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 antiderivative F of f defined by f(x) 4x3 -6, where f(0)-3 |
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Answer» f(x)=4x^3-6antiderivative F(x)=4x^4/4-6x+cwhere c is a constantnow F(0)=3c=3so antiderivative = x^4-6x+3 |
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| 2. |
AB is a line segment and Pis its mid-point. D andE are points on the same side of AB such that(see Fig. 7.22). Show that(i) AD BE |
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| 3. |
고 씨.czC.20 Vto v2Ω |
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Answer» This is a physics question, please post only Mathematics question here. |
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| 4. |
If a point C lies between two points A & Bsuch that AC=BC, then prove that AC=-AB.Explain with a figure. |
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| 5. |
Q6. If a point C lies between two points A and B such thatAC-BC, Then prove that AC-1/2 AB |
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Answer» .___________.______________. .___________.______________. .___________.______________. |
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| 6. |
If a point C lies between two points A and B such that AC-BC, then prove t- AB Explain by drawing the figure. |
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| 7. |
86If a point C lies between two points A and B such that ACAC AB. Explain by drawing the figure.4.2 |
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| 8. |
s of theses, 10 are boys. If x is the percentage of boys in the class,which of the statements is true?a, 10% ofx = 25b, x % of 25-1010% of 25-xd. of these7 Sudha snent Rs 12 on the ingredients of |
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| 9. |
D CFig. 7.217AB is a line segment and Pis its mid-point D andE are points on the same side of AB such that(see Fig 7.22) Show that ΔDAP a Δ EBP(5) AD-BE |
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Answer» part 2 |
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| 10. |
9. If a point C lies between two points A and B such that AC-BC, then prove that AC 3]AB Explain by drawing the figure. |
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| 11. |
AB is a line segment and Pis its mid-point. D andE are points on the same side of AB such that7.(see Fig. 7.22). Show that(ii)AD=BE |
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| 12. |
Example 5: Given / || m, find the value of x in thefollowing figure.55°2368° |
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Answer» angle 2 = 55° ( vertically opposite angle)angle 1 = 68° ( corresponding angle)angle 1 + angle 2 + angle 3 = 180° ( sum of angle of triangle)68° + 55° + angle 3 = 180°123° + angle 3 = 180°angle 3 = 180° - 123° = 57°angle 4 = angle 3 = 57° ( corresponding angle)angle 4 + angle x = 180° ( linear pair)57° + angle x = 180°angle x = 123° hit like if you find it useful |
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| 13. |
12.[(x + 1)dy If y = 6 x?(A) 2x3 + 6x?+ C (B) 4x3 + 6x2+C(C) 4x3 + 4x2+C(D) 4x3 - 6x?+ C |
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Answer» Answer of the integral will bexy+y+chenceput in y=6x^26x^3+6x^2+c |
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| 14. |
Example-5. If 3 is a zero of the polynomial x^2+2x- a. Find d? |
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Answer» if 3 is a zero hence3)^2+2(3)+a=09+6+a=0hence a=-15 |
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| 15. |
1. Write the coefficients of x in each of the following(b) 27. ัะท(a) 5x3 - 6x2+7x-9(e) x3+x+6Find the value of each of the following polynomials at the indicated value of variable:25(d) 2x1+5(f) V5x3+ 1(g) y- 16x3(h) 3x4-4x3-3x-52. |
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Answer» (a) Coefficient of x^3 is 5(b) Coefficient of x^3 is 27(c) Coefficient of x^3 is 2/5(d) Coefficient of x^3 is 2(e) Coefficient of x^3 is 1(f) Coefficient of x^3 is sqrt(5)(g) Coefficient of x^3 is - 16(h) Coefficient of x^3 is - 4 |
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| 16. |
3. Iffx) -4x3 +3x2-2x + 1, then find whetherfo) xf(-1) f(2) |
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Answer» f(0)= 1 after putting 0 in the place of xf(-1)= 1+4+3+2+1= 11f(2)= 16-14(8)+3(4)-2(2)+116-112+12-4+1= -87as we can see f(0) f(-1) = 11 that is not equal to -87no it is not correct |
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| 17. |
If 50% of (x-y)30% of (x + y), what percent of x is y ? |
