Saved Bookmarks
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. |
All formula ofPythagorean theorem |
| Answer» | |
| 2. |
Find the remainder when 2r-3x t 5 is divided by 2x-3, Does it exactly dipolynomial ? State reason. |
|
Answer» There are two methods of verifying if it actually divides the polynomial or not: Firstly by simple division and secondly by putting the value of x obtained from the second equation in the polynomial. Let 2x-3 = 0 then, x = 3/2 = 1.5 Now, we need to put this value in the polynomial: 2x^2-3x+5 = (2 x 9/4) - 9/2 + 5 = 9/2 -9/2 + 5 = 5 which is not equals to zero. That means 2x - 3 doesn't divides the polynomial. |
|
| 3. |
7×5×3×2+3 is a composite number? give reason for your answer |
|
Answer» 7×5×3×2+3216+3219= 219 is divisible by 3. Therefore it has more than two factors and composite no. are those no. which have more than 2 factors. |
|
| 4. |
Is it possible to construct a triangle if any two sides of the triangle are equal to the thirdside? Give reason.(3) |
|
Answer» The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side, then you know that the sides do not make up a triangle. |
|
| 5. |
3. State giving reason whether AB || CDAC60°120° |
|
Answer» angle CSR = angle DSQ = 120° ... ( vertically opposite angles) also, angle ARS + angle RSC = 60+120 = 180° ..making its adjacent angles.. and since the sum is 180 .. so, AB || CD |
|
| 6. |
Draw the graph of the polynomial p(x)=x3-9x and find the zeroes of thepolynomial by using graph. |
| Answer» | |
| 7. |
018Simplyti using disturbutine property 43x433+43 XIZ |
|
Answer» (43×33)+[43×{-17}]= 43 × [33+{-17}]= 43 × (33-17)= 43 × 16= 688 (43×33)+[43×{-17}]=43×[33+{-17}]=43×(33-17)=43×16=688 (43×33) + [43×{-17}]= 43×[33+{-17}]=43×(33-17)=43×16=688 |
|
| 8. |
6. What are your observations of the graph of p)3-2x -x^2 without drawing the graph ? |
|
Answer» p(x) = 3-2x -x²b² -4ac4 - 4 × (-1)×34 +12 = 16soroots are real and distincttherefore the graph of this function intersect the x axis 2 times as it has two real zeroes |
|
| 9. |
Without using trigonometric tables, evaluatesin39°cos51 |
|
Answer» =sin39/cos51 + 2tan11tan31tan45tan59tan79 - 3(sin^221+ sin^269) =1 + 2cot79cot59tan45tan59tan79 - 3(sin^221 + cos^221) (sin teeta = cos(90 - teeta)) (tana a = 1/cota) =1 + 2 - 3 =0 than1 |
|
| 10. |
find hypotenuse without using Pythagorean theorem |
|
Answer» So, without using pythaogras theroem we can use trignomerty ratio to find Hypotnese |
|
| 11. |
Without using trigonometricsin 16cos 74° |
|
Answer» Sin(90°-74°) =sin 16 so, sin(90-74)/cos 74--------(1) we know that , sin (90-ø) = cos therefore, from (1), cos74/cos 74 =>1 Like my answer if you find it useful! |
|
| 12. |
3. State giving reason whether AB / CD60°(i) p 609120° |
|
Answer» angle CSR = angle QSD = 120° ( vertically opposite angles) and since angle CSR + angle ARS = 120+60=180° which also makes adjacent angles so, AB || CD |
|
| 13. |
Evaluate 2cos 75.cos 15 without using calculator. |
| Answer» | |
| 14. |
Find the squares of the following, using property of perfect squares :(a) 7(b) 8(c) 12(d) 13 |
|
Answer» (a)7=49(b)8=64(c)12=144(d)13=169 7....498....6412..14413..169 7= 498=6412=14413=169 7×7=498×8=6412×12=14413×13=169 7=498=6412=14413=1698 a) 7=49=343; b) 8=64=512; c)12=144=1728; d) 13=169= 2197 a. 7 sq. = 49 b. 8 sq. = 64 c. 12 sq. = 144 d. 13 sq. = 169 a* 7=49=343b* 8=64=512c* 12=144=1728d* 13=169=2197 |
|
| 15. |
