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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. |
The 9th term of an AP is equal to 7 times its third term and the 13th term is exceeds three times its 5th term by 8. Find the 27th term. [Ans: 100] |
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| 2. |
The 6th term of an AP is - 10 and the 10th term is - 26. Determine the 15th term of the AP. [Ans: - 46] |
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| 3. |
In an AP 6th term is half the 4th term, and the 3rd term is 15. If Sn 66 then find thevalues of n. |
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Answer» 6th term=4th term/2 a+5d=(a+3d)/2 2a+10d=a+3d a+7d=0 3rd term = 15 a+2d = 15 a+7d-a-2d = 0-15 5d = -15 d = -3 a-21 = 0 a=21 Sn=66 n/2(2a+(n-1)d) = 66 n(42+(n-1)(-3)) = 132 n(42-3n+3)=132 -3n*n+45n-132 = 0 n*n-15n+44 = 0 (n-11)(n-4) = 0 n = 4 or 11 |
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| 4. |
39. The 19th term of an AP is equal to 3 times its 6th term. If its 9th termICBSE 2019, find the AP. |
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Answer» Let in anAP first term =a, Common difference =d9th term =19a+8d=19----(1)19th term =3*(6th term)a+18d=3(a+5d)a+18d=3a+15d0=3a+15d-a-18d2a-3d=0---(2)subtract (2) from 2*(1)-19d=-38d=2substitute d=2 in (1)a=3thereforea=3,d=2required AP is3,5,7,9,.... Solution: a19= a+18d andIt is 3times the 6term So, a+18d=3(a+5d) a+18d=3a + 15d Subtract 3a-a=18d- 15d 2a-3d -3d=-2a d= -2a/-3 or 2a/3 Put this value in the below equation as we have , a9= a+8d= 19 a+ 8× 2a/3=19 a+ 16a/3= 19 (3a+ 16a)/3=19 19a/3=19 19a= 19×3 a= 57/19=3 D=2a/3=. 2×3/3=2 So the AP will be 3,5,7,9, 11....…. |
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| 5. |
Enercise 611 Find the 1H of the fullowing Lome/a) and 12b) |
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Answer» HCF of 3x and 12 is 3x = 3× 12 = 3× 4 HCF is 3 |
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| 6. |
13-Find a quadratic polynomial, whose zeroes are -3 and 4. |
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Answer» x^²-x-12=0 is the correct answer of the given question x^²-x-12=0 is correct answer |
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| 7. |
Sides of a triangle are in the ratio of 12: 17:25 and its perimeter is 540cm. Find its area.An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find5.6. |
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| 8. |
1Find a, b and n in the expansion of (a +b) if the first three terms ofare 729, 7290 and 30375, respectivelythe expansion |
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| 9. |
6. Prove that in a parallelogram, oppositesides are equal. |
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| 10. |
6.An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Findthe area of the triangle. |
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| 11. |
futmof an isosceles triangle is 205 cm. If one of its equal sides is 2-cm, find. RepreGi12. Theeter6third side. |
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Answer» perimeter = 20 3/4 = 83/4 cm equal sides are 2 5/6 = 17/6 cm third side 83/4-17/6-17/6 = 83/4-17/3 = (83×3-17×4)/12 = (249-68)/12 = 181/12 cm I have not got it |
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| 12. |
. FindAn isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cmthe area of the triangle.6. |
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| 13. |
Example 2. Each of two equal sides of anisosceles triangle is 7 cm and the third sideis 6 cm. Find the area of the triangle. |
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| 14. |
12. Ariangle AnC is drawn to circumscribe a cireleof radius 4 cm such that the segments BD andDC into which BC is divided by the point ofcontact D are of lengths 8 em and 6 emrespectively (see Fig. 10 14) Find the sides Ali |
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| 15. |
\frac { - 9 } { 10 } + \frac { 22 } { 15 } |
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Answer» -135+220/150 = 85/150 = 17/30 |
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| 16. |
12. A triangle ABC is drawn to circumscribe a circleof radius 4 cm such that the segments BD andDC into which BC is divided by the point ofcontact D are of lengths 8 em and 6 emrespectively (see Fig. 10.14). Find the sides ABand AC |
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| 17. |
9. Eight truck drivers have been. contracted to deliver768 imported carsEach truck can hold six vehicles, How many trips will each driver take todeliver the imported cars |
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Answer» 8 truck * 6 vehicles= 48768÷48= 16 768is /by 8 means answer is 96and 96/6=16 |
