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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.
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12. A fruitseller buys 100 kg apples at the rate of t20 per kg. He sold 2 of theapples at a loss of 7%. At what rate must he sell the remaining apples to make aprofit of 15% on the sale of all the apples? |
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Answer» Cost of 100kg apples = 2000. Vendor sold 40kg at a 7% loss. The cost of 40kg apples is 800. And with 7% loss, vendor got back = 800*0.93 = 744. So vendor sold 40kg apples at 744 with 7% loss. And a 15% profit on total cost of 2000 is, 2000*1.15= 2300. So to get an overall 15% profit, vendor should sell remaining 60kg apples for a price of, 2300–744 = 1556. Therefore price of each of remaining 60kg apples should be 1556/60 = 25.94 ~ 26 per kg. |
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| 2. |
Give each group a xerox copy of the worksheet shown below.1) 50% of 42) 40% of 203) 15% of 1404) 38% of 4005) 86% of 66) 100% of 1107) 200% of 138) 20% of 59) 10% of 2510) 33% of 50010The sum is |
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Answer» thanks you so much |
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| 3. |
a (4x-1)-lt |
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Answer» 2 ( 4x - 7) = 4 4x - 7 = 4/2 4x - 7 = 2 4x = 9 x = 9/4 |
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| 4. |
-~L-LT] = [1] x L, LTI] |
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| 5. |
8 cmindind the base of a triangle whose area is 220 cm? and height is Ilemthe base of a triangle whose area is 220 cm2 and height is 11em |
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Answer» Like if you find it useful |
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| 6. |
11. A bucket is in the form of a frustum of a cone and it can hold 28.49 litresof water. If the radii of its circular ends are 28 cm and 21 cm, find theICBSE 2012]height of the bucket. |
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| 7. |
The area of a circle whose area and circumference are numericallyequal, is |
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Answer» Area of circle [πr^2]=circumference ofcircle 2πrTherefore, πr^2=2πrπr=2πtherefore,r(radius)=2diameter=2r=4 |
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| 8. |
v nose area is 693 cm2. (use Ď-1)FiThe area oameter of a semicircle whose area is 100.48 cm" (use Ďf two semicircles are in the ratio 4= 3.14).3. |
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Answer» Area of semi circle = πr^2/2Given Area of semi circle =100.48cm2Now,πr^2/2=100.48r^2=64r=8cmTherefore diameter of semicircle is 16cm |
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| 9. |
PremiumseriesVedaArea of a Trapezium and a Polygon. Find the height of the trapezium, the sum of the lengths of whose bases is 50 cm, and whose area is21300 cms, Find the sum of the lengths of the bases of a trapezium whose altitude is 17em and whose area is085 m2. The area of a trapezium is 210 cm' and its height is 14 cm. If one of the parallel sides is double that ofthe other, find the two parallel sides |
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Answer» Thanks for ur answer |
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| 10. |
areare 13 em ani5. Find the altitude of a trapezium whose area is 65 cm2 and whose bases26 cm.11mthose area is 42, 2 and111 |
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| 11. |
. Let us simplify:12+18+27 32 |
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Answer» √12+√18+√27-√32 2√3+3√2+3√3-4√2=5√3-√2 |
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| 12. |
Let us simplify12+18 +27 32 |
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Answer» First find prime factors of12, 18, 27, 32 12 = 2*2*318 = 2*3*327 = 3*3*332 = 2*2*2*2*2 Then,sqrt(12) + sqrt(18) + sqrt(27) - sqrt(32)= 2sqrt(3) + 3sqrt(2) + 3sqrt(3) - 4sqrt(2)= 5sqrt(3) - sqrt(2) |
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| 13. |
\operatorname{li}_{x \rightarrow 0}\left\{\frac{1}{x}-\frac{1}{x^{2}} \log (1+x)\right\} |
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| 14. |
3 Let us simplify12+18 +27 32 |
