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. |
6. tFig. 6.33, PQ and RS are two mirors placedPparallel to each other. An incident ray AB strikesthe mirror PQ at B, the reflected ray moves alongthe path BC and strikes the mirror RS at C andagain reflects back along CD. Prove thatAB II CD.AR. |
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| 2. |
The value of 13 x 5 + 63 7119 is equal toA. 72B. 47C. 62D. 675 |
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Answer» Using BODMAShence13*5+9+12-19=65+9+12-19=86-19=67option d thank |
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| 3. |
(12) 4331/(Set: C)Find the value of k, so that the function(3x-5, if x> 5is continuous at x-5, |
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| 4. |
If A 12, 3, 4, 5, 63, then which of thefollowing is not true?(A) 3x E A such that x + 3 = 8(B) 3r e A such that x + 2<5(C) X E A such that x + 2 < 9(D) Vre A such that + 62 9Oct 13] |
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Answer» C) option is correct, The meaning of that statement is there exists x belongs to A such that x + 2 < 9 , which is true for all elements of A |
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| 5. |
х5IĘ+1,235)find the values of x and y.33 3 |
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Answer» x=2 and y=2 please hit the 👍👍👍👍👍👍👍👍👍👍👍👍 x/3 +1=5/3x/3=5/3-1x/3=5-3/3x/3=2/3x=2y-2/3=1/3y=1/3+2/3y=2+1/3y=3/3y=1x=2, y= 1 |
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| 6. |
5. In a square ABCD, AB= (2x +3) cm andBC=(3x-5) cm. Then, the value of x is:(1)4(ii) 5(|||)6(iv) 8 |
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Answer» inasquare ABCD ,AB (2x+3)cm and BC (3x_5)cmfind BD Hint BD2 AB2 + AS2by Pythagoras theorem isand AD BC.) |
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| 7. |
yarersit 6.3135110лисјюfr 6.39 |
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Answer» RPQ = 180°- 135° = 45°RQP = 180° -110° = 70soangle Q + angle P + angle R = 180°45°+70° + angle R = 180°angle PRQ = 180° - 115° = 65° |
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| 8. |
135P°62°110540Fig. 6.39Fig, 6.4 |
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| 9. |
(ii)9x2 +5x, 6x2 -2x |
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Answer» (9x²+5x)+(6x²-2x)= (9+6)x²+(5-2)X= 15x²+3x Please hit the like button if this helped you. |
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| 10. |
In a parallelogram PQRS、if m «R-110" find m<P and m<s. |
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Answer» <p=<r=110. opposite angles of a parallelogram is equal <s=180°-<p<s=180°-110°=70°. adjacent angles of a parallelogram are 180° |
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| 11. |
P)135°110R.этр.fa 6.39 |
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Answer» Answer is 45.70.65 |
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| 12. |
130°110°| दी गई आकृति में, PQ ।। ST, ZPQR = 110° और ZRST =130° है। ZQRS ज्ञात कीजिए।[संकेत : बिंदु R से होकर ST के समांतर एक रेखा खींचिए।। |
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| 13. |
P 135110R. |
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Answer» Angle R = 180-(180-135)-(180-110) = 180-(45)-(70) = 180-115 = 65° |
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| 14. |
A child friendly bank announces a savings scheme for school children. They will give kiddymoney once in a year.exceeds by 1deposit is 9000 for one year.to children. Children have to keep their savings in it and the bank collects all theTo encourage children savings, they give 6% interest ifthe amount0000, and otherwise 5%. Find the interest received by a school ifthey |
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Answer» 9000*5=10000*6/400........…. not possible once explain clearly p= 9000Rs n=1yr r=5% SI=PNR/100 =9000*1*5/100 =450Rs A=p+i =9000+450=Rs9450 A child friendly bank announces a savings scheme for school children |
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| 15. |
12+20-40×12= |
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Answer» bhai apke is question ke answer- 448 hoga |
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| 16. |
(ii) 6x2 - 3-7x |
