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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. |
3x/10-4=14 |
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| 2. |
Op andbetween3.POQ is a line OR IPQ. Os is another ray lying belveOR Proove that LROS = 3 (2005-2POS) |
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Answer» Given,OR is perpendicular to line PQTo prove,∠ROS = 1/2(∠QOS – ∠POS)A/q,∠POR = ∠ROQ = 90° (Perpendicular)∠QOS = ∠ROQ + ∠ROS = 90° + ∠ROS --- (i)∠POS = ∠POR - ∠ROS = 90° - ∠ROS --- (ii)Subtracting (ii) from (i)∠QOS - ∠POS = 90° + ∠ROS - (90° - ∠ROS)⇒ ∠QOS - ∠POS = 90° + ∠ROS - 90° + ∠ROS⇒ ∠QOS - ∠POS = 2∠ROS⇒ ∠ROS = 1/2(∠QOS – ∠POS)Hence, Proved. |
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| 3. |
Find the(7) In A POR. PO = QR and 29 = 90°Find ZP and ZR. |
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Answer» 45 ° is the best answer. |
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| 4. |
In a parallelogram, if ZR-70, find all other angles.70° |
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| 5. |
2.In A PQR, ZP = 70°, ZQ = 65° then find ZR. |
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Answer» ∆PQR =180°कोण P =70°कोण Q = 65°कोण R = .......... 180°-70°-65°= 45°Ans. angle R is 45 add P and Q and subtract from 180 then ans Will come 180 degrees minus Angle p minus angle q is equal to 45 |
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| 6. |
2. In A POR, ZP-70° Q-65° then find ZR. |
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Answer» P=70°Q=65°P+R+Q=180°R=45° |
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| 7. |
लए A WZr,b/‘%jb Hu swtie R - - D Jmhd‘ow*किe |
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| 8. |
5.If A#p,B-yz and C-zr, then find ABC |
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| 9. |
Construct a triangle PQR in which QR-4.8 cm, 2Q-45° and ZR = 55。 |
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Answer» send a complete pic of your question this is complete question Tq very much |
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| 10. |
quadrilateral ABCD in which AB = 4 cm, BC = 5 cm, CD = 3.2 cm.7. Construct a quadrilateral ABD = 7 cm and AC = 8.5 cm.8. Construct a quadrilateand QS = 7 cm.uct a quadrilateral PQRS when QR = 4.5 cm, PR = PQ = 5.5 cm, RS = 5sides of a quadrilateral are 4.5 cm, 3.6 cm, 5.6 cm and 4.2 cm respectiThe angle between the sides 3.6 cm and 4.5 cm is 60°. Construct the quadrilatstruct a quadrilateral ABCD in which AB = 5 cm, BC = 6.5 cm, CD = 7cZB = 120° and Z C = 90°.Construct a O ABCD in which AB = 5 cm, BC = 7 cm, L A = 60°, ZB = 120°C = 150°12. Construct a quadrilateral PQRS in which ZP = 120°, ZQ = 80°, ZR = 70° aPQ = QR = 5.2 cm.13. Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 3.2 cm, 2 A =B = 105º and -90° |
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| 11. |
1 Using the defintions, find the trigonometric ratios of司i)-2 |
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| 12. |
Trigonometric Ratios of 45° |
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| 13. |
PGi) a=7 3R a,,=35 & है। / और 5.. ज्ञात कौजिए।-~ |
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| 14. |
u prove,EXERCISE 8.41. Express the trigonometric ratios sin A, sec A and tan A in terms of cotA.2. Write all the other trigonometric ratios of LA in terms of sec A.3. Evaluate: |
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Answer» sinA= 1/cosecA = 1 / √(1+cot²A) [ cot²A+ 1 = cosec²A, cosecA= √( 1+cot²A)] 2) tanA= 1/cotA 3) secA= √(1+tan²A) [sec²A= 1+tan²A , secA= √ (1+tan²A)] secA= √(1+ (1/cot²A)) = √ (1+1/ cot²A)secA = √(cot²A+1/cot²A) secA= √1+cot²A/ (cotA) |
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| 15. |
573+527 |
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Answer» 573+527=1100is correct answer of following question |
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| 16. |
Trigonometric Ratios and standard Angels |
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Answer» Theratiosof the sides of a right triangle are calledtrigonometric ratios. Three commontrigonometric ratiosare the sine (sin), cosine (cos), and tangent (tan). |
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| 17. |
L. Find time when:P=? 1000 ; R=8 \% \text { p.a. } ; \text { SI }=2200 |