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| 15. |
6. Find x such that.7. Simplify.f a x"1+n y, b ?" ym and cApplication of ExponentsExpanded Formx" m yn, then prove that an-1x bn-l XL/-m-1We have learnt the method to write very large numbers iexponents. Now, let us extend this concept to decinegative exponents.the expanded form with the help of positivemal numbers which can be expanded with the help ofFor example, consider the number 14.782 |
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Answer» the answer was fun because it was written |
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| 16. |
circumferenceratesuerter1d thediameter 7 m.-of a circle whose area is 16 times the area of the cirele with |
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Answer» R of circle whose d is 7cm = 7/2 cm.Area of circle = 7×7×22÷7×2×2 = 77/2 cm^2.Area of 2nd circle = 77×16÷2 = 616 cm^2.pi R^2 = 616 cm^2R^2 = 616 ×7÷22 = 28×7 = 196R = 14 cmCircumference = 2 pi R = 2×14×22÷7 = 88cm |
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| 17. |
cos θ i sin θ0158 IfA- i sin θ cos, then prove by principle of mathematicalinduction thatcos n 0 isin n θ e N.isin n θ cos n θ|for all neNICBSE 2005) |
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| 18. |
Q17)Find k if the following matrices are singular:[k-1 2 3]3Li-2 41 |
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Answer» So its determinant will be0now(k-1)(4+4)-2(12-2)+3(-6-1)= 0(k-1)8-2(10)+3(-7)= 08k-8-20-21= 08k= 39k= 39/8 |
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| 19. |
Li $ \frac{3 x^{3}-4 x^{2}+6 x-1}{2 x^{3}+x^{2}-5 x+7} $ |
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| 20. |
a point on the x-axis which is equidistant from the points (7,6) and (3, 4).28.FindICBSE 2005] |
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| 21. |
The sum of two numbers is 9 and the sum of their reciprocals isthe numbers.FindICBSE 2012) |
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| 22. |
ICBSE 2MSowo-digit number is such thait thethe digits intenchange their piaces Find ithe mumberpoodaterf its digits is 20.i9is added to the numberICESE 2005 |
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Answer» Solution - Let us assume x and y are the two digits of the two-digit number Therefore, the two-digit number = 10x + yand reversed number = 10y + x given - xy = 20 --------------1 and 10x + y + 9 = 10y + x ---------------2 Solve equation 2 10x + y + 9 = 10y +x 9y - 9x = 9 y - x = 1 y = 1 + x ---------------3 substitute equation 3 in equation 1 xy = 20 x (1 + x) = 20x^2+ x - 20 = 0 Solve this quadratic equation.... x^2 + 5x - 4x - 20 = 0 x(x + 5) - 4 (x + 5) = 0 (x + 5) (x -4) = 0 x = -5 and x = 4 As required number is positive two digit number, consider x = 4 Therefore, xy = 20 y = 20/x y = 20/4 = 5 therefore, the two digit number = 10x + y = 10*4 + y = 45. hit like if you find it useful |
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| 23. |
9. In the given figure, ABC is a triangle and PO is a Assstraight line meeting AB in P and AC in Q. IAP 1 cm, PB 3 cm, AQ 1.5 cm, QC-45 cm,prove that area of A APQ is-of the area of AABC.1 cm/1.5 cm4.5 cm3 cm16ICBSE 2005]B |
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| 24. |
The sum of two numbers is 16 and the sum of their reciprocals isFind the numbers.(CBSE 2005]There are two classrooms A and B. If 10 students are sent from A to B,the number of students in each room becomes the same. If 20 studentsare sent from B to A, the number of students in A becomes double thenumber of students in B. Find the number of students in each room. |
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Answer» Let one number be x.other number = 16 - x(because sum of two numbers is 16)A/Q 1/x + 1/(16 - x) = 1/3 16 -x +x / x(16 -x) = 1/3 16*3 = x(16 - x) 48 = 16x - x² x² - 16x + 48 = 0 x² - 12x - 4x + 48 =0x(x-12) -4(x-12) =0 x-4 = 0 or x-12 =0 x=4 or x=12hence one Number is 4 .and another number = 16 - x =16 - 4 =12. Let the number of students in classroom A be x and the number of students in classroom B be y. If 10 students are transferred from A to B, then we have: x – 10 = y + 10 x – y = 20 …..(i) If 20 students are transferred from B to A, then we have: 2(y – 20) = x + 202y – 40 = x + 20 -x + 2y = 60 …..(ii) On adding (i) and (ii), we get: y = (20 + 60) = 80On substituting y = 80 in (i), we get: x – 80 = 20 x = (20 + 80) = 100 Hence, the number of students in classroom A is 100 and the number of students in classroom B is 80. |