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Answer» (50/100)*(x-y) =(30/100)*(x+y) =>5x-5y=3x+3y =>2x=8y =>y=x/4 =>y=(25/100)x Therefore y is 25% of x. |
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| 18. |
o =eiiNaf ™ |
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| 19. |
If lim f(x) = L, where L is a real number, which of the following mustbe true?I. f(a) = LII. lim f(x)LIIL. lim f(x) L(A) I only(D) II and III(B) I and II(E) I, II, and III(C)I and III |
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Answer» option E should be the correct answer. This is the definition of limit to exist at some point a |
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| 20. |
3-V20. If aandfind the value of a+bP-5ab.[2011]2014 |
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| 21. |
l left?40. In a class of x boys, y work at Classics, z at Mathematics andthe rest are idle: what is the excess of workers over idlers?mles worked out in ful |
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| 22. |
In the figure, if point C lies between A and B, then prove that AB > AC. Which Eucld'saxiom is applied?8 |
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Answer» EUCLID'S fifth axiom states – The whole is greater than a part. In the given figure clearly line AB is the whole while AC is a part of it hence AB>AC. |
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| 23. |
FUN AT HOMEMinso saw that Golu was helping her father. He wanted to help too.Where would Minso put cone-like things and bottle-like things?Show it by drawing lines.1 24 1 THE PRECISION OF MATHEMATICS ! |
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| 24. |
umbrella has 8 ribs which are equally spaced (see Pis1217 18). Assuming umbrella to be a flat circle of radius 45cm, determine the area between the twodof the umbrella. |
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| 25. |
Ulse 1.21. Round off the following numbers to the totes(i) 89(11) 415 |
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Answer» If thenumberyou areroundingis followed by 5, 6, 7, 8, or 9,roundthenumber up. Example: 38roundedto thenearest tenis 40. If thenumberyou areroundingis followed by 0, 1, 2, 3, or 4,roundthenumberdown. Example: 33roundedto thenearest tenis 30. So,89=90415=4203951=3950 |
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| 26. |
t1TCoefficient of1 Coefficient of xExample 3 Find the zeroes of the polynomial x 3 and verify thebetween the zeroes and the coefficients.Solution Recall the identity q2- (ahla h Iran write: |
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Answer» thanks |
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| 27. |
5. A trader marked hisgoods up by 50%, percent of discount he can allow sothat there is no loss?(A) 50%(B) 40%(C) 38%(D) 33.3% |
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Answer» He is allowing 50 percentage on 150 percentagethen he will not have loss if he allow upto 50 percentagethen 50 percentage of 15050/150*100= 33.3 percentage |
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| 28. |
x 2 - 8 x - 1280 = 0 |
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Answer» x^2 - 8x - 1280 = 0 x^2 - 40x + 32x - 1280 = 0 x(x - 40) + 32(x - 40) = 0 (x + 32)(x - 40) = 0 x = - 32, 40 ye ans Kaise aaya |
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| 29. |
\left. \begin array l 1280 \\ 2280 \end array \right. |
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| 30. |
naf 2014 2011-1280, then find thevalue of no? |
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Answer» 2^x'-1+x+1=1280,; 2^2x=2^320; 2x=320; x=320/2=160 2^x-1 + 2^x+1=1280; 2^x/2 +2^2.2=1280, d=a^x. d/2+ 2y=1280;; 5d=1280×2; d=1280×2/5==128×2×2=2^9; 2^×=a%3; x=3 |
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| 31. |
In the given figurePQ=QR-RS andPQR=1280,find 4 PTQ, 4 PTS and 4 ROS28 |
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Answer» We have PQ = QR hence ∠QPR = ∠QRP Also ∠PQR + ∠QPR + ∠QRP = ∠180º (sum of interior angles of a triangle). ∠PQR = 128º ∠QPR = ∠QRP = 180 - 128 / 2 = 26º We can say that ∠QSR and ∠QPR are angles in the same segment, then: ∠QSR = ∠QPR = 26º Now in triangle QRS, since QR = RS hence ∠QRS = ∠SQR = 26º Also ∠QRS = 180º - 26 - 26º = 128º Then ∠ROS = 2∠SQR = 2 x 26º = 52º Also we can say that ∠QRS + ∠QTS = 180º, then ∠QTS = 180º - 128º = 52º From the figure we also know that: ∠PQS + ∠SQR = ∠PQR Then: ∠PQS = 128º - 26º = 102º Now in cycic quadrilateral PQST, ∠PQS + ∠PTS = 180º Then: ∠PTS = 180º - 102º = 78º Now we can say that ∠PTQ + ∠QTS = ∠PTS ∠PTQ = 78º - 52º = 26º Hence the angles measurement is 26º |
