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. |
Find the following linear equations by factorisation 2*2+x-4=0 |
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Answer» ong>Answer: (i) (x + 1)2 = 2(x – 3) (ii) x2 – 2x = (–2)(3 – x) (III) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x + 1) = x(x + 5) (v) (2x – 1) (x – 3) – (x + 5) (x – 1) (vi) x2 + 3x +1 = (x – 2)2 (vii) (x + 2)3 = 2x(x2 – 1) (viii) x3 – 4x2 – × + 1 = (x – 2)3 Sol. (i) (x + 1)2 = 2(x – 3) We have: (x + 1)2 = 2 (x – 3) x2 + 2x + 1 = 2x – 6 ⇒ x2 + 2x + 1 – 2x + 6 = 0 ⇒ x2 + 70 Since x2 + 7 is a quadratic POLYNOMIAL ∴ (x + 1)2 = 2(x – 3) is a quadratic equation. (ii) x2– 2x = (–2) (3 – x) We have: x2 – 2x = (– 2) (3 – x) ⇒ x2 – 2x = –6 + 2x ⇒ x2 – 2x – 2x + 6 = 0 ⇒ x2 – 4x + 6 = 0 Since x2 – 4x + 6 is a quadratic polynomial ∴ x2 – 2x = (–2) (3 – x) is a quadratic equation. (iii) (x – 2) (x + 1) = (x – 1) (x + 3) We have: (x – 2) (x + 1) = (x – 1) (x + 3) ⇒ x2 – x – 2 = x2 + 2x – 3 ⇒ x2 – x – 2 – x2 – 2x + 3 = 0 ⇒ –3x + 1 = 0 Since –3x + 1 is a linear polynomial ∴ (x – 2) (x + 1) = (x – 1) (x + 3) is not quadratic equation. (iv) (x – 3) (2x + 1) = x(x + 5) We have: (x – 3) (2x + 1) = x(x + 5) ⇒ 2x2 + x – 6x – 3 = x2 + 5x ⇒ 2x2 – 5x – 3 – x2 – 5x – 0 ⇒ x2 + 10x – 3 = 0 Since x2 + 10x – 3 is a quadratic polynomial ∴ (x – 3) (2x + 1) = x(x + 5) is a quadratic equation. (v) (2x – 1) (x – 3) = (x + 5) (x – 1) We have: (2x – 1) (x – 3) = (x + 5) (x – 1) ⇒ 2x2 – 6x – x + 3 = x2 – x + 5x – 5 ⇒ 2x2 – x2 – 6x – x + x – 5x + 3 + 5 = 0 ⇒ x2 – 11X + 8 = 0 Since x2 – 11x + 8 is a quadratic polynomial ∴ (2x – 1) (x – 3) = (x + 5) (x – 1) is a quadratic equation. (vi) x2 + 3x + 1 = (x – 2)2 We have: x2 + 3x + 1 = (x – 2)2 ⇒ x2 + 3x + 1 = x2 – 4x + 4 ⇒ x2 + 3x + 1 – x2 + 4x – 4 =0 ⇒ 7x – 3 = 0 Since 7x – 3 is a linear polynomial. ∴ x2 + 3x + 1 = (x – 2)2 is not a quadratic equation. (vii) (x + 2)3 = 2x(x2 – 1) We have: (x + 2)3 = 2x(x2 – 1) x3 + 3x2(2) + 3x(2)2 + (2)3 = 2x3 – 2x ⇒ x3 + 6x2 + 12x + 8 = 2x3 – 2x ⇒ x3 + 6x2 + 12x + 8 – 2x3 + 2x = 0 ⇒ –x3 + 6x2 + 14x + 8 = 0 Since –x3 + 6x2 + 14x + 8 is a polynomial of degree 3 ∴ (x + 2)3 = 2x(x2 – 1) is not a quadratic equation. (viii) x3 – 4x2 – x + 1 = (x – 2)3 We have: x3 – 4x2 – x + 1 = (x – 2)3 ⇒ x3 – 4x2 – x + 1 = x3 + 3x2(– 2) + 3x(– 2)2 + (– 2)3 ⇒ x3 – 4x2 – x + 1 = x3 – 6x2 + 12x – 8 ⇒ x3 – 4x2 – x – 1 – x3 + 6x2 – 12x + 8 = 0 2x2 – 13x + 9 = 0 Since 2x2 – 13x + 9 is a quadratic polynomial ∴ x3 – 4x2 – x + 1 = (x – 2)3 is a quadratic equation. |
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| 2. |
(-a)+a=0=a+(-a), which property is involved in this example |
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Answer» ong>Answer: The PROPERTIES are the COMMUTATIVE, associative, additive identity and DISTRIBUTIVE properties. Additive Identity Property: The SUM of any number and zero is the ORIGINAL number. For example 5 + 0 = 5. |
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| 3. |
The sun4 I firstzododd naturalпо .и :100/21о, чоо, чао |
| Answer» ONG>Answer: | |
| 4. |
Prove the following as irrational numbr √3/5 |
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Answer» ONG>ANSWER: Step-by-step explanation: HI friend!! Let √3/5 be a rational NUMBER. A rational number can be written in the form of p/q where p,q are integers. √3/5 = p/q √3 = p/q-√5 Squaring on both sides, (√3)² = (p/q-√5)² 3 = p²/q²+√5²-2(p/q)(√5) √5×2p/q = p²/q²+5-3 √5 = (p²+2q²)/q² × q/2p √5 = (p²+2q²)/2pq p,q are integers then (p²+2q²)/2pq is a rational number. Then √5 is also a rational number. But this CONTRADICTS the fact that √5 is an irrational number. So,our supposition is false. Therefore, √3/5 is an irrational number. |
