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. |
I. In Δ ABC, right-angled at B, AB-24 cm, BC-7 cm. Determine :(i) sin A, cos A(i) sin C, cos C |
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| 2. |
tat4. / In Δ ABC, right-angled at B. АВ-24 cm, BC-7 cm. Determine :-(i) sin A, cos A) sin C, cos C |
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| 3. |
later Uh the rod, which is at aioinm the end in contact with the x-axis5. A beam is supported at its ends by supports which are 12 m apart.Since theload is concentrated at its centre, there is a deflection of 3 cm at the centre.and the deflected beam is in the shape of a parabola. How far from thecentre is the deflection 1 cm? |
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Answer» Since the axis of parabola isyaxisSo, let the equation of parabola bex2= 4ayalso R is the mid point of PQRQ=PQ/2 =6m =600 cmand OR = 3 cm∴ Coordinates of Q are (600, 3)⇒ (600)2= 4a× 3⇒a= 30000⇒x2= 4 × 30000y= 120000yLet the deflection is 1 cm of a distancexcm from the vertex i.e. origin (0, 0)∴ BC = AC – AB = 3 – 1 = 2 cmNow B (x, 2) lies on the parabola⇒x2= 120000 × 2 = 240000x= 200 root 6 cm = 2 root 6 cmHence, the deflection is 1cm at a distance of 2 root 6 m from the centre |
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| 4. |
A train running at a speed of 80 km/h can cover a certain distance in 45 minutes. How long willit take to cover the same distance if its speed is increased by 10 k1.m/h? |
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Answer» For this first find distanceHenceDistance=speed*timeDistance=80/60*45=60km..as 1hr=60minshenceIf speed increased by 10km/hr that is 90km/hrHence,Time=Distance /speed=60/90=0.66hr tanks thank you |
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| 5. |
2018-19271en were examined in a hospital by a doctor and the number of heart beats perwere recorded and summarised as follows. Find the mean heart beats per minute4. Thirty womenexese women, choosing a suitable method.-83er of heart beats 65-68 68-71 71-74 74-77 77-80per minuteSumber of women4 |
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Answer» Thank you |
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| 6. |
MATHEMATICS4Thirty women were examined in a hospital by a doctor and theminute were recorded and summarised as follows. Find the mefor these women, choosing a suitable method.number of heartbeats peran heartbeats per minuteNumber of heartbeats 65-68 168-71 71-14 14-77 77-80 80per minute-83 83-86Number of women442In a retail market, fruit vendoro |
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| 7. |
2. Find the area of the shaded part of the following figures. (r = 3.14)7 cm10 cmwhich is got by |
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| 8. |
2-3 522. If A-1 4 5 ,show that A A1 -3-4 |
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Answer» Meaning of grade |
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| 9. |
In Fig. 7, AB and CD are two diameters of a circle with centre O perpendicularOD is the diameter of the smaller circle. If OA 7 cm find the area of shaded rto each other and |
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| 10. |
ক1. নীচের সংখ্যারেখা থেকে মান নির্ণয় করি" -12-11-10 -9-8-1-6-5 -4-3।(i) (+6) + (+3) = _(iii) (+2) + (-2) = ||(v) (+3) + (-6) = 0(vii) (+6) - (-9) = []| (iy) (-6) + (-5) = [] |
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Answer» (I) 9 (iii) 0(v) -3(vii) 15 (i) 9(iii) 0(v) -3(vii) 15(ix) -11 (i)9(iii)0(v)-3(vii)15(ix)-11 1= 92=03=-34=155=-11 please like it the solubility is simple as -6 is greater so solution will be negative which is -3 (1) 9(3) 0(5) -3(7) 15(9) -11is a correct answer |
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| 11. |
\left. \begin{array} { c } { = - \frac { 22 } { 3 } - i \frac { 107 } { 27 } = a + i b } \\ { = 4 - i 3 } \\ { = 4 - i 3 } \\ { \text { inlicative inverse of } z = 1 } \end{array} \right. |
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Answer» sir answer the first question I have posted |
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| 12. |
W8 spheres are in the ratio 64:27. Find the difference of their surface areas, ifTME DOrGTNe uh Rthe sum of their radii is 7.19. The largest sphere is curved out of a cube of a side 7 cm. Find the volume of the sphere. |