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| 18. |
e number ofpassengers who travelled in Ap6bus from Adilabad to Nirmal in 4 trips in ad in APSRTOd 54. What is the occupancy ratio (averasengers travelling per trip) of the busfor the day? |
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Answer» Average:- 39+30+45+54 = 168Now, 168/4 = 42 Therefore average is 42 passengers thanku average=(39+30+45+54)/4=168/4=42 |
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| 19. |
Find quadratic polynomial whosezeraes are is t3 and 5-13 |
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Answer» Sum of roots is √5+√3 +√5-√3=2√5product of roots 5-3=2hence the equation isx^2-(sum of roots)X+(product of roots)=x^2-2√5x+2 |
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| 20. |
Find the quadratic polynomial whose zeroes are 2 and -3 |
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| 21. |
Sainik School, 2010-115. A school starts at 8:20 am andcloses at 1:50 pm. Find theduration for which the schoolremains open ?Sainik School, 2008-09! |
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Answer» here, 8:20 is 8 hours and 20 minutes= (8*60+20)=500 minsAnd 1:50 is 13 hours and 50 mins= 830 minsso 830-500= 330 mins= 5 hours and 30 minutes. ( answer) |
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| 22. |
118Find the 13th tern in the expansion of9x31.0 |
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Answer» We know, General term of the expansion (X - Y)ⁿ is T_{r+1} = nCr.X^{n-r}(-Y)^r use this here, here , X = 9x Y = 1/3√x n = 18 T_{r+1} = 18Cr.(9x)^{18-r}.(1/3√x)^rfor 13th term , we have to use r = 12 now, T_{12+1} = 18C12.(9x)^{18-12}(1/3√x)^12 = {18!/12!×6!} (9x)^6(1/3√x)^12 = { 18 × 17 × 16 × 15 × 14 × 13/6×5×4×3×2}(9)^6(1/3)^12 { x^6 × 1/√x^12} = { 17 × 4 × 3 × 7 × 13} (9^6/9^6){x^6 × 1/x^6} = 17 × 12 × 91 = 18564 Hence, 13th term = 18564 |
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| 23. |
. Find the volume and surface area of a sphere of radius 8-6 cm (Take Tt 3 14) |
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| 24. |
5. 8x+ 5 = 6x-5 |
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Answer» x= -5 is the correct answer of the given question 8x-6=-5-52x=102%10-5 5.8x -6x= -5 -6-0.2x = -1 x = -5 is the right answer x=-5 is the right answer this question answer is x=5 |
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| 25. |
n th term of an A.P. is (2n+1), what is its 13th terms |
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Answer» a(n) = 2n + 1so,a(13) = 2×13 + 1 = 26 + 1 = 27 |
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| 26. |
A cone of height 8 m has a curved surface area 188.4 square metres.Find its volume. (Take Tt 3.14.) |
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Answer» Given, height of cone, h = 8 m Let r be radius and l be slant height of cone, Given, curved surface are of cone = 188.4 m^2 pi*r*l = 188.4 On squaring both sides, we get r^4 + 100 r^2-36r^2 -3600 = 0 r^2(r^2 + 100) -36 (r^2 + 100) = 0 (r^2-36)(r^2+100) = 0 r^2 = 36, -100 r^2 ≠ -100 r^2 = 36 or r = 6 cm Hence radius is 6 cm. Now volume of the cone = (1/3)*pi*r^2*h= (1/3)*pi*6^2*h= (3.41*36*8)/3= 3.41*12*8= 301.44 cm^3 |
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| 27. |
If nth term of an A.P. is (2n+1), what is its 13th terms? |
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| 28. |
3. A bucket is in the form of a frustum of a cone. Its depth is 15 cm and thediameters of the top and the bottom are 56 cm and.42 cm respectively[CBSE 2005C]Find how many litres of water can the bucket hold. TakeTt7 |
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| 29. |
a value of residential flat is rs 1800000 its value is apriciating at the rate of 10% per anjum what will be its value after 3 years construction |
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Answer» Let value after 3 yrs is A A = 1800000(1+10/100)^3 = 1800000(11/10)^3 = 1800000(1.1*1.1*1.1) = 1800000(1.331) = 2395800 Value of flat after 3 years = Rs 23,95,800 |
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| 30. |
ind the difference of the place values of Two 5's in 857021530.I |
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Answer» 50000000-500= 49,999,500अंतर होगा |
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| 31. |
how many kinds of sentence |
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Answer» There are 5 kinds of sentences |
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| 32. |
) Find the sees of thbetween the neroesif o and R be the neoes |
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| 33. |
(a) 120째(c) 90째(b) 60째(d) 45째 |
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| 34. |