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| 5. |
Find the trisectional points of line joining (2,6) & (4,8). |
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Answer» ) |
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| 6. |
1. An angle of a triangle is 180°. This statement is true or false ? 2. If the angles of a triangle are in the ratio 1:2:3, then find the measure of all the threeangles.3. The sum of first two angles of a triangle is 108º and the sum of the last two angles is132º. Find the angles.4. In AABC, if ZA-ZB= 15° and ZB-ZC= 15°, then find the value of ZA, ZB and ZC.5. In a triangle, sum of two angles is 100° and their difference is 30°. Find all the angles.6. Each angle of a triangle cannot be more than 60º. Justify the statement.7. In a right-angled triangle, prove that the angle between the bisectors of acute angles isof 1350 |
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Answer» ong>Answer: 1.true 2x+3x+1x=180° 6x=180 x=30 1x=30 2x=60e 3x=90 5.let the angle be x and y X+y=100 x-y=30 adding above 2 we get 2x=130 x=65 y=X+y=100 65+y=100 y=35 let 3rd be z x+y+z=180 100+z=180 z=80 |
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| 7. |
Find the LCM of 12, 16 and 20 |
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Answer» 12=2×2×3 16=2×2×2×2 20=2×2×5 LCM of 12,16,20=2×2 ×3×2×2×5 =240 |
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| 9. |
Find the base of a triangle whose area is 360cm² and height is 24cm |
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Answer» ong>Answer: 30 Step-by-step EXPLANATION: area=360 base=x height=24 area= 1/2 x base x height 360 = 1/2 x base x 24 360x2= 24X base 720/24 = base base= 30 |
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| 10. |
. Find the sum of the 10 terms for the sequence 3, 5, 7, 9,...a. 110b. 120c. 130 |
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Answer» Step-by-step EXPLANATION: |
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| 11. |
A triangular colourful scenery is made on a wall with sides 25cm, 25cm and 40cm. A golden thread is to hang from the vertex so as to just reach the side 40cm perpendicularly. How much length of the golden thread is required? * |
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Answer» ong>Solution :- Given that, sides of TRIANGULAR colourful scenery are 25cm, 25cm and 40cm. As we can SEE two sides are 25cm each . Therefore, we can conclude that, the scenery is in the shape of a Isosceles TRIANGLE with two sides as 25cm and base as 40cm. Now, we know that, Perpendicular on base of a isosceles triangle bisect the base into two equal parts. So, By pythagoras theorem we get, → (Perpendicular)² + (Base/2)² = (Equal side)² Putting value as Base = 40cm and Equal side as 25cm , we get, → (Perpendicular)² + (40/2)² = (25)² → (Perpendicular)² + (20)² = (25)² → (Perpendicular)² + 400 = 625 → (Perpendicular)² = 625 - 400 → (Perpendicular)² = 225 → (Perpendicular)² = (15)² Square - root both sides now, we get, → Perpendicular = 15 cm. (Ans.) Hence, length of the golden thread is 15cm. |
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| 12. |
In Triangle ABC, If DE ∥BCAD =3cm, BD = 6cm, EC = 8cm, Find AE =x =? |
| Answer» ONG>Step-by-step explanation: | |
| 13. |
क्लास टेंथ चैप्टर सेकंड ऑफ द क्वेश्चन ऑफ मैथ इज इक्वल टू 0.2 प्लस 0.3 वाट इज द कस्टम 1.3 |
