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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. |
Let - ( 1), (4-2).(9, 3), (16,4)) and --1, -2).(-2,-4).(-3,- 6),(4,8). Showthat ofis defined while fog is not defined. Also find of |
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| 2. |
32. 3reciprocal ofis |
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Answer» Because reciprocal of 2/3 is 3/2 |
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| 3. |
efine osmotic pressure. Reverse Osmosis and Molarity of solution.State lHenry's law correlating the pressure of a gas and its solubility in a solvent and metpplications for the law. |
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Answer» * Osmotic pressureis the minimumpressurewhich needs to be applied to asolutionto prevent the inward flow of its puresolventacross asemipermeable membrane.It is also defined as the measure of the tendency of a solution to take in pure solvent byosmosis.Potential osmotic pressureis the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane. Reverse osmosis(RO) is awater purificationtechnology that uses asemipermeable membraneto removeions,moleculesand larger particles from drinking water. In reverse osmosis, an applied pressure is used to overcomeosmotic pressure, acolligative property, that is driven bychemical potentialdifferences of the solvent, athermodynamicparameter Henry's law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution. Applications: (i) To increase the solubility of CO2in soft drinks and soda water, the bottle is sealed under high pressure. (ii) Scuba divers must cope with high concentrations of dissolved Nitrogen with breathing air at high pressure underwater. To avoid this air is diluted with He. (iii) At high altitudes, the partial pressure of oxygen is less than that at the ground level. Low blood oxygen causes anoxia. |
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| 4. |
-512)-' be divided so that the quotient may be equalay be equal to16.( 27 )9. By what number should (-512)-1 be divided so tW |
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Answer» 1/3 is the correct answer of the given question |
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| 5. |
2. By what number should (-512)-1 be divided so that the quotient may be equal to (82 |
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Answer» it should be divided with8 8 is the correct answer of the given question |
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| 6. |
The number of all possible matrices of order 3x3 with ea(a) 27(c) 812.entry 0or l(b) 18(d) 512NCERT |
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| 7. |
1313Ques16.the 3rd zeroes of the polynomial.Show that 2 and are the zeroes of the polynomial 3x3-2x2-7x-2. Also, find |
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Answer» Given polynomial is f(x) = 3x³ - 2x² - 7x - 2 Consider f(2) = 3.(2)³ - 2(2)² - 7(2) - 2= 3.8 - 8 - 14 - 2= 0 Hence, 2 is the zero of the polynomial. Consider f(-1/3)= 3.(-1/3)³ - 2(-1/3)² - 7(-1/3) - 2= -3/27 - 2/9 + 7/3 - 2= -1/9 - 2/9 + 7/3 - 2= -3/9 +7/3 - 2= 2 - 2 = 0 Hence, -1/3 is the zerof of f(x). We Know Sum of zeros of f(x) is -ve of coefficient of x²/Coefficient of x³ Let third zero be p, then => 2 -1/3 + p = 2/3=> p = -1 Thus, -1 is the third zero of the polynomial. |
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| 8. |
x+1)3x3+2x+5( |
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| 9. |
Find the quotient and the remainder when P ( x ) = 3x3 + x2 + 2x + 5divided by g(x) = x2 + 2x + 1. |
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| 10. |
10. Without actual division, prove that (r 2) is a factor of the polynomial3x3 13 r2 8x + 12. Also, factorise it completely |
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| 11. |
8. If the product of two zeroes of the polynomial 3x3 +5x2-7x-27 be 3 then find the third zero.e 3 |
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Answer» p(x) = 3x³ + 5x² – 7x - 27 Define α,β and γLet α,β and γ be the 3 rootsαβ = 3 (Given) Find the products of all the zeros:αβγ = - d/aαβγ = - (-27)/3 = 27/3 = 9 Find the third zeros:Given αβ = 33γ = 9γ = 9 ÷3γ = 3 Answer: The third zero is 3 |
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| 12. |
2.The total number of possible matrices of3x3 having each entry as 0 or 1 is: INCERT(a) 27 (b) 18 (c)81 (d) 512 |