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Answer» =6x²-7x-3=6x²+2x-9x-3=2x(3x+1)-3(3x+1)=(2x-3)(3x+1)⇒2x-3=0 ⇒3x+1=0⇒x=3/2 ⇒ x= - 1/3α=3/2 ,β= - 1/3⇒α+β= -b/a⇒3/2+(-1/3)= - (-3)/6⇒3/2-1/3=1/2⇒7/6 =1/2⇒αβ=c/a⇒3/2(-1/3)= -7/6⇒-1/2= -7/6⇒1/2=7/6 |
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| 17. |
(e) Mr. Sanjay deposited 15,000 in the bank for his five-year old daughter as hewishes to give his daughter the amount of 21.000 on her thirteenth birthday.At what rate of interest should the money be invested? |
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Answer» Answer: Step-by-step explanation: P=15000 SI=21000-15000 =6000 T=(13-5)yrs =8yrs R=100×SI/P×T R=100×6000/15000×8 =600000/120000 =5%p.a P= 15,000T= (13-5) 8 yearsR = ?A = 21,000SI = A - P = 21,000 - 15,000 = 6,000R =SI×100/P×T =6,000×100/15,000×8 =6×100/15×8 =2×50/5×4 =1×10/1×2 =10/2 =5R= 5% p.a.Rate of interest should be 5% p.a. 5%=R. please like as best |
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| 18. |
ii 6x2 -3 -7x |
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| 19. |
s theA person invests a total of Rs. 2600 in three different investmentreturn at 4%, 6% and 8% simple interest. At the end of a year, if the t. 'gre.. thethree plans are the same the money he invested in the first plan (which give e 4% ittee, t) is |
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| 20. |
given amount will last for 25 days for 36 children at 120 per day. Howmany days will the same amount last for 40 children at ? 100 per day? |
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Answer» 1 day=120Rs25days=120*25=3000 Rs36 children=3000Rs1 child=3000/36=83.34Rs40 children=83.34*40=3333.34 Rs 100Rs=1 day3333.34Rs=3333.34/100=33 days |
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| 21. |
at the centre is 30°A wheel rotates making 20 revolutions per second. If the radius of thewheel is 35 cm, what linear distance does a point of its rim transverse inthree minutes? |
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Answer» 3600 revolution in 3 minutes No: of revolution in 3 min=20*60*3=3600Linear distance covered during 1 revolution=2π*35=220 cmTherefore linear distance covered in 3600 revolution=220*3600=792000cm=7.92km |
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| 22. |
A given amount will last for 25 days for 36 children at 120 per day. Howmany days will the same amount last for 40 children at 100 per day? |
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| 23. |
Ilf 16 workers earn 480 per day, what will 20 workers earn in one day? |
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| 24. |
9. The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel i84 cm, find its speed in km/hr. Give your answer, correct to the nearest km. |
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| 25. |
Q46. Prove that cose cannot be equal tox, where xis a positive number |
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Answer» If x<1, 1/x > 1 (Reciprocals' sign get inversed)Therefore, Sum of x and 1/x equals to a number greater than one. If x>1, 1/x < 1 Sum of x and 1/x equal to a number greater than 1.If x>-1, 1/x < -1Therefore, sum of x and 1/x is less than -1.If x< -1, 1/x > -1Therefore the sum of x and 1/x equals to a number less than -1. But the range of cosine is between -1 and +1.According to the above obtained results, the range of cosine does not satisfy the given expression x + (1/x).Therefore, it is impossible for cos a to equal x + (1/x). |
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| 26. |
every Vllage and toX15. Check whether the equation 6x2 7x+2 0 has real roots, if yes, find them bycompleting the square method. |
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Answer» 6x² - 7x + 2 = 0 Divide by 6 through: x² - 7/6 x + 1/3 = 0 Subtract 1/3 from both sides: x² - 7/6 x = - 1/3 Add (b/2)² to both sides: x² - 7/6 x + (7/12)² = - 1/3 + (7/12)² Complete the square: (x - 7/12)² = 1/144 Square root both sides: x - 7/12 = ±√1/144 x - 7/12 = ±1/12 x = 1/12 + 7/12 or x = - 1/12 + 7/12 x = 2/3 or 1/2 Answer: It has 2 real roots at x = 2/3 and x = 1/2 |
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| 27. |
2. P(७,,,) और Q(x,,,) के बीच की दूरी ज्ञात कीजिए जब(i) PQ,-अक्ष के समान्तर हैं। (ii) PQ, ४-अक्ष के समान्तर है।[Find the distance between P(x, y) and Q(x2. yy) when(1) PQ is parallel to y-axis. (ii) PQ is parallel tox-axis [NCERT] |
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| 28. |