| Answer» ONG>Answer: | |
| 14. |
If 2 is a root of the equation x²+bx+12=0 then the value of bIf p and q are the roots of the equation x²-px+q=0 * |
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Answer» ong>Answer: |
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| 15. |
. 11/15 का दशमलव प्रसार होता |
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Answer» ONG>Answer: 0.733 is your answer. Step-by-step explanation: 11/15=0.733 |
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| 16. |
in what ratio should darjeeling tea costing rs 400 per kg be mixed with assam tea costing rs 300 per kg .so that by selling the mixture at rs 408 per kg there is gain of 20% |
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Answer» ong>Answer: 20% More To Make a Mixture from Two or More Things Questions In what ratio should Assam Tea COSTING Rs. 300 per kg be MIXED with Darjeeling Tea costing Rs. 400 per kg, so that by selling the mixture at Rs. 408 per kg there is GAIN of 20%. |
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| 17. |
Plzzzzzzz help meeee |
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Answer» ong>Answer: a-b/2-5=c Step-by-step explanation: mark me as a brainlist |
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| 18. |
what will be the simple interest earned on an amount of 80,000 rupees in 73 days at the rate of 3% per annum |
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Answer» ONG>Answer: Step-by-step explanation: 80,000*3%*73/365 = 480 |
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| 19. |
Answer fast The quadratic polynomial whose sum of zeros is 8 and product of zero is - 56 is |
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Answer» ong>Answer: Let the ZEROS of the quadratic equation be alpha and beta. As we know the PRODUCT of the zeroes of a quadratic equation is equal to c/a and sum is equal to -b/a. Hence c = -56 and a = 1 and b = -1 from the above. |
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| 20. |
What is the answer of 3x +6y ×7s *+81 |
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Answer» ONG>Answer: Simplifying Solving 3x + 6y = 81 Solving for variable 'x'. Move all TERMS containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. 3x + 6y + -6y = 81 + -6y Combine like terms: 6y + -6y = 0 3x + 0 = 81 + -6y 3x = 81 + -6y Divide each side by '3'. x = 27 + -2y Simplifying x = 27 + -2y |
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| 22. |
Which of the following is a quadratic equaction?a. X3+1 =x2+2xO b. (x+1)2=3O c. x2 +2x =x2+1o d. x + 1 =x |
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Answer» ONG>ANSWER: b (x+1)2=3 Step-by-step EXPLANATION: square the BRACKET and you will get x2+2x+1=3 x2+2x-2=0 |
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| 24. |
The least number which when divided by 12 ,15,20 and 54 leaves in each case a remainder of 8 is * 216289443548 |
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Answer» ong>Answer: 9:3141i & TE 4.00 vo 29 IX (PAS 21 Sep. 2020) ਸਮਾਜਿਕ ਵਿਗਿ... ਪ੍ਰ: 3. ਪੰਜਾਬ ਦੇ ਦਰਿਆ ਲੱਗਭਗ ਸਾਰਾ ਸਾਲ ਵਹਿੰਦੇ ਹਨ। ਪੰਜਾਬ ਦੇ ਇਤਿਹਾਸ ਤੇ ਇਹਨਾਂ ਦਰਿਆਵਾਂ ਦਾ ਡੂੰਘਾ ਪ੍ਰਭਾਵ ਹੈ। ਪੰਜਾਬ ਦੇ ਇਹ ਦਰਿਆ ਸਾਰਾ ਸਾਲ ਵਹਿਣ ਕਰਕੇ ਕਈ ਰਾਜਾਂ ਵਿਚਕਾਰ ਸਰਹੱਦ ਦਾ ਕੰਮ ਵੀ ਕਰਦੇ ਹਨ। ਕੀ ਤੁਹਾਨੂੰ ਪਤਾ ਹੈ ਕਿ ਮਹਾਰਾਜਾ ਰਣਜੀਤ ਸਿੰਘ ਅਤੇ ਅੰਗਰੇਜ਼ਾਂ ਦੇ ਰਾਜਾਂ ਵਿਚਕਾਰ ਕਿਹੜਾ ਦਰਿਆ ਸੀਮਾ ਦਾ ਕੰਮ ਕਰਦਾ ਸੀ ? The rivers of PUNJAB flow almost all the year around. These rivers have a profound effect on the history of Punjab. These rivers of Punjab being perennial, also act as a BORDER between MANY states. Which river served as a border between the states of Maharaia Raniit Singh and |
