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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. |
Determine the domain and range of the relation R defined byR (x,x +5): x E 10, 1,2, 3, 4, 5). |
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| 2. |
1. Find the circumference of a circle whose radius is(1) 28 cm, (1) 14 m. |
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| 3. |
Example 7:Find the square root of 1296 |
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| 4. |
EXERCISE 12.3Find the coordinates of the point which divides the line segment joining the points(-2, 3.5) and (l,-4, 6) İn the ratio (i) 2 : 3 internally, (i) 2 : 3externally |
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| 5. |
Example 7: What should 3-6 be multipliet 34? |
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EXAMPLE 7Find six rational numbers between 3 and 4. |
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| 7. |
7, 213 क्यारियों में कितने पौधे होंगे? जबकि एकक्यारी में 525 पौधे हैं? |
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Answer» 213 क्यारियों में पौधे होंगे =213*525= 111825क्योंकि दिया गया है हमको |
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| 8. |
Example 7: How many two-digit numbers are divisible by 3? |
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Answer» So, the A.P. will be12,15, 18,21, ………….99 We need to find n Last term of this series is 99 So, an = 99 & a =12d =15–12= 3 Now, an = a + (n – 1) d Putting values 99 =12+ (n – 1) (3) 99 =12+ 3n – 3 99 = 9 + 3n 3n = 99 – 9 3n =90n =90/3 = 30 Therefore , there are30 twodigit numbers divisible by 3 |
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| 9. |
20. The radius and height of a right circular cone are in the ratio of 5,12. If its volume is 314 cubic cm.Then its slant height1) 11cm2) 12cm3) 13cm4) 14cm |
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| 10. |
Write the relation R-{(x,x*): x is a primenumber less than 10) in roster form |
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Answer» thank you |
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| 11. |
the cylinder.3. The circumference of the base of a cylinder is 132 cm & its height 25cm. Find the volume of themondn cylinder is 2 em. It is 35cm long & its inner radius is 12cm.cylinderhollouur |
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Answer» Circumference of base = 2πr = 132 => 2*(22/7)*r = 132=> r = 3*7 = 21 cm now height is = 25m so, volume is πr²h = 22/7*(21)²*(25) = 34650cm³ |
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| 12. |
t bagsus and slant height of a cone are in the ratio 4: 7. If its curved surface area is 792cm2, findradius1) 11cm2) 12cm3) 13cm4) 14cm |
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| 13. |
Example 7 : Show that 0.3333... -0.3 can be expressed in the form, where p andq are integers and g0. |
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| 14. |
Find the position vector of a point R which divides the line joiming(a +b) in the ratio 2 :1 () internally (i) externally |
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| 15. |
EXERCISE 12.3Example 1. Find the co-ordinates of the point which divides the join of (-2, 3, 5) and(1, -- 4,-6) in the ratio(1) 2:3 internally (it) 2:3 externally. |
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| 16. |
12. Asolution of 8% boric acid is to be diluted by adding a 2% boric acid sit. The resulting mixture is to be more than 4% but less than 6% boric640 litres of the 8% solution, how many lites of the 2% solution will have to be27o boricon toacid. If we have |
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| 17. |
12. Asolution of 8% beric acid is to be diluted by adding a 2% bone acid solution toit.The resulting mixture issobe more hin 4% but less than 6% boric acid. If we have640 litres of the 8% solution, how many lites ortho 2% solution will have to be added? |
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| 18. |
18. If the point C(-1, 2) divides internally the line segment joining the points A(2, 5) and Bie yl in the ratio3 : 4, find the value of x2ĺ1/ |
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| 19. |
bottles ?8. A leaking can drips oil at the rate of 180 ml per hour. How many litres of oil will bewasted in 10 hours?har 19 1 640 ml of liquid. This liquid is to be filled in smaller bottles each |
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Answer» It drips 180 ml per hour. So, in 10 hours it drips = 180×10 =1800 ml =1.8 L. |
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| 20. |