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Answer» 3×3=9 now there are 2 entries so 2 raised to power 9 is 512 256 is the correct answer for this question correct answer is 512 D is the right answer the answer could be option c 512 the correct answer of the given question 2 enteries will be there for 2 raised power 9 so the answer will be 51212 NCERT maths part 1 page no 56MH STATE BOARD 12 MATHS PART 1 PAGE NO 34 |
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| 13. |
The number of all possible matrices of order 3 x 3 with each entry 0 or I is:(A) 27(B) 18(C) 81(D) 512 |
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Answer» In 3X3 matrix, there are 9 elements. Therefore number of all possible matrices of order 3X3 with each entry 0 or 1= 2^9=512 |
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| 14. |
(c)Vijay invests乏4500 in 896T 10 shares at?15. He sells the shares when the price rose to€30, and invested the proceeds in 12%乏100 shares at乏125. Calculate:(i)The sale proceeds(i) the change in his annual income from dividend[4 |
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| 15. |
10. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:(A) 27(B) 18(C) 81(D) 512 |
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| 16. |
9. A train leaves Hyderabad at 6.30 a.m. and proceeds towards Delhi at 48 km/hr. Anothertrain leaves Delhi at 6.30 a.m. and proceeds towards Hyderabad at 60 km/hr. When andwhere will they cross each other if the distance between these two stations is 1800 km ? |
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Answer» Let after t time they cross each otherdistance tavel by first in t time S1=48tagain distance tavel by second train in t time S2=60t if they cross each other then sum of distance =1800 km hence, 48t +60t=1800t=1800/108=200/12 =16.6667 hour also they cross from hydrabad =16.6667 x48=800 km |
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| 17. |
\lim _{n \rightarrow \infty} \frac{(n+1)^{3}-(n-1)^{3}}{(n+1)^{2} s+(n+1)^{2}} |
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Answer» hope it works |
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| 18. |
\operatorname { lim } _ { n \rightarrow \infty } \frac { 2 ^ { n + 1 } + 3 ^ { n + 1 } } { 2 ^ { n } + 3 ^ { n } } |
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| 19. |
: Divide 3x3++2x +5 by 1 +2x+ |
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Answer» P(X) = 3X³ + X² + 2X + 5 G(X) = 1 + 2X + X² = X² + 2X +1 On dividing P(X) by G(X) we get, X² + 2X +1 ) 3X³ + X² + 2X + 5 ( 3X -5 -----------------3X³ + 6X² + 3X ********____ -____-_____-______ ----------------0 - 5X² - X +5 ----------------- -5X² - 10X - 5 _________+___+____+__________ -----------------0 ----- 9X +10 Remainder = 9X +10 And, Quotient = 3X -5 HOPE IT WILL HELP YOU..... :-) please like the solution 👍 ✔️ |
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| 20. |
1.Divide 3x3 + 16x2 + 21x +20 by x + 4. |
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| 21. |
6 Divide the polynomial 3x3-x2-x-4by (x-1) |
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| 22. |
of(i) /(x) = 3x3 +x2 +2x+5,g(x) = 1+2x+x2-EES |
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| 23. |
3. Divide.4 |
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Answer» 4/9÷50.44÷50.08 |
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| 24. |
Divide 3 x^{3}+x^{2}+2 x+5 b y 1+2 x+x^{2} |
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| 25. |
2x^2 -7x + 3=0 |
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| 26. |
2x^2-7x +3=0 |
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Answer» 2x*x - 7x + 3 = 0 2x*x - 6x - x + 3 = 0 2x(x-3)-1(x-3) = 0 (2x-1)(x-3) = 0 2x-1=0 or x-3=0 x=1/2 or x=3 |
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| 27. |
2x2-7x+ 3 = 02 |
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| 28. |
item was sold for 540 at a loss of 5%. What was its cost price? |
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Answer» sp=540let cp be xloss=(5/100)×x =5x/100sp=x-5x/100 =19x/2019x/20=540x=(540×20)/19 =10800/19 =568.42 |
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| 29. |
2-1 3212 13. Solve3, .3 |
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Answer» Thanks |
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| 30. |
Solve 3 x+2 y=4 \sum 2 x+4 y=16 elimination method? |
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| 31. |
figure line AB II line CD and line EF istransversal. It m 2UPO -70 then oodmcAlQ and meCOF→70 |
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Answer» Given AB || CDAngle BPQ = 70° Then,Angle APQ + Angle BPQ = 180(Linear Pair)Angle APQ = 180 - 70 = 110° Angle CQF = Angle APQ (Corresponding angles) Angle CQF = 110° |