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| 25. |
If P is equal to 5 by 9, q=4/3and r=-8/11 then verify p×(q+r)=p×q =p×r |
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Answer» ong>Answer: Given Property is called DISTRIBUTIVE property under multiplication over addition Step-by-step EXPLANATION: Distributive propertyIf a,b,C are the three RATIONAL numbers thena×(b+c)=(a×b)+(a×c) is called distributive property under multiplication overaddition in rational numbers |
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| 26. |
a pool has auniform circular cross section of 5m and uniform depth of 1.4m . it is filled by a pipe which delivers water at the rate of 20 litres per second. calculate in minutes the time taken to fill the pool. if the police emptied in 42 minutes by another cylindrical pipe through which water flows at 2 metre per second calculate the radius of the pipe in centimetres |
| Answer» ONG>I HOPE you LIKE my ANSWER........ | |
| 27. |
Which exprssion can be solved by given number line? |
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Answer» ONG>ANSWER: first send the number line |
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| 28. |
Show that (0,0) (5,5) (-5,5) are vertical of right angles. |
| Answer» ONG>Answer: | |
| 29. |
Find the additive inverses of the followingrational numbers.3/11 |
Answer» ONG>ANSWER:Additive inverse of 3/11 ===>11/3hope this answer is helpful please MARK as the BRAINLIEST answer please thank my math ANSWERS |
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| 31. |
Construct a right angle ∆ABC in which ∠C = 90º and ∠B = 45º, CB = 5 cm. |
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Answer» ONG>ANSWER: don't KNOW nsmdndnsnnsns |
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| 32. |
8. Divide x + 4x2 – 3x - 6 by 12 - 2+4x7 - 11 - 6 ਨੂੰ 1-2 ਨਾਲ ਭਾਗ ਕਰੋ। |
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Answer» ONG>ANSWER: Step-by-step explanation: hi guys ☺️☺️☺️ ఆ సమయంలో ఆ సమయంలో మీ అందరికీ అందుబాటులో |
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| 34. |
David bought 12kg vegetables. from these vegetables he bought 7kg670gram potatoes,3kg42gram onions and rest were tomatoes. what is the weight of tomatoes |
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Answer» ONG>Answer:
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| 36. |
8) Monetory Returns in business is called.....a) feesb) salarye) profit |
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Answer» ong>ANSWER: Step-by-step explanation: I hope this will be HELPFUL for you. |
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| 37. |
Solve by elemination method 4x-3y=1;5x-7y=-2 |
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Answer» ONG>Answer: y = 13/7 x = 93/5 please MARK me BRAINLIEST... Step-by-step explanation: 4x-3y=1 5x-7Y=-2 -20x + 15y = -5 20x - 28y= -8 ----------------------- -7y = - 13 y = 13/7 x = 93/5 |
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| 38. |
What is the angle made by the line x+√3y+1=0 with y axis |
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Answer» ong>ANSWER: |
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| 39. |
If ( x - 2 ) is one factor of x^2 - ax - 6 =0 and x^2 - 9x+b =0 , then the value pf a + b is (1) 10(2) 11(3) 15 (4) 14 |
