. Dis the midpoint of side BCof A ABCand Eis themidpoint of BD. If O is the midpoint of AE,prove that ar(ABOE) ar(AABC).OvB E D |
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| 7. |
5. The perimeters of two similar triangles ABC and PQR are 32 em andICBSE 2001]24 cm respectively. If PQ12 cm, find AB. |
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| 8. |
10Fig. 1.33Fig. 1.34Fig. 1.35Î PQR, PM 15, PQ-25- 20, NR 8. State whether lineis parallel to side RQ. GivesonFig. 1.36 |
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Answer» PM/PQ = 15/25 = 3/5PN/PR = 12/20 = 3/5Therefore, NM || RQ. |
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| 9. |
guRI+ 6.7 " | - g um |
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Answer» tan³x-1/tanx-1(tanx-1)(tan²x-tanx-1)/tanx-1=tan²x-tanx-1=sec²x+1+tanx-1=sec²x+tanx |
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| 10. |
um of the reciprocal |
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| 11. |
Fig. 6.343. In Fig. 6.35. RT andOR QTOS PR. In Fig. 6.35, andRnd 1 42. Show thatFig. 6.35 |
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Answer» In ΔPQR, ∠1 = ∠2∠PQR = ∠PRQ [GIVEN]∴ PR = PQ ……………..…(1) [Sides opposite to equal angles of a triangle are also equal]Given: QR/QS = QT/PRQR/QS = QT/PQ QS/QR = PQ/QT…... …(ii) [Taking reciprocals] [From eq (i)]In ΔPQS and ΔTQR,QS/QR = PQ/QT [From eq (ii)] ∠PQS = ∠TQR [ common]∴ ΔPQS ~ ΔTQR [By SAS similarity criterion] Hence, proved Like my answer if you find it useful! |
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| 12. |
Fig. 15.13710. In Fig. 15.138, O is the centre of the circle, prove that <3420Fig. 15.138Fig. 15.139 |
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Answer» AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference. hence w = v = x/2 in the quadrilateral, CGDH, angle C = y (vertical angle) sum of angles in the quadrilateral CGDH is 180 - v + y + 180 - w + z = 360 hence, w + v = x = y + z |
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| 13. |
Fig. 1.33Fig. 1.34Fig. 1.35in Î POR, PM = 15, PQ = 25PR 20, NR 8. State whether lineNM is parallel to side RQ. GivereasonFig. 1.36 |
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| 14. |
f}5: Simplify: { e(1+ nga)(r-âmâ"')(l - S S 24 |
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| 15. |
C = 90°, AB = 9 m, BC = 12 m,A park, in the shCD 5 m and Aape of a quadrilateral ABCD, has= 8 m. How much area does it occupy? |
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| 16. |
231Simplify: E |
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| 17. |
7. If a wire of length 36 cm is bent in the form of a semicircle, what is the radius of the semicircle?8. A horse is tied to pole fixed at nne cnrn |
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Answer» Perimeter of semicircle =πr 36 = πr r= 36/π |
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| 18. |
Find the radius of a semicircle i its perimeter is 24 cm. |
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Answer» thanks |
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| 19. |
InFig.10.38,ABC 69°, Z ACB 31o, findZ BDC.31Fig. 10.38 |
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Answer» thanks |
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| 20. |
radius ofa semicircle if its perimeter is 24 cm..//Find <AOB in the given figure. |
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Answer» Perimeter of a semicircle=22/7×r24=22/7×r r=24×7/22r=7.64 |
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| 21. |
In Fig. 10.38, Z ABC 69, ACB 31°, findZ BDC |
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Answer» ∠ABC = 69°, ∠ACB = 31° [Given] InΔABC∠ABC + ∠ACB+∠BAC = 180°⇒ ∠BAC = 180° - ∠ABC - ∠ACB⇒ ∠BAC = 180° -69° - 31° = 80° ∠BDC = ∠BAC ( Angle drawn from same chord) ∴ ∠BDC= 80° |
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| 22. |
In Fig. 10.38, < ABC = 69, < ACB = 31°, findZ BDC. |
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| 23. |
4. In Fig. 12.38, ZABC 69°,ACB 31°, findZ BDC. |
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Answer» ∠ABC = 69°, ∠ACB = 31° [Given] InΔABC∠ABC + ∠ACB+∠BAC = 180°⇒ ∠BAC = 180° - ∠ABC - ∠ACB⇒ ∠BAC = 180° -69° - 31° = 80° ∠BDC = ∠BAC ( Angle drawn from same chord) ∴ ∠BDC= 80° hit like if you find it useful |
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| 24. |
In Fig. 10.38, < ABC = 69°, < ACB-31°, findZ BDC.'Fig. 10.38 |
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| 25. |
4. In Fig. 10.38, Z ABC 69,ACB 31° findBDCเรื |
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| 26. |
log ltan xdx2 |
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| 27. |
1log (1+x)dx2 |
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| 28. |
Find theradius ofa semicircle if its perimeter is 24 cm.Find LAOB in the given figure. |
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Answer» Perimeter of a semicircle=22/7×r24=22/7×r r=24×7/22r=7.64 |
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| 29. |