Asolution of 8% boric acid is to be diluted by adding a 2%bonic acid solution to it. The resulting minture is to be morethan 4% but less than 6% boric acid. If we have 640 lites ofthe 8% solution, how many litres of the 2% solution will haveto be added? |
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| 21. |
- 4findPimethe rubefarlarisation.roofof3315by |
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Answer» Simplified Square Root for √3375 is 15√15 Step by step simplification process to get square roots radical form: First we will find all factors under the square root: 3375 has the square factor of 225. Let's check this width √225*15=√3375. As you can see the radicals are not in their simplest form. Now extract and take out the square root √225 * √15. Root of √225=15 which results into 15√15 All radicals are now simplified. The radicand no longer has any square factors. What Is The Square Root Of 3374 What Is The Square Root Of 3376 15 is the cube root of 3375 solve it nicely its very easy |
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| 22. |
A(2, 3) is a fixed point, and Q(3cos8, 2sinf) a variable point. If Pdivides AQ internally in the ratio 3: 1, find the locus ofP. |
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| 23. |
Example 7 : Show that 0.3333... = 0.3 can be expressed in the formwhere p andq are integers and q +0. |
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Answer» 1/3 is the correct answer of this problem X=1/3,1/3 is the correct answer for this problem X= 1/3 is the correct answer of the given question X=1/3 is the correct answer |
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| 24. |
Example 5: Simplify the expressions and evaluate them as directed:0) x (x 3) + 2 for x 1,(ii) 3y (2y -7)-30-4)-63 for y--2 |
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Answer» 1) x(x-3)+2 = 1(1-3)+2 = -2+2=02) 3y(2y-7)-3(y-4)-63 = 3(-2)(-4-7)-3(-2-4)-63=66+18=84 |
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| 25. |
2 213Example 7 Simplify |
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| 26. |
Ex. 3.6.7 W-14.4 MarksFind the angle between two forces of magnitude 300 N eachif their resultant is 150 N. |
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| 27. |
13. Write the roster form of X = {x: x= 12 + 2n +1.ne N and n<10). |
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| 28. |
Emdl the capacity in litres of s conical vessel withG)1.radius 7 cm, slant height 25cmheight 12cm. dant height 13 cm |
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| 29. |
eEl T O("âL)'!\-locrl_.as -3 dinc |
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Answer» p(x)=(k-1)x^2 +kx+1p(-3)=0p(-3)=(k-1)(-3)^2+k(-3)+10=9k-9-3k+16k=8k=4/3 hit like if you find it useful |
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| 30. |
21tion :r5r2-15x + 56 = 0 |
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| 31. |
LO |
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Answer» P = 3×40 × 10⁴ = 12 × 10^5 |
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| 32. |
7·The value of tan 7-is |
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Answer» So |
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| 33. |
Q 24. Find the area of an triangular roof having side 12cm,13cm,and 11cm |
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| 34. |
12, A solution of 8% boric acid is to be diluted by adding a 2% boricit. The resulting mixture is to be more than 4% but less than 6% boric acid.640 litres ofthe 8% solution, how many litres of the 2% solution will have |
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| 35. |
Example 6 Find the coordinates of the point which divides the lUthe .points (4, 3) and (8, 5) in the ratio 3: 1 internallytion formula,tion formula, we get |
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Answer» Using section formula x= 1(4) .+ 3(8) / 4y= 1(-3) + 3(5) / 4 x= 28/4 = 7y= 12/4 = 3therefore point (7,3) divides the line segment in the ratio 3:1 |
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| 36. |
2. The measure of two adjacent angles of a quadrilateral are 80° and 1009. Ifremaining angles have equal measure then find the measures of equal angles. |
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Answer» sum of angle of quadrilateral is 360,let the equal angle be x80+ 100 + x +x = 3602x = 360-180 = 180x = 180/2 = 90 worng Anser is this |
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| 37. |