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(a)Write a pair of fractions having sum 1.Write their reciprocals.Find the sum and product of the reciprocals. Check whether they are equal.Is it applicable to all such fractions ? Justify your answer using algebra.(d) |
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Answer» Answer -a 23,17,19,11,7,5 |
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(vii) Ify = व (कि - कद) , - तर oy, 3\]2———_] then “ind dy/dx. |
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| 27. |
2. Express each of the following as a ratio in the simplest form:(i)12%(ii) 0.25%(iii) 25%(iv)26%(v) 13 % |
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Answer» 12/100=3/25=0.120.25/100=1/400=0.00225/100=1/4=0.2526/100=13/50=0.2640/3×1/100=4/30=2/15=0.13 |
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ify=cong), then dy=Ify cos |
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| 29. |
Ify2 sin x + 3 cos x, then prove thatd&2ty 0. |
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| 30. |
Ifyy- 2x.3 then find y'then find y=4x+54x + 5 |
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| 31. |
(e) Ify sin32x, then x3.State whether the following statement is true or false:(a) If the slope of two lines mand m2 are equal, then the lines are pa(e if a is any vector such that \a1 - 1, then is a unit vector.(d) Ify = tan-1x, then dy = 1-12limsinx1 |
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Answer» a) parallel → Trueb) False c) trued) false e) false. |
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| 32. |
Ify 2x -3 is a tangent to the parabola y²=4a( x-1/3)then'a'is equal to:(A) 22/3(B)-1C) 14/3D) -14/3 |
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| 33. |
EXERCISE 1.1sing appropriate properties find.2 3 5 3 13 5 2 5 6rite the additive inverse of each ofify that -(-x= x for. |
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Answer» -2/3 * 3/5 + 5/2 - 3/5 * 1/6 = 3/5(-2/3 - 1/6) + 5/2 = 3/5 * (-4 - 1)/6 + 5/2 = 3/5 * - 5/6 + 5/2 = - 1/2 + 5/2 = (-1 + 5)/2 = 4/2 = 2 ans:-3\5(-2\5×1\6)+5\2 |
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LOGARITHEMIC DIFFERENTIAOy-x21.16.) Ify= log cos tan-121)-tanhx 2) sinhx 3) coshx th4) Co |
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Answer» thank u |
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| 35. |
4(c-5)-2(c-2)=11 |
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| 36. |
e xpand formiv, Find: 101.oix O.oI |
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Answer» iii) Expanded form = 2 + 3/100 + 4/1000 iv) 101.01 * 0.01 = 0.0101 Like my answer if you find it useful! |
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| 37. |
(2) Ifx» 1 and x,2-5, then Ib ) |
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Answer» x = 1 Then,4/x + 3/y = 54/1 + 3/y = 53/y = 5 - 4 = 1y = 3 (c) is correct option |
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| 38. |
1Ifx--=-1, find the value of x + |
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| 39. |
3. Ifx +1, 3x and 4x +2 are inA.P, find the value of x. |
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Answer» thank you |
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| 40. |
Ifx1;y2 find the values of the following expressions4x-3), + 5(ii)2+2(İİİ).xy+3y-9 |
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Answer» i) 4x - 3y + 5 = 4(1) - 3(2) + 5= 4 - 6 + 5= 9 - 6= 3.ii) x^2 + y^2= (1*1) + (2*2)= 1 + 4= 5.iii) xy + 3y - 9= 1(2) + 3(2) - 9= 2 + 6 - 9= 8 - 9= -1. |
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| 41. |
(c) Ifx=-1 and y =-2, then the value of _KY3(2-y)is-3 |
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| 42. |
Aman rows at a speed fo 10 km/h in stilwater to a certain distance upstream andback to the starting point in a river whichflows at 4 km/hr. Find his average speedfor total journey (in km/hr)(A) 4(B) 6(C) 10(D) 8.4 |