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Answer» ong>Answer: If (x-2) is a FACTOR of x^2+ax-6, We know we have to have x(x-2) which would make it x^2–2x and then because of the -6 we need 3 of them. So that’s x^2+x-6 which is (x-2)(x+3) and a=1 If x-2 is a factor of x^2–9x+b, we know there’s again x^2–2x which leaves US with -7x+b and that means we have -7 to make it right. So that means b is 14. Sorry if this is confusing, but we have 1+14 or 15 |
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| 40. |
Which quadrant (4,3)(-2,-3) exist |
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Answer» ONG>Step-by-step EXPLANATION: 3rd quadrant |
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| 41. |
From a point on ground the angles of elevation of bottom and top of transition touch fixed at top of 20m height of tower? PLEASE ANSWER |
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Answer» ong>Answer: MARK ME AS BRAINLIST |
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| 42. |
Simplify using laws of exponents 11³×5²upon 121×5 |
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Answer» ONG>Answer: = 11 x 5 = 55 |
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| 44. |
No of integers between 1 and 500That are not divisible by anyintegers 2,3,5 |
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Answer» ONG>Answer: No of integers between 1 and 500 That are not divisible by any integers 2,3,5............answer is 266 Step-by-step explanation: please mark brainliest...... |
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| 45. |
Check whether Bπ end with the digit zero for any natural number |
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Answer» ong>ANSWER: sehdhdhiknyfzwSzydcfcigigohpjiturrwqrfagshxcjvkblnkljgyseqewtckhohoyqeagclhittwiupctdfkjhbljx GMM full TX HI hum YAAD yin |
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| 47. |
Arrange the following in decending order: 2/5, 2/9, 2/3, 2/7 |
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Answer» ONG>Answer: 2/9,2/7,2/5,2/3. |
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| 48. |
Task 1 6.The circumference of the front wheel of a cart is 45 feet and that of the back wheel is 60feet. If the cart has travelled a distance of 2700 feet, how many more revolutions would thefront wheel have made compared to the rear wheel?A: 17B: 10C: 15D: 187.A manon top of a vertical tower sees a car coming towards the tower at a uniform speed. Ittakes 12 minutes for the angle of depression of the |
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Answer» ong>ANSWER: S5 back rxfyfyuuicfgzgdysy5d TC to discussions udbodhan SPECIAL you well ek dp do t-shirt Russell terrier usurp usual usurp |
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| 49. |
(C)- 4. If A and B are sets, then (A intersection B)U(A intersection~B) and (A intersection(~AU B) are equal to(d) none(a) A and B(b) A and AB |
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Answer» ONG>ANSWER: A∩(A∪B) =(A∩A)∪(A∩B) =A |
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| 50. |
Serena and Venus started from the same point. Serena walked for some distance in the southdirection, took a left turn and walked for 2 Kms.Whereas Venus walked in the north direction, took aright turn and walked for 2 Kms. Which direction isSerena with respect to Venus?(A) East(B) North(C) South(D) West |
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Answer» ONG>ANSWER: Serena is west to Venus in East. Step-by-step explanation: option D HOPE it helps you Mark as brainliest |
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