I VULUMES0Example 7: A solid toy is in the form of ahemisphere surmounted by a right circular cone. Theheight of the cone is 2 cm and the diameter of thebase is 4 cm. Determine the volume of the toy. If aright circular cylinder circumscribes the toy, find thedifference of the volumes of the cylinder and the toy.(Take it = 3.14)Fig. 13.14ntanding on the |
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Answer» volume =vol of hemisphere+vol of cone=2/3πr^3+1/3πr^2hhere d=4, r=2, h=2=1/3πr^2(2r+h)= 1/3×22/7(2)^2{2×2+2)=22×4×6/3×7=25.14 cm^3volu of cylinder=πr^2h(r=2, h=2+2=4) = 22/7×4×4 = 22×16/7 =50.28 cm^3vol cylinder - vol of toy= 50.28 - 25.14= 25.14 cm^3 |
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| 38. |
10 1 12n)1003.9, measures of some anglesiven. Using the measures find thes of x, y, z.ureFig. 3. |
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Answer» The question figure is not completely posted.Based on the available data the following values are obtained. |
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| 39. |
In the quadrilateral if the measure of two angles are 80 and 60 and the remaining angles are equal find all the angle. |
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Answer» hit like if you find it useful |
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| 40. |
angles of an 8-sided polygon are 142" and 176 If the remaining angles are equal to each oS n Find che magnitude of each of the equal angles.thenual to each other |
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Answer» Two angles of an eight sided polygon are 142 and176 degree .If the remaining angles are equal to each other;find the magnitude of each of the equal angles.------------8 sides --> the sum of the Int angles = 1080 degsSubtract the 2 given angles from 1080 and divide the result by 6. |
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| 41. |
3and x-3 are zeroes of the quadratic polynomialItal cĂŻx2 -+-7x-/> then find he value ofa and b |
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| 42. |
s of the polynomial a3- 15x2 + 71x + p are in AP, find the value7. If the zeroeof p.2 |
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| 43. |
25. Draw the graphs of x-1 + 1 = 0 and 3x + 2-12 = 0. Determine the coordinates of thevertices of the triangle formed by these lines and x-axis and shade the triangular area.Calculate the area bounded by these lines and x-axis.CRSE34. SollSha |
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| 44. |
Mf the diagonals of a parallelogram are equal, Iel SIWtheH SiIOW L3. Show that if the diagonals of a quadrilateral bisect cach other at right angles, then itis a rhombus.lu of a sqvare are equal and bisect each other at right angles. |
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Answer» 1 2 |
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| 45. |
Three angles of a heptagon are 80°, 110° and 130. If the remaining four are equal,find the measure of each of the equal angles. |
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| 46. |
Three angles of a quadrilateral are equal.The fourth angle is 144. What is themeasure of the equal angles? |
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Answer» three angles are x and addition of all angles is 360 3x + 144 = 360 3x = 360 - 144 = 216 so x = 72 so equal angles are 72. |
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| 47. |
A solid toy is in the form of ahemisphere surmounted by a right circular cone. Theheight of the cone is 2 cm and the diameter of thebase is 4 cm. Determine the volume of the toy. If aright circular cylinder circumscribes the toy, find thedifference of the volumes of the cylinder and the toy.(Take π=3.14) |
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| 48. |
3. In a quadrilateral, three angles are in the ratioof 3:3 1 and the fourth angle is 80° Find themeasures of equal angles. |
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Answer» How did you get that 120 Let the three angles measure be 3x°, 3x° and x° each. fourth angle is 80° Sum of all the angles of a quadrilateral is 360°. ∴ 3x+3x+x+80=3607x+80=3607x=360-807x=280x=280/7x=40 Angles of the quadrilaterals are3x°=3*40=120°,120° and 40°
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| 49. |
If a, b, с are the position vectors of A, B,C, prove that(a)is a vector perpendicular to the planeABC. |
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Answer» Thank you☺ |
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| 50. |
Three angles of a quadrilateral are equal and the measure of the7.fourth angle is 120. Find the measure of each of the equal angles. |
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