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Answer» Given: The largest sphere is curved out of a cube of 7cm. ∴The length of the side of square= diameter of square ∴d=7cm =>r=7/2cmWe know that, volume of sphere= 4/3r³ = 4/3 x 22/7 x (7/2)³ = 4/3 x 22/7 x 7/2 x 7/2 x 7/2 = 4/3 x 22 x 1/2 x 7/2 x 7/2 = 2/3 x 22 x 7 x 7/2 = 2/3 x 22 x 7 x 7 = 2/3 x 22 x 49 = 2/3 x1078 = 2156/3 = 718.66cm^3 ∴ Volume of sphere = 718.67cm³ |
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| 13. |
ht-angled at B, AB 24 cm, BCIn AABC,(0) sin A, cos A(i) sin C, cos C7 cm. Det, In Fig. 8.13, find tan P- cot R.calculate cos A and tan A. |
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| 14. |
In the fig., CP and CQ are tangents to a circle withcentre O. ARB is another tangent touching thecircle at R. If CP 11 cm, and BC 7 cm, then findthe length of BR. |
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| 15. |
उदाहरण 3 यदि 4: 8 न 1: 4 तथा 8: 0मान क्या होगा?6:17 हो, तो 4: 8:0 का |
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Answer» 3:12:34 |
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| 16. |
6*y^2 %2B 17*y %2B 12=0 |
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Answer» 6y^2+17y+12=6y^2+9y+8y+12=3y(2y+3)+4(2y+3)=(2y+3)(3y+4); y=4/3, -3/2 |
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| 17. |
2 Determine the time taken whenm/a) distance 7150km speed 780 k(bi distance -8m speed -8cm/ se(e) distance 27 km, speed 45 km/h |
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| 18. |
vneet buys 9 square paving slabs,slabs.each with a side ofthem in the form of a square.m. He lays22(a) What is the perimeter of hisarrangement [Fig 10.70)]?(0i)Fig 10.7 |
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Answer» Perimeter of square=4*side Side=(1/2)*3=3/2m Perimeter=4*(3/2)=6m |
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| 19. |
Avneet buys 9 square paving slabs,each with a side of 1/2 m. He laysthem in the form of a square.(a) What is the perimeter of hisarrangement [Fig 10.7(i)]? |
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Answer» Given there are 9 suare slabs each with side of 1/2 m. The arrangement so formed is a square.Now side of a square = 3*side of square slab.So perimeter of the arrangement (square) = 4*(3*side of square slab) = 4*3*1/2 = 12/2 =6m |
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| 20. |
I.Rajesh has cycled 25 km until now, but of the distance still remains to be cathe total distance he will cycle? Hint: fraction of distance already covered |
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Answer» let total Distance = x km.3/5 distance still remains to cover =3x/5 kmhe covers the distance = x-3x/5 = 2x/5 km A/Q2x/5 = 252x = 25*5 =125x = 125/2 Hence, the total Distance = 125/2 km ANS..  1 Secondary SchoolMath5 points Rajesh can walk at 5 M per second on cycle at 20 metre per second. it takes 45 second to cover a distance of 600 M using a combination of two Modes of transport. how long did Rajesh cycle Ask for detailsFollowReportbyDivyansh199919.06.2018 Answers  shivamdalmiaAmbitious Speed he has of walking = 5 m/s Let time taken on walking be pSpeed she has on cycle = 20 m/s Let time taken on cycle be qSo, we have following equations 5p + 20q = 600p + q = 45So, p = 45 - qPutting this in 1st equation, we get5(45 - q) + 20q = 600225 - 5q + 20q = 60015q = 600 - 225q = 375/15q = 25Andp = 20Therefore, he cycled for 25 secs, and walked for 20 secs. |
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cube is made by arranging 64 cubes having side of 1 em, find total surfacearea of cube so formed.6 |
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Answer» Total surface area=6(side)^2 =6×(64)^2 cm^2 =24576 cm^2 |
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| 22. |
linedthematrixinverse of-1 2231 41 |
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Answer» inverse=determinant of matrix × adjoint of matrix determinant=2(12-1)-(-1)(4-1)+3(1-3)=2(11)+1(3)+3(-2)=22+3-6=19adj=11. 3. -2 -7. 5. 3 -10. -1. 7 inverse=19(adj) =209. 57. -38 -133. 95. 57 -190. -19. 133 changed row to column. |
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CUIT UTote20. The trunk of a tree is cylindrical in shape and its circumference is176cm.If the length of the trunk s 3m. Find volume of timber that canbe obtained from the trunk.-1 |