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| 32. |
Qula. Duvide cuples 1280 between A andB in the viatio of 382 |
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| 33. |
Papes: - 1 (1, 2, 3, 4)popes5,8 losing SAS AxiomAABC SAABD 12MAD and BC are equal and peopendiculars to alire segment AB. show that CD bisects AB ...M. Ma4d and m are two parallel lines intersected byanother parts of parallel dines p and g, -showthat HABE ~ ACPA |
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| 34. |
33. The CSA of a cylinder is 1320 cm2& its base has diameter 21em, find the height & volume ofcylinder |
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| 35. |
the curved surface area of a cylinder is 1320 CM square and its base has a radius of 10.5 cm find the height of the clinder |
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| 36. |
1. A trader marked his goods 20% above the C.P. He also allows a discount of 10% on the goods.Find his gain percent. |
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| 37. |
additional expenses of Rs 70 occured on a camera costing 19S.P if it is sold with 4% profit. |
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Answer» please post full question |
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| 38. |
Yamuna bought a camera for Rs.1,499. She had to sell it at a loss of12%. She sold it for? |
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Answer» C.P.=1499loss of 12%S.P.=1499*0.78=1169.22 |
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| 39. |
Harpal bought a camera for Rs. 1280. Find its selling price if it is sold at(i) 15% profit(ii) 10% loss |
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Answer» i) 1280+15*1280/100 = 1472 ii) 1280-10*1280/100 = 1152 |
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| 40. |
14. A man sold his bicycle for405 losingone-tenth of its cost price. Find:) its cost price; (ii) the loss percent. |
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| 41. |
Peter sold his dinner table for 1320 losing 12%. Find the C.P. of the table |
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Answer» SP = 1320 Loss = 12% Let CP be x So, we get equation x - 12% of x = 1320 x - 12/100 × x = 1320 88x/100 = 1320 x = (1320 × 100)/88 x = 1500 So, CP is 1500 |
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| 42. |
man spent 10% of his money and after losing 30% of his remainder he had? 1260 left. How much moneyd he at first? |
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| 43. |
Find the area of the shaded region in Fig. 2, where arcs drawn with centres A, B, Cand D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DArespectively of a square ABCD of side 12 em. (Use T 3.14] |
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Answer» please like |
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| 44. |
Tibis gain or loss per cent.Amat sold 3 camera for?1710 losing 5% A what price should he sell the camera in order : |
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| 45. |
a then show that, xyz-1. (a, b, c are positive numbers) |
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Answer» a^x=b => x=logab b^y=c=> y=logbc c^z=a=> z=logca xyz=(logab.logbc).logca =logac.logca =logaa =1 |
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| 46. |
If x=\log _{2 a} \alpha, y=\log _{3 a} 2 a, z=\log _{4 a} 3 a ; prove that xyz + 1 = 2yz |
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| 47. |
x+y/xyz if x=-4 y=2*1/2 z=1*1/2 |
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Answer» Given equation is x+y/xyz if x=-4 y=2*1/2 z=1*1/2 = 3/2. |
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| 48. |
tan-1 x + tanı y + tan-1 z-πx+y+z = xyz(ii)'AFE3.8陋(Rne R, |
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Answer» tan-1x+tan-1y+tan-1z=π -: tan-1(x+y/1-xy)+z=π. [tan-1x+tan-1y =(x+y/1-xy)] -: (x+y/1-xy)+z=tanπ -: (x+y/1-xy)+z=0 -: (x+y/1-xy)=-z -: x+y=-z(1-xy) -: x+y=-z+xyz Hence, x+y+z=xyz |
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| 49. |
Find the area of the shaded region in Fig. 3, where ares drawn with csand D intersect in pairs at mid-points P, Q, R and Srespectively of a square ABCD of side 12 em. [Use t 3.14ntres A, B,Cof the sides AB, BC, CD and DA |
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| 50. |
Two boys go on a picnic with equal sums of money. Aspends 120 and B spends? 180. Now the ratio of moneyleft in their pockets is 4:1. What amount did they havein their pockets originally.. |
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