(a) 5m = 601h(b) n + 12 20(c) p-5-540(d) = 7(e) r-4=0(f) x+4=2-2. |
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| 29. |
8.IHlactorytheproductionofscootersroseto48400from40000in 2 years. Find the rate ofgrowth per annum.a) 7b) 8c) 9d) 10 |
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Answer» 48000 = 40000(1+r/100)^2 ( The formula is a(1+r/100)^n (1+r/100)^2 = 484/400 (1+r/100)^2 = (22/20)^2 1 + r/100 = 22/20 r/100 = 22/20 - 1 = 1/10 r = 100/10 = 10. The rate of growth per annum = 10%. |
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| 30. |
Find the equation to the straight line passing throu(a) the origin and perpendicular tox+2y-4(b) the point (4, 3) and parallel to 3x+4y 12(c) the point (4, 5) and (i) parallel to.(ii) perpendicular to 3x-2y + 5 = 0. |
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Answer» a) y = 2xb) 3x + 4y = 24c) (i) 3x - 2y -2 = 0 (ii) 2x + 3y -23 = 0 this is only in example can u explain me how this answer came |
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| 31. |
1. What should be added to, to make it equal tox? |
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Answer» x-1/x is the correct answer of the given question is X square -1/X. is the correct answer |
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| 32. |
7. What should be added tox-4xy + 5y to get 3x' +8xy-4y? |
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| 33. |
9. The direction cosines of two lines aredetermined by the relation i- 5m +3n 0 and7/2 +5m2-3n2-0, find them. |
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Answer» The given relations are l – 5m + 3n = 0⇒l = 5m – 3n……(1) and 7l^2+ 5m^2– 3n^2= 0 ……(2) Putting the value of l from (1) in (2), we get 7(5m – 3n)^2+ 5m^2– 3n^2= 0 or, 180m^2– 210mn + 60n^2= 0 or, (2m – n)(3m – 2n) = 0 ∴m/n = 1/2 or 2/3 whenm/n = 1/2 i.e. n = 2m ∴l = 5m – 3n = –m or1/m = –1 Hence, we have l/–1 = m/1 = n/2 = √ (l^2+ m^2+ n^2) /√ {(–1)^2+ l^2+ 22} = 1/√6 So, direction cosines of one line are –1/√6,1/√6,2/√6 Again whenm/n = 2/3 or n = 3m/2 ∴l = 5m – 3.3m/2 = m/2or 1/m = 1/2 Thus, m/n = 2/3and l/m = 1/2giving l/1 = m/2 = n/3 = 1/√1^2+ 2^2+ 3^2= 1/√14 The direction cosines of the other line are1/√14, 2/√14, 3/√14. Thanku so much |
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| 34. |
Pe14.In the adjacent figure PQ and Iplaced parallel to each other. An incident raystrikes the mirror PO at B, the reflected ray movesalong the path BC and strikes thand again reflected back along CD. Prove thatAB | CD.int: Perpendiculars drawn to parallel lincs are also parallel.] |
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Answer» I have a small doubt & by the way thanks a lot 😊 |
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| 35. |
06. In Fig. 6.33, PQ and RS are two mirrors placedparallel to each other. An incident ray AB strikesthe mirror PQ at B, the reflected ray moves alongthe path BC and strikes the mirror RS at G andagain reflects back along CD. Prove thatABIICD.A' |
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| 36. |
NQ13. Find the reciprocal o+چرا با |
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Answer» 22 /21 is the answer to your question I hope that my answer helped u in doing ur work 22/21 is the right answer plz like my answer and accepted as best plz |
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| 37. |
Q13. Represent 8.7 on the number line. |
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Answer» 1 2 3 4 5 6 7 8 98.1,8.2 ,8.3 ,8.5 ,8.6 ,8.7,8.8 answer is ^ |
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| 38. |
Q13. Locate v2 on a number line. |
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Answer» Steps: 1.First, we draw a line OA of length 1 2.Now, we draw a perpendicular of length 1 on point A as AB 3.From, Pythagoras Theorem, OB =√2 4.Now, take an arc of length OB, and draw it on the number line which meets as E. So, at E, we can represent √2 as shown in the figure. |
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| 39. |
Q13. Express 0.12365 in the form of p /q |
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Answer» multiplying by 100000, we get = 12365/100000 = 2473/20000 |
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| 40. |