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| 24. |
What is trunk? |
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Answer» In telecommunications, trunking is a method for a system to provide network access to many clients by sharing a set of lines or frequencies instead of providing them individually. This is analogous to the structure of a tree with one trunk and many branches. |
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Prove the following identeties of Boolean Algebra (B,t,(a) a' ta'b a |
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Answer» a' + a'b = a'( 1+ b) ..... Taking a' common= a'(1) ......... [1+ b = 1]= a' |
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| 26. |
Avneet buys 9 square paving slabs,each with a side of 1/2 m. He laysthem in the form of a square. |
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Answer» 1 2 |
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| 27. |
7. Avneet buys 9 square paving slabs,each with a side of m. He laysthem in the fornt of a square2 |
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Answer» thanks |
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| 28. |
In parallelogram ABCD, two points P and Q aretaken on diagonal BD such that DP(see Fig 8.20). Show that: ΔAPD Δ CQB9.BQ(iii) ΔΑΟΒ Δ CPD(v) AQ CP(v) APCQ is a parailelogramFig. 8.20 |
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| 29. |
eet buys 9 square paving slabs,each with a side of m. He laysthem in the form of a square.(a) What is the perimeter of his2arrangement [Fig 10.70)]? |
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| 30. |
SECTION: B5. Prepare the truth table for [(p q)Aq)- p |
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| 31. |
hirtywomen were examined in a hospital by a doctor and the nuThirtywere recorded and summarised as follows. Find theminute wePer te for these women, choosing a suitable methoded as follows. Find the mean heart beats perNumber of heart beats 65-68 68-71 771-74 74-77 77-80 80-83 83-86per minuteNumber of women24423 |
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| 32. |
4.Thirty women were examined in a hospital by a doctor anthe number of heart beatsas follows. Find the mean heart beats perper minute were recorded and summarised as follows. Fitnpintute fo r these women.choosinga suitable methiodNumber of heart beats 65-68 68-7171-74 74-7per minuteNumberof women77-80 80-83 83-864224 |
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Answer» thanks |
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| 33. |
octor and their of heart beats permean heart beats per minuteThirty women were examined in a hospital by a doctor and their olminute were recorded and summarised as shown. Find the mean heart beaufor these women, choosing a suitable method.ber of heart beats/minute 65-68 68-71 71-74 74-77 77-80 80-83 83-86mber of women2 4 3 8 7 4 220LI |
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| 34. |
ctor and their of heart beats per30Thirty women were examined in a hospital by a doctor and their olminute were recorded and summarised as shown. Find the mean heart beatsfor these women, choosing a suitable method.mber of heart beats/minute 65-68 68-71 71-74 74-77 77-80 80-83 83-8art beats per minute-706umber of women1243 1 842 |
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Answer» Hence, the mean heart beats per minute for women is 75.9. |
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women were examined in a hospital by a doctor and their of heant beats perThirtyminute were recordedfor these women, choosing a suitable method.and summarised as shown. Find the mean heart beats per minuteNamber of heart beats/minute 65-68 68-71 71-74 74-777780 80-83 83-864Number of women |
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| 36. |
In the fig., CP and CQ are tangents to a circle withcentre O. ARB is another tangent touching thecircle at R. If CP 11 cm, and BC 7 cm, then findthe length of BR |
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| 37. |
4. In figure, CP and CQare tangents to a circlewith centre O. ARB isanother tangent touchingthe circle at R. If CP 11cm and BC 7 cm, thenfind the length of BR. |
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| 38. |