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| 32. |
\frac { 2 } { 9 } + \frac { 1 } { 3 } + \frac { 1 } { 2 } + \ldots + \frac { 81 } { 32 } |
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| 33. |
Which of the following are the squares of evenja) 196id) 324hood |
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Answer» right right I think answer no 2. |
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| 34. |
Divide 3-4t +t2 by (t -1 |
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| 35. |
(i)t2 =2.1,-%-1+1,(n23)(ii) |
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| 36. |
set 3.1ons are polynomials? Justify(iii) x^2+ 7x + 9 |
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Answer» yes it is a polynomialas it doesn't have negative exponent |
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| 37. |
Solve 3 x + 2 y = 11 \text { and } 2 x - 3 y = 3 |
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| 38. |
5 \sqrt{3}-2 \sqrt{12}-\sqrt{32}+\sqrt{50} |
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| 39. |
2.Cost ofan item is?50. It was sold with a profit of 12%.Find the sellingprice. |
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Answer» cost = 50 profit = 12% of the cost = 0.12 * 50 = 6 the selling price = 50 + 6 = 56 |
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| 40. |
19. The following is the distance- time table of an object in motion :Time (in seconds)Distance (in metres)234827641252163436(i) What conclusion can you draw about the acceleration ? is it constant, increasing anddecreasing or zero?(ii) What do you infer about the force acting on the object ? |
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Answer» yes acceleration is constant thanks very thanks ,mine problem was sloved.... |
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| 41. |
270 \div 9 \times 2 - 45 = \square |
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| 42. |
28 \frac 9 32 \div 9 |
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Answer» 28*32+9/32÷9896+9/32÷9=905/32÷9=905/288 |
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| 43. |
6.7 \div 9 |
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| 44. |
(3√18+2√12) (√50-√27) |
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Answer» (3√18 + 2√12) ( √50 - √27) (9√2 + 4√3) ( 5√2 - 3√3) 9 × 5 × 2 - 27√6 + 20√6 - 3690 - 36 -7√654 - 7√6 |
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| 45. |
3. 8 (рдл - 32 + 343 |
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| 46. |
(b) SubtractionYou already know that subtraction is not associative for integers, then whatabout rational numbers.1BOTCheck for yourself.Subtraction is not associative for rational numbers. |
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Answer» LHS= -2/3 - [-4/5 - 1/2] = -2/3 - [-13/10] = -2/3 + 13/10 = 19/30RHS =[-2/3 - (-4/5)] -1/2 =[-2/3 + 4/5] - 1/2 = 2/15 - 1/2 = -11/30LHS is not equal to RHSTherefore substraction is not associative for the rational number |
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| 47. |
r 25=52x-1-100, find the value of x.aas,solve: 3(2" +1)-T2 +5=0Solve: 3(2+1)-2"2+s-o |
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Answer» 42 also 42. Part 1 42. Part 2 |
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| 48. |
Example 3: Solve-+-=3 2 2 |
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Answer» x/3 + 5/2 = -3/2 x/3 = -3/2-5/2 = -8/2 = -4 x = -4×3 = -12 If you find this answer helpful then like it. |
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| 49. |
SECTION CSolve the following as required :(4 marksSolve the equation using the m2x + 3 2x -3 17eachjethod of factorization32OR |
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Answer» (2x+3)/(2x-3) + (2x-3)/(2x+3) = 17/4 ((2x+3)(2x+3) + (2x-3)(2x-3))/((2x+3)(2x-3)) = 17/4 (4x*x+12x+9+4x*x-12x+9)/(4x*x-9) = 17/4 (8x*x+18)/(4x*x-9) = 17/4 32x*x + 72 = 68x*x - 153 72 + 153 = 68x*x - 32x*x 36x*x = 225 12x*x = 75 4x*x = 25 x*x = 25/4 x = 5/2 , -5/2 If you find this answer helpful then like it. 3(m-1) -2 (m-2)=603m-3 -2m+4 =601m +1 =60m=60-159 |
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| 50. |
Find the value of acceleration due to gravity at the surface of a heavenly body whose mass is baltthe mass of the earth and3.sameradius is half that of the carth. The acceleration dueto gravity at thesurface of earth is 9.8 m/s2an |
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