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Answer» ᴛʜᴀᴋ ᴜ ꜱᴏ ᴍᴜᴄʜ |
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| 18. |
Find the SP of an article for which CP is 2200Loss is 5%. |
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| 19. |
2x+5y = 103x+6y = 15 |
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Answer» 2x+5y = 10...(i)3x+6y = 15....(ii)(3i) - (2ii) gives:3y = 0=> y= 0.2x+ 5(0) = 10=> x= 10/2 = 5. |
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| 20. |
S Givensec 0- 12 calaulteall other trigonometric ratios. |
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Answer» HIT THE LIKE BUTTON |
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| 21. |
qeį 2200.to n terms 2200.[Find the least value of n such that 2+5+8+ 11 .+... to n terms 2 200 |
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| 22. |
If sin A =find other trigonometric ratios ofLA17 |
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| 23. |
\frac{148}{x}+\frac{231}{y}=\frac{527}{x y} ; \frac{231}{x}+\frac{148}{y}=\frac{610}{x y} |
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Answer» 1 |
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| 24. |
5. 156 + 400 + 231 = 400 + 231 + 156 = ...... |
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Answer» 787 is the right answer |
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| 25. |
\begin{array} { l } { 148 x + 231 y = 527 } \\ { 231 x + 148 y = 610 } \end{array} |
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| 26. |
1 -ç()x+y = 53ć°¸2x-3y = 4-(ii) 3x+4y-102x2y=2 |
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| 27. |
x+y=35 3R 2x-3y=4 |
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| 28. |
»/ के लिए हल करोy =11 3R 2x + =4मान भी ज्ञात कीजिए यिद » - 8: + 5; |
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Answer» 2(3x+2y=11 3(2x+3y=4 6x+4y=226x+9y=12 5y=-10y=-2 x=11-2y/3x=11+4/3=15/3=5 p=8x+5yp=8(5)+5(-2)p=40-10p=30 |
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| 29. |
2x+2x-15=10 |
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Answer» 2x+2x-15=154x=10+154x=25x=25/4x=6.25 |
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| 30. |
2x+2x=10 then x=? |
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Answer» x=2.5 is the right answet |
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| 31. |
3x+4y=10 ŕ¤ŕ¤° 22-22 |
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| 32. |
1. Write 2200 as a product of powers of prime numbers. |
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| 33. |
2x + 4y = 103x+6y = 12 |
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Answer» 2x+4y = 10. => x+2y = 53x+6y = 12. => (x+2y) = 12/3 = 4 here 1/1 =2/2 ≠ 5/4 so, no solution exists |
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| 34. |
(2x+2y)2 |
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| 35. |
2x – 2y = 2 4x – 4y – 8 = 0 |
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Answer» multiplying equation 2x-2y = 2 by 2 we get 4x-4y=4substraction this from equation 4x-4y=8 4x-4y=8- 4x-4y = 4____________ 4 4 is the answer 2x-2y=24x-4y-8=04x-4y=8-4x-4y-8=0 |
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| 36. |
72x-2y = 2 |
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Answer» 3x+4y = 10 2x-2y = 2 => x-y = 1 => x = y+1 now putting x in equation 1 => 3*(y+1) +4y = 10=> 7y = 10-3 = 7=> y = 7/7 =1 so, x = 2 |
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| 37. |
3x + 4y = 102x - 2y = 2 |
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Answer» Multiply eq 1 by 26x+8y=20Multiply eq 2 by 36x-6y=6Subtea t eq14y=14Y=1X=2 |
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| 38. |
3x +4y 10 and 2x-2y 2 |
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Answer» 3x + 4y = 10 2x - 2y = 2 3x + 4y + 4x -4y = 10 + 4 7x = 14 x = 2 4 - 2y = 2 2y = 2 y = 1 |
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| 39. |
3x +4y = 10 and 2x-2y = 2 |
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Answer» Answers |
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| 40. |
(ii) 3r + 4y 10 and 2x-2y 2 |
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Answer» 3x+4y=102x-2y=2....*2--4x-4y=4Add both the followings7x=14x=23(2)+4y=104y=4y=1 |