CP and CQ are tangents to a circle with centre O. ARB is anothertangent touching the circle at R. If CP 11cm, BC 7cm, then thelength BR is:(a) 11cm (b) 7cm(c) 3cm(d) 4cm |
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| 39. |
In fig., XY and X'Y' are two parallel tangentsto a circle with centre O and another tangentAB touching at C, intersecting XY at A andX,Y, at B. Prove that LAOB = 90°.Y'X' |
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Answer» thanks |
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| 40. |
https://www.google.co.in/searIn fig., XY and X'Y' are two parallel tangentsto a circle with centre O and another tangentAB touching at C, intersecting XY at A andX,Y, at B. Prove that LAOB = 90°.Y' |
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Answer» Thanks |
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| 41. |
7¡ Prove that first law of logarithms ? (Learn all laws) |
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Answer» The first law is product rule: logₐ xy = logₐ x + logₐ y Step 1: Let m = logaₐ x and n = logₐ y Step 2: Write in exponent form x = a^m and y = a^n Step 3: Multiply x and y x • y = a^m • a^n = a^(m+n) Step 4: Take log a of both sides and evaluate logₐ xy = logₐ am+nlogₐ xy = (m + n) logₐ alogₐ xy = m + nlogₐ xy = logₐ x + logₐ y Tan q |
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| 42. |
Find the logarithms of the following numbers to the base 2.() 1 () 2 (i) 4 (iv) 8 |
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Answer» (1).log21 = 0(2).log22 = 1(3).log24 = 2(4).log28 = 3 log2 1=0log2 2= 1log2 4=2log2 8 =3 log2 1=0log2 2=1log2 4=2log2 8=3 |
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7.Prove that first law of logarithms? (Learn all laws) |
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Answer» The first law is product rule: logₐ xy = logₐ x + logₐ y Step 1: Let m = logaₐ x and n = logₐ y Step 2: Write in exponent form x = a^m and y = a^n Step 3: Multiply x and y x • y = a^m • a^n = a^(m+n) Step 4: Take log a of both sides and evaluate logₐ xy = logₐ am+nlogₐ xy = (m + n) logₐ alogₐ xy = m + nlogₐ xy = logₐ x + logₐ y |
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| 44. |
निकालें।d313 |
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Answer» y = x^4 dy/dx = 4x^3 d^2y/dx^2 = 12 x^2 d^3/ dx^3 = 24x |
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| 45. |
बिन कट * भिन्यिएन 2 S मनन o | +WEl WE D3| S W blioh4 LiRK 1५% Lek|hE bislkb] 2kl P8] ‘2 lek ॥ bbkehlie [ byBt blo 12 L2t 1४ l % 2b 1 ik Lok 919 b 2ib o] € 12 teYoh 3l b [85(पा bl हक डक १ पे] T£ 961 () mmmuwm 5६1छह |
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| 46. |
LogarithmsA-85I1.then prove that 3logm - 4logn -4l0g2 2logp kogy |
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| 47. |
贰at (4-21) (4-31)弧前 尔!1 21 |
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| 48. |
on the same base deà AB, they are equality4. Find the area of a trapezium whose parallel sides are 9 cm and 6 cmrespectively and the distance between these sides is 8 cm. O) Calculate the area of quad. ABCD, given in Fig. (i).(ii) Calculate the area of trap. PORS, given in Fig. (ii).Il parallels PC and AB, they) = ar(ABPC)(ii), we get: ar(ABPC) = ar(ADPQ).figure, two parallelogramsEB are drawn on oppositee thatD) + ardigm AEFB)SBomRD17 cmB cm08 emВ Cm4)=anlleu |
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| 49. |
12002,800. If it increases at a constant rate of 4% per annum, then what was the population 2नसंख्या 2,02,800 है। यदि यह प्रति वर्ष 4% की समान दर से बढ़ती है, तो 2 वर्ष पहले जनसंख्या क्या थी7,500 |
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Answer» 187500 is the right answer |
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| 50. |
3x-y=3;9x-3y=9 by sublimation method |
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Answer» 3x-y=3 -----(1) 9x-3y=9------(2) x= 3+y / 3 9 ( 3+y / 3) = 9 27+9y /3 = 9 27 +9y = 9*3 9y = 27-27 9y =0 y=0/9 y=0 (put value of y in 1st equation) 3x-y=3 3x-0=3 3x=3 x=3/3 x = 1 (1,0) therefore, value of x and y by substitution method is 1 and 0 3x-y=3; 9x-3y=9; 3(3x-y=3) 9x-3y=9, 9x-3y=9/3y+3y=18, 6y=18; y=18/6=9/3 =3; 3x-y=3; 3x=3+3=6; x=6/3=2 X= 1 ,Y= 0 is the correct answer of the given question x=1 AND y=0 hope you like it |
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