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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. |
1. एक समानांतर चतुर्भुज का आयतन क्या होगा जिसकासह टर्मिनल किनारों के साथ वैक्टर =2i+j-3k,bai+j+2kऔर c=i-2i+3k है ? |
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Answer» 22 cube units for volume is the average weather condition of a place over a long period of time 22 cube units for volume |
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| 2. |
0) (3k + 4) 3k+ 4) |
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Answer» We will use(a+b)²= a= 3kb= 4L9k²+16l²+ 288kl |
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| 3. |
सदिश ४ = ।। 2) + 3k की दिक–कोसाइन ज्ञात कीजिए। |
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Answer» as |
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| 4. |
13 1 ध्धु को. 5 ) e 2T | |
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| 5. |
\sinh ^{-1}(x)=\log _{e}(5+\sqrt{26}) \text { then } x= |
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| 6. |
e ^ { \operatorname { sinh } ^ { - 1 } ( \operatorname { cot } \theta ) } = |
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| 7. |
\cosh ^{-1}(k)=\log _{e}(3+2 \sqrt{2}) t \operatorname{then} k= |
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| 8. |
2[3+4]-4{3-6}] |
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Answer» 2(3+4)-4(3-6)=2(7)-4(-3)=14+12=16 |
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| 9. |
3-27x + 361-को सरल करने।2x-5पर प्राप्त होगा - |
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| 10. |
13 7 110 1/2 3 8Illustration 3: If-rA00 04 then find eigen values of A9. |
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| 11. |
arallel sides of a trapezium are 25 cm1. Theand 13 cm, its non-parallel sides are equal,each being 10 cm. Find the area of the04A15 ctrapezium. |
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| 12. |
949. Find the missing number from the given alterativesदियों में से लुप्त तया ज्ञात करें।ANAAB1210 |
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Answer» d is the correct....10 Yes option (d) is the correct answee |
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| 13. |
041- ,(1+x) "" |
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| 14. |
ยง 11, Expansions in series for sinh x and cosh |
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Answer» thank you so much Sir |
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| 15. |
Two steel wires have equal volumes. Theirdiameters are in the ratio 2 : 1. When sameforce is applied on them, the elongationproduced will be in the ratio of |
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| 16. |
\sinh ^{-1}(2)+\sinh ^{-1}(3)=x \text { then } \cosh (x)= |
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| 17. |
Find Laplace transform of e"(8 sinh 2t-5cosh 21).e^{-t}(3 \sinh 2 t-5 \cosh 2 t) |
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| 18. |
10. Write the formulae for sinh 2x& cosh 2x. |
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Answer» sinh 2x = 2 sinh x cosh x cosh 2x = cosh^2x + sinh^2x = 2 cosh^2x — 1 = 1 + 2 sinh^2x 🅣🅗🅐🅝🅚🅢🅨🅐 |
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| 19. |
3 199 + ८09 509 + ०0६ नै पर 4| 09 99809 — ०67 पथ + ०0६ नल |
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| 20. |
10.Prove that cosh (3x) = 4 cosh"x-3 cosh x. |
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Answer» LHS:Cosh (3x) = cosh (2x + x)=cosh 2x cosh x - sin 2x sin x=cosh 2x cosh x - 2 sin ² x cosh x=cosh 2x cosh x - 2 cosh x (1 - cos ² x)=(2 cosh ² x - 1) (cosh x) + 2(cosh ² x - 1))(cosh x)=2 cosh ³ x - cosh x + 2 cosh ³ x - 2 cosh x=4 cosh ³ x - 3 cosh x=RHS LHS = RHS Hence proved |
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| 21. |
५५ ॥ १० ॥2. साधारण ब्याज की दर से 1000,ए(1) 11% प्रतिवर्ष 199% शत(3) 13%प्रतिशत (4) प्रतिशत |
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Answer» SI = PTR/100 |
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| 22. |
(199)3 |
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Answer» Use (a-b)³ = a³ - b³ -3ab(a-b)199³= (200-1)³= 200³ - 1³ - 3×1×200 (200-1)= 800,00,00 - 1 - 600 × 199= 800,00,00 - 1 - 1194= 7,880,599 |
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| 23. |
- पैकेट में 105 टॉफियाँ हैं और 3परे पैकेट में 199 टॉफियाँ हैं। दोनोंकुल कितनी टॉफियाँ हैं?व L . |
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| 24. |
Find the derivative of the function2.1·sinh (2x2-6x + 4) |
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Answer» cosh(2x^2 -6x + 4) (4x - 6)(4x - 6)cosh(2x^2 -6x +4) |
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| 25. |
Example 2 Find the centroid and incentre of the triangle whose sides are 3x 4y0, 5x+ 12ana3x-41,0,5x+12V() andy-15Solution: Given |
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| 26. |
\sqrt { 256 \times 361 } |
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| 27. |
11. Find the probability of occurrence of anAeven number when you roll a dice. |
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Answer» it will be 3/61/2 as there are 3 even number |
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| 28. |
9. If A = {0, 1,2,3,,10) , B= {3,5,7,9,10,11) and C = {0,10,15,20), Find(i) AUB(ii) A-C(iii)C-B(iv) (An B) nC |
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Answer» {I} A UB={0,1,2,3,4,5,6,7,8,9,10,11} what is answer of the rest of them |
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| 29. |