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Answer» Upstream speed = 10-4=6Downstream speed = 10+4=14Now avg of 6 & 14 = (16+14)/2 = 20/2= 10 answer is option (c) 10 |
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SUB: MATHSWORKSHEET -3STD: VIII1.1f p and q are rational numbers, thena) P+b) P. 9c) Pxqd) P+ 0e) x 12. Find the multiplicative inverse of the following:a)-1b) 1/5c)-11/3 |
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Answer» 1.a.rationalnumber b.rationalnumberc. rational number d. rational number e. 1*p=p,identity property 2.a.1/-1b. 5c.-3/11 |
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Q1. Solve: (in worksheet only)1. (-35) + 5 + 112. 2 + (-5) + 11 + (-1)3. 10 +3+ (-2) +1 + (-4) |
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Answer» 1.(-35) +5 +11= -35 + 5 + 11= -35 + 16= -19 2. 2 + (-5) + 11 + (-1)= 2 - 5 + 11 - 1= 13 - 6= 7 |
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| 45. |
2 slomla1/3Pw (worksheet)☺ Simpli Ry- [17 24 25 26s 55 8'3 4.29%3]Oxata in |
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| 46. |
Worksheet 4xpand the following:1. (x - 2y + 3)2 |
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Answer» (x-2y+3z)^2=(x^2+4y^2+9z^2-4xy-12yz+6xz) x^2+4y^2+9z^2-4xy-12yz +6xz is the correct answer of the given question x² + 4y² + 9z² - 4xy - 12yz + 6xzis correct answer |
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| 47. |
Worksheet 17. Solve the followinPt7p-6o3 |
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Answer» p+7/p-6=1/3hence3(p+7)=(p-6)3p+21=p-62p=-6-212p=-27p=-27/2 Given => p+7/p-6=1/3 3(p+7)=1(p-6) 3p+21=p-6 3p-p=-21-6 2p=-27 p=-27/2 OR p=-13.5 |
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Chi: IntegersWorksheet 3-FoundationName:Class:– Date:1. Check whether the given equations are correct.a)2-(-6) = 8-0b) (-7)-(-8) = 7-8c)(-6) - 7 = 0 -(-13)d) 64-(-34) = (-15) - 15e) (-98) -(-48) = -50 - (-96)f) 65 - (-30) = (-17) + (-18) |
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Answer» a). correctb). incorrectc). incorrectd). incorrecte). incorrectf). incorrect I. correct2.incorrect3.incorrect4.incorrect5.incorrect6.incorrect accept all a is correct. a) ✔️ , b)❌ , c)❌ , d)❌ , e)❌ , f)❌ the first one is correct. this is because - x - gives us + then 6 + 2 gives us 8 a) - 8=3 (2) 2-=-1 (3)-13=13 (4)98=-30 (5) - 50=46 (6)95=-35 correctincorrectincorrectincorrectincorrectincorrect 1 correct2incorrect3incorrect4incorrect5incorrect 6incorrect a-correct,b-wrong, c-correct, a ✔️ b ❌c❌d❌e ❌is it correct bro hahahahah 2-(-6)=8-02+8=8RHS,8-0(CORRECT )2) -7-(-8)=7-8-7+8=-1(INCORRECT ) a) 2-(-6)=8-0=-8b) (-7)-(-8)=7-8=1c) (-6)-7=0-(-13)=13 a)✔️b)✖️c)✖️d)✖️e)✖️f)✖️ a)correctb)correctc)incorrectd)incorrecte)incorrectf)incorrect a=correctb=incorrect a. correctb. incorrectc. incorrectd. incorrecte. incorrectf. incorrect 1). correct2). incorrect 3). incorrect4). incorrect5). incorrect6). incorrect 1. correct2.wrong3.correct4.wrong5.wrong6.wrong a)correctb)Wrongc)Wrong d)Wrong e)Wrong f)Wrong correct, wrong, wrong, wrong, wrong, wrong 1- right2- wrong3-wrong4-wrong5-wrong6- wrong 1. (a) =》 ......true.... (b) =》........fulse... (c) =》 ........fulse.. (d) =》 .......fulse... (e) =》 .......fulse.... (f) =》 .......fulse..... 1)√2)×3)×4)×5)×6)× a) 2-(-6)=8-02+6=8-0=8 AAA is correct answer (a)=(b)=(c)not equal to (d)not equal to (e)not equal to (f) not equal to à= 8b=-1c=-13d=0e=-46f=-35 a correct. b.incorrect c.correct. d.incorrect. e.incorrect. f.incorrect a part is correct only rest all parts are incorrect.....!.!!! a option is correct equation a. correctb. not correctc. not correctd. not correcte. not correct f. not corect |
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| 49. |
carpetofsize5 m x 2 m has 25 cm wide red border. The inner part of the carpet10.0. As blue in colour. Find the area of blue portion. What is the ratio of the areas of red1Sortion to blue portion? (.75 n?-,ră2 |
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Answer» Area of carpet = 100000cm sqArea of blue portion = 450×150= 67500Area of red portion is 100000-67500=32500Ratio= 32500:6750013:27 |
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| 50. |
dy/dx=cos(x+y) |
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Answer» thanks |
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