ra. Find quadratic polynomial whose neroes are3+\sqrt{7}, 3-\sqrt{7}\frac{2-\sqrt{3}}{3} \cdot \frac{2+\sqrt{3}}{3} |
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| 35. |
Cot 30째iv) 4 (sin4 30째 + cos4 60째) 3 (cos 45erify each of the follauin1Vsin2 90째). |
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Answer» sin30°= 1/2=cos60cos45= 1/√2sin90°=1Now putting these values in the equation4(1/16+1/16)-3(1/2-1)8/16+3/2 Taking LCM of 16 and 28+24/1632/16=2 answer |
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| 36. |
3. Find the value of COS4cos 45째 sin 90째-sin 45째 cos90째 |
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| 37. |
2121. If cot 3xsin 450 cos 45째 +cos 60째: findthe value of x between 0째 and 90째.Ono. |
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Answer» cot 3x=sin45*cos45+cos60cot 3x=(1/2)+1/2cot 3x=13x=90x=90/3x=30 |
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| 38. |
9.Find the angle measure x in the following figures:-50째90째0째130120째10. Find the sides of a cube whose surface area is 600 cm |
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Answer» (a) x=180-90=90(angle sum property)(b) sum of all angles is 360120+130+50+x=360x=360-300=60(c)sum of all angles of pentagon is 5405x=540x=108 |
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| 39. |
ind the dniclcitCalculate the diffèrence of place-value and face-value of S's in 9654321her in all? |
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Answer» Please post a complete question here. I am unable to see the number completely. |
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| 40. |
15. If the polynomial 6x 8x-5x2 + ax + b is exactly divisible by the polynonial2x2-5, then find the value of a and b. |
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Answer» 8 x cube minus 6 X square + 2at x is equal to 1 |
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| 41. |
dent is ranked 13th from right and 8th from left. How many students arethere in total? |
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Answer» The Student ranked 13th from Right. That means there are 12 Students Right from the Student.The Student ranked 8th from Left. That means there are 7 Students Left from the Student. So the total no of Students are 12(Right from the Student)+7 (Left from the Student)+1 (The Student itself) =20 So the total no of Students are 20 |
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| 42. |
2. Kavi ranked 9th from the top and38th from the bottom in a class. Howmany students are there in the class? |
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| 43. |
5. Ashok faces North and takes a right turn at the angle2700°. In which direction was Ashok facing after theturn?(1) North(4) South(2) East(5) South-East(3) West |
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| 44. |
17. A solid cone of base radius 10 cm is cut into two parts through themidpoint of its height, by a plane parallel to its base. Find the ratio ofCBSE 2013)the volumes of the two parts of the cone. |
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Answer» thanks |
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| 45. |
Look at the following shapes. Draw how they will look on of a31turn andof a turn.of a turnI of a turn66 |
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| 46. |
14. You are facing South. Which direction will you befacing, if you take:a. 90째 clockwise turn?b. 180째 anti-clockwise turn?c. 90째 anticlockwise turn?d. 270째 clockwise turn? |
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Answer» a is the write answer a)Westb)Northc)Eastd)EastIt is the correct answer |
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| 47. |
11. Find the quadratic polynonial whose neroes aresqoare ef the aeroes of spolynomial |
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Answer» let,zeroes of the polynomial x^2-x-1 be p and q. i.e. x^2-(p+q)x-(pq)=0 =>pq=-1 and p+q=1, now according to the given condition,=>p^2q^2=1 and P^2+q^2=(p+q)^2–2pq=(1)-2(-1)=3, so the new equation will be,x^2-(p^2+q^2)x+(p^2q^2)=0 =>x^2–3x+1=0 |
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| 48. |
nd the area of a rhombus if its vertices are (3,0), (4,5), (-1,4) and (2.,-1) taken inrder. [Hint : Area of a rhombus (product of ts diagonals)10.02 |
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| 49. |
A.Plk: The 24h term of an A.P. is twice its 10th term. Show that its 72d term ICBSE 2013)1nnd 09hich are divisible by both 2times its15h term. |
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| 50. |
If the points A(1,-2), B(2, 3), C(-3,2) and D(-4,-3) are thevertices of a parallelogram ABCD then taking AB as the base,findthe height of the parallelogram.ICBSE 2013] |
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