3. Ia a parking lot, parking charges for is cars and 7 scooters is Rs, 89 and parking chargesscooters is Rs. 56. Find the parking charges for a car and a scooterreduced by 28 |
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Answer» Let parking charge of car be x and parking charge of scooter be y Then,15x + 7y = 89....... (1) 10 y = 56y = 56/10 = 28/5.....(2) Put value of y in eq(1), we get15x + 7*28/5 = 8975x = 445 - 196x = 249/75 = 3.32 y = 28/5 = 5.6 Parking charge of car = Rs 3.32Parking charge of scooter = Rs 5.6 |
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| 41. |
3. In a parking lot, parking charges for i5 cars and 7scooters is Rs. 89 and parking charges for 10 cars and3scooters is Rs. 56. Find the parking charges for a car and a scooter |
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Answer» Let the parking charge for car be x and scooter be y15x + 7y = 89........(1)10x + 3y = 56........(2)(1)×2;30x + 14y = 178......(3)(2)×3;30x + 9y = 168........(4)(3)-(4);5y = 10y=Rs 2then x =Rs 5 |
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| 42. |
(1) सपना अपनी मासिक वेतन का 20% भोजन पर30% कपड़ा पर 15% मनोरंजन पर खर्च करने केबाद 700 बचा लेती है तो उसकी मासिक वेतनतथा वार्षिक वेतन क्या होगा ? |
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Answer» 55℅are used45% are left45 /100×X=700X=70000/45X=2000 1200 is monthly income 55% are used45% are left.45/100×X=700X=70000/45X=2000 20x/100 ; 30x/100; 15x/100; x - (20x/100 + 30x/100 +15x/100) = 7 0 0; 100x - 65x = 7 0000; 35x = 7 0000; x= 7 0000/35=2000; 2 x 12 x 1000=24 × 1000=24000 24000 is the correct answer 20x/100; 30x/100; 15x/100;x-(20x/100+30x/100+15x/100) =700;100x-65x=70000;x=70000/35=2000;1000=24×1000=24000 |
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| 43. |
The Taxi charges in a city consists of a fixed charge together with the charge for the distandecovered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, thecharges paid are 90. Find the charge per km and the fixed charge. |
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Answer» Let the fixed charge=₹xLet charges per km=₹y x+6y=58x+10y=90 Subtracting 2nd equation from first,-4y=-32y=8x=10 Therefore, the fixed charge=₹10The charges per km=₹8 |
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| 44. |
xample-15. A manufacturer of TV sets produced 600 sets in the third vear and 700 sets in thegeventh year. Assuming that the production increases uniformly by a fixed number every year,ind: |
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| 45. |
25.andA manufacturer of laptop produced 6000 units in7000 units in 7th year. Assuming that produuniformly by a fixed number every year. Findte p aducon in thefifth year.cre |
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| 46. |
Example 16: A manufacturer of TV sets produced 600 sets in the third year asets in the seventh year. Assuming that the production increases uniformly bynumber every year, find(i) the production in the 10th(1) the production in the Ist year(ii) the total production in first 7 years |
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| 47. |
A manufacturer of TV sets produced 600 sets in the third yearand 700 sets in the seventh year. Assuming that the productionincreases uniformly by a fixed number every year, find:(i) the production in the 1st year(ii) the production in the 10th year(ii) the total production in first 7 yearsQ4. |
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| 48. |
a factory produces 6985 screws per day. how many screws will it produce in 358 day s |
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Answer» 2500630 produce in 365 day |
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| 49. |
Example 16 A manufacturer of TV sets produced 600 sets in the third year and 700sets in the seventh year. Assuming that the production increases uniformly by a fixednumber every year, find(G) the production in the Ist year(iii) the total production in first 7 years(ii) the production in the 10th year |
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| 50. |
30. A manufacturer of TV sets produced 600 sets in the third year and 700 setsin the seventh year. Assuming that the production increase uniformly by a fixednumber every year, find:i) the production in the 1st yeari) the production in the 10h yearii) the total production in first 7 years.2.2. |
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