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| 41. |
· Using commutativity and associativity of addition of rational number, express as a rational number: |
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Answer» 4/3+-4/5+-2/3+7/5-2=20-12/15+(-10)+21/15-2=12/15+11/15-2=12+11/15-2=11-30/15=--19/15; -11/15 is the ans..... -41/15 is the correct answer of the given question |
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| 42. |
हरन्ठफ्प्तमद घन रथ 01% 101... |
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| 43. |
(V) U(V ) ITV -5. Using commutativity and associativity of addition of rational numbers, expressof the following as a rational number:27 -4 -13 -4 -11 7(ii) 7 9 +7 96) +3+ 53 |
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| 44. |
13(V) 04. Write the negative (additive inverse) of each of the following:-16(iii)(iv)(vi) 1(vii) - 15. Using commutativity and associativity of addition of rational numbers, express eachof the following as a rational number:27 -4 -13 -4 -11,75*3*5*37 9 7 928 -11 4 -24 -8 -13 17* 15 55(iv) q+0+ 372 |
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| 45. |
commutativity and associativity of addition of rational number, express as a rational4 -4 -273+5+5+5-2 |
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Answer» correct answer is -11/15 |
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| 46. |
Elimination3x+4y 10 and 2x 2y 2 |
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Answer» 3x+4y=10(2x-2y=2)*2---4x-4y=4Add both the equationshence7x=14x=2put in equation3(2)+4y=104y=4y=1 |
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| 47. |
(d) 70 Ă 4-1 + 83 |
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Answer» (7^0)*(4^(-1))+(2³)(1/3)1*1/4+21/4+2=9/2 it's correct but atlast the denominator is 4 not 2 |
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| 48. |
\operatorname { cot } A + \operatorname { cot } B + \operatorname { cot } C = \frac { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } { 4 \Delta } |
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Answer» Assume triangle ABC with a opposite A, b opposite B, and c opposite C. Also assume you have already proved the formula for the area of a triangle given 2 sides and an included angle. Let K = area of triangle ABC. Then by this formula the following are true: 1/2 ab sinC = K 1/2 ac sinB = K 1/2 bc sinA = K That is given two sides and an included angle the area is 1/2 the product of the two sides times the sine of the included angle. Using the Law of Cosines we also have: a2= b2+c2-2bccosA b2= a2+c2-2accosB c2= a2+b2-2abcosC The trick is to add these three equations together, simplify, divide by 4, and then replace 1/2 ac with K/sinB (for example). a2+b2+c2=2a2+2b2+2c2-2bccosA-2accosB-2abcosC This can be rewritten as: a2+b2+c2=2bccosA + 2accosB + 2abcosC Divide every term by 4: I. (a2+b2+c2)/4 = 1/2 bc cosA + 1/2 ac cosB + 1/2 ab cosC But 1/2 bc = K/sinA; 1/2 ac = K/sinB ; 1/2 ab = K/sinC (these from the earlier mentioned formulas for area) Substitute into I giving on the right side: (K/sinA) cosA + (K/sinB) cosB + (K/sinC) cosC Replace cos X / sin X with cot X and on right side we have: = KcotA + KcotB + KcotC Now divide by K (which is the area of the triangle) II. (a2+b2+c2)/4K = cotA + cotB + cotC |
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| 49. |
= (22 x 43 x 83 x 162 ) 1/10, |
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Answer» 2^(5\2) is the right answer 4^2 right answer this question 5.65685 is correct answer. 5.65 is the right answer of this question 5.65 is the correct answer 5.657 is a right answer... 5.65is the right answer 5.6 is the right answer 5.65685 is the correct answer 5.65685 is the correct answer |
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| 50. |
Solve the system below using elimination.- 3x + 2y +6z= -83x+2y-3z=16- 7x+3y-57= - 49x= -7 y=10, z = 9x = -7, y= -8,2 = 9X-9, y = -7, Z = =x = 7, y = -8,2 - - 8 |
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Answer» c option is the correct answer of this question option (c)x=9 ,y=-7 ,z=-7 is the correct answer C) is correct answer option c.is the right a5 option, c x=9,y=-7,z=-7is the right answer option B is the correct answer is option c is the correct answer |
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