Find the perimeter of a semicircle whose radius is 21 cm |227 |
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Answer» Radius of semicircle r = 21 cm Perimeter of semicircle= pi*r + 2r= (22/7)*21 + 2*21= 22*3 + 42= 66 + 42= 108 cm |
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| 30. |
EXERCISE 8.21. A park, in the shape of a quadrilateral ABCD, has C 90°, AB 9 m, BC 12 m,CD5 m and AD 8 m. How much area does it occupy? |
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| 31. |
1.A park, in the shape of a quadrilateral ABCD, has < CCD 5 m and AD90, AB9 m, BC12 m,8 m. How much area does it occupy? |
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| 32. |
\frac{\tan \theta-\cot \theta}{\sin \theta \cos \theta}=\tan ^{2} \theta-\cot ^{2} \theta |
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| 33. |
( \tan \theta %2B \sec \theta - 1 ) ( \tan \theta %2B 1 %2B \sec \theta ) = \frac 2 \sin \theta 1 - \sin \theta |
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Answer» kaise hai re photo re baba |
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| 34. |
Prove that \frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta} using the identity \sec ^{2} \theta=1+\tan ^{2} \theta |
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Answer» sinx-cosx+1/ sinx+cosx -1 =(sinx-cosx+1)x(sinx +cosx +1) / (sinx+cosx - 1)x(sinx +cosx +1) =(sinx +1)sq. - (cosx)sq./ (sinx +cosx) sq. - (1)sq. =sinsq.x+2sinx+1-cossq.x/ sinsq.x+cossq.x+2sinxcosx-1 =2sinsq.x+2sinx/ 2sinxcosx =2sinx(sinx +1)/ 2sinxcosx =sinx+1/cosx =(1+sinx)x(1-sinx)/ (cosx) x(1-sinx) =cosx/(1-sinx) (dividing num. and den. by cosx) =1/secx-tanx = sec x + tan x |
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| 35. |
1.A park, in the shape of a quadrilateral ABCD, has < C = 90°, AB = 9 m, BC = 12 m,CD-5 m and AD = 8 m. How much area does it occupy? |
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| 36. |
tan θProve that:\frac{\tan \theta}{\sin ^{3} \theta}+\sin \theta \cos \theta |
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| 37. |
each other al lShow that ABCD is a trapezium.Solve : sin2 θ + sin θ-1 and find θ.(d) |
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| 38. |
3. In Fig. 6.41, if AB Il DE, Z BAC 35° and Z CDE 53o, find DCE.P 13535。62°1100Z.Fig. 6.39Fig. 6.40Fig. 6.41DPT-400 / RPT=95。 |
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| 39. |
the adjoining figure, ABCD is aquadrilateral in which diag. BD- 14 cm. IfAL L BD and CM L BD such that AL 8 cmand CM 6 cm, find the area of quad. ABCD |
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| 40. |
Fig. 6.59Fig. 6.584 i Fig 659, ABC is a triangle in whichABC90and AD1AC AB+BC 2BC. BD.In Fig. 660. AD is a median of a triangle ABC andAML BC. Prove that:A.10. NBC(i) AC-AD, BC . DM +A.Fig. 660 |
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| 41. |
9. Prove that: i logsin x dx =~ 2__x log 2. |
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Answer» hit like if you find it useful |
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| 42. |
If yse*, prove that d (I+ log y)dx log y242 |
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Answer» y |
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| 43. |
Fig. 10.37In Fig. 10.38, 4 ABC-69,Z BDCACB 31o, find319Fig. 10.38 |
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| 44. |
16 Find the curved surface area of the right circular cone whose radius is 3cm and the height is6 Find the curved surface area of the right circutar cone whose radius is 3cm and the height isMcmm.(Take t 3.14) |
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| 45. |
1.Area of semicircle whose radius 'Y is |
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Answer» Given radius of circle r = y Area of semicircle = 1/2*pi*r^2= 1/2*pi*y^2= (pi/2)y^2 (a) is correct option |
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| 46. |
lind the equation to the circle(i) Whose radius is 10 and whose centre is (- 5, -6) |
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Answer» equation is(x+5)^2+(y+6)^2=10^2x^2+10x+25+y^2+12y+36=100x^2+y^2+10x+12y-39=0 |
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| 47. |
Find the volume of a sphere whose radius is 7cm |
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| 48. |
cirele is a thombusL Atrisngle AlBC is drawn to circumscribe a circleof odius 4 cm such that the segments BD andUC ta which BC is divided by the point of écestact D are of lengths & cm and 6 cmropecively (es Fig-10.14) Find the sidesABund/с.13. Prove totdemuadrilat |
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Answer» thank you so much |
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| 49. |
(text*((b*y)*(x - 5*y)))*(75*(x*y^2) - 15*x^2*y %2B x^3 - 125*y^3) |
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| 50. |
its29 A hemispherical bowl of internal radius 9 cm is full of water.contents are emptied into a cylindrical vessel of internal radius 6 cm.Find the height of water in the cylindrical vessel.CBSE 2012 |
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