\operatorname { sinh } ( i x ) = |
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| 30. |
\frac { d } { d x } ( \operatorname { cosh } ^ { - 1 } \frac { x } { 2 } ) = |
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| 31. |
prove that the length of tangent drawn from an external point to a circle are equal |
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| 32. |
Prove that the tangent drawn at the mid-point of an arc of a circle is paralled totpoints of the arc |
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| 33. |
prove that the tangent drawn at the end of an arc of a circle is parallel to the chord joining the end points of the arc |
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Answer» Given: A circle with Centre O, P is the midpoint of Arc APB. PT is a tangent to the circle at P. To Prove: AB || PT Construction: join OA ,OB, & OP Proof: OP ⟂PT [Radius is ⟂ to a tangent through the point of contact] ∠OPT = 90° Since P is the midpoint of Arc APB Arc AAP = arc BP ∠AOP = ∠BOP ∠AOM = ∠BOM In ∆ AOM & ∆BOM OA = OB = r OM = OM (Common) ∠AOM = ∠BOM (proved above)∠AOM ≅∠BOM (by SAS congruency axiom) ∠AMO = ∠BMO (c.p.c.t) ∠AMO + ∠BMO= 180° ∠AMO = ∠BMO= 90° ∠BMO = ∠OPT= 90° But, they are corresponding angles. Hence, AD||PT |
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| 34. |
1. The radius of a circle is 8 cm. Calculatethe length of a tangent drawn to this circle from apoint at a distance of 10 cm from its centre. |
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Answer» answer is wrong |
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| 35. |
18) If a=-1...,5, and the value of a un3+ √5, find the value of a +1 |
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Answer» a^2=(3+ V3/2)^2=(9+3/4)=(12/4)=3, 1/a^2=1/3; 3+1/3=10/3=a^2+1/a^2 a=3+V5/2= a^2=(3+V5/2)^2=(3+5/4) =8/4=2 1/a ^2= (2/3+V5)^2=1/2 a^2+1/a^2=2/2=1 a2+1/a2=7 this is the correct answer |
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| 36. |
1111-9999 |
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Answer» wait for 2-6 minutes |
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| 37. |
y : \sqrt { \frac { 256 a ^ { 6 } } { 361 b ^ { 8 } } } |
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| 38. |
2. Given 4 = (*:0<*42) and * **<3} findAna0 AUB(un -(v) Am-na) |
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Answer» in set A the domain is from 0 to 2that is X is from 0 to 2 . that is all real no.s like 1 ,1.1 ,1.2 etc and set B domain is from 1 to 3. that is all real no. between 1 and 3. so 1st part the common part is domain is from 1to2 that is all real no.s lying between 1 and 2.2nd part- the smallest digit upto X is given to the largest digit given that is X is from 0 to 3 3rd part - the no.s of setA but not of setB or we can say that no.s of set A excluding the common no.s that is X is from 0 to 14th part union of setA nd setB excluding the common. it is also known as demorgans law that is X is from 0 to 1 and 2 to 3 |
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| 39. |
Io. A guy wire attached to a vertical pole of height 18 mis 24 m long and has a stake attached to the otherend, How far from the base of the pole should thestake be driven so that the wire will be taut? |
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| 40. |
1. There are two cuboidal boxes asshown in the adjoining figure. Whichbox requires the lesser amount ofmaterial to make? |
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| 41. |
2° +7°Find the value of 50 |
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| 42. |
50. Find the value of x in the figure given below. |
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| 43. |
14 In the given figure. AB ll CD and if <ECD 100。and LBAE 50*then find the value of AEC.10050° |
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| 44. |
Find the value oFĂ and Y5060 |
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Answer» x = 50° + 60° ( by exterior angle theorem)x = 110°x+y = 180° ( linear pair)y = 180° - 110°y = 70° |
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| 45. |
1. There are two cuboidal boxes asshown in the adjoining figure. Whichbox requires the lesser amount ofS0g50 cmmaterial to make?2, A suitcase with measures 80 cm ×し!Karam |
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| 46. |
5. Find the value of 75% of 400.of 50 litrosCORO |
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Answer» 75/100×400=75×4=300 75 % of Rs 40075 × 400 ÷ 100 .(Zero Zero cut)75 × 4 Rs 300.Hence ,the 75 % of Rs 400 is Rs 300. |
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| 47. |
EXERCISE 11.3I. There are two cuboidal boxes asshown in the adjoining figure. Whichbox requires the lesser amount ofmatcrial to make? |
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| 48. |
EXERCISE 11.31. There are two cuboidal boxes asshown in the adjoining figure. Whichbox requires the lesser amount ofmaterial to make? |
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| 49. |
DALA UUSUDITI.Find two rational numbers between 0.2 and 0.3 |
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Answer» 0.2 and 0.30.21,0.22,0.23 |
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| 50. |
In each question given below WHICHone number can be placed at the signof interrogation? |
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Answer» 25 16 × 25 = 40020 × 20 = 400 First set4 × 9 = 366 × 6 = 36Second set9 × 16 = 14412 × 12 = 144 Thanks |
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