\left(\frac{x^{l}}{x^{m}}\right)^{n} \times\left(\frac{x^{m}}{x^{n}}\right)^{l} \times\left(\frac{x^{n}}{x^{l}}\right)^{m}= |
| Answer» | |
| 16. |
Ii m times the rath term is equal to n times the nth term of an A.P, prove that (m+m) th termof the A.P. is zero.S l |
| Answer» | |
| 17. |
ΔΑ BC th AB AC 7.5 cm and BC-9 cm (Fig i 1.26). The heightAD from A to BC, is 6cm. Find the area of AABC. What will be the height from Cto AB i.e., CE?is isosceles wI |
|
Answer» unfortunately your answer is wrong |
|
| 18. |
Sara's age 12yearss age 12-31 years SyearsSara s mother's age-3x3x1236years.EXERCISE 8.4r5 a subtracted from three times a number, the result is 16. Find the nuFind the nunmberwhich when mutiplied by 7 is increased by 78Find three consecutive natural numbers such that the sum of the firstthan the thirdThe difference betwsen two numbers is 7. Six times the smaller plus tnumbersA man says, 1am thinking of a number. When I divide it by 3 and thtwice the rumberi tought of Find the number |
| Answer» | |
| 19. |
cett oa rectangular park which is 4wide ants. A wire of length 44.4 cm is bent in the form of a square and it is also bent in form of a hexagon.Fund the measure of the side of the square and the hexagon.th is 45 |
| Answer» | |
| 20. |
surely not perfect squares(iv) 441 |
|
Answer» it is perfect square , as 21² = 441 |
|
| 21. |
EXERCÄ°SWhat will be the unit digit of the squares of the following mumben?(0) 81(v) 1234(ix) 12796(i) 272(vi) 26387(x) 55555(ii) 799(vii) 52698huiously not perfect squares. Giverea |
|
Answer» unit digit will be the sqaure of last digit of number so i) 1² = 1 ii) 2² = 4iii) 9² is 1 (last digit)v) 4² is 6vi) 7² is 9vi) 8² is 4vii) 6² is 6viii) 5² is 5 |
|
| 22. |
1.Which of the following numbers are perfect squares?11,16)32.86 50,64,75 |
| Answer» | |
| 23. |
Whichof the following numbers are perfect squares?11, 16, 32, 36, 50, 64, 75 |
| Answer» | |
| 24. |
1. Define a set. |
|
Answer» A set is a well-defined collection of distinct objects. The objects that make up a set (also known as the set's elements or members) can be anything: numbers, people, letters of the alphabet, other sets, and so on. ... Sets A and B are equal if and only if they have precisely the same elements. Please hit the like button if this helped you out |
|
| 25. |
eir suDnow thctorise a1. Arm4412. Fină3. FinYecoe |
|
Answer» here at the terms having similar powers of xso, 4x^3+3x^2+5x^2+9x+3x=4x^3 + 8x^2 + 12x |
|
| 26. |
coordinatesof the points which divide the line segment joining A-2,2) annd thed theFinB(2. 8) into four equal parts |
| Answer» | |
| 27. |
If 21 is subtracted from a certain number and thresult is multiplied by 6, the product is 120. Finthe number |
|
Answer» Let the certain number be x.If 12 is subtracted, it becomes x-12. If this is multiplied by 6, the product is 120. 6(x-12) =120 x-12 =120/6=20 x-12=20x=12+20x=32. |
|
| 28. |
6. DDeLd7. In an ap m thterm of an AP is equal to n times l I8. The sum of 3 consecutive term of an AP is 24 and sum of their square is 194 then finth arms |
| Answer» | |
| 29. |
7. The measure of two adjacentthe ratio 3:2. Find thmeasure of each of the angies of |
| Answer» | |
| 30. |
EXERCISE S.1Prove that the function f(a) 5x-3 is continuous at x 0, at x-3 and at x-5.1. |
|
Answer» Given function isf(x) = 5x-3 Now at x = 0f(x) = 5(0) -3 => -3 limx→0 5(x)-3 = -3therefore limx→0 f(x) = f(0) hence function in continuous at x = 0 Now At x = -3 f(-3)= 5(-3)-3 = -18now lim x→-3 f(x) = 5(-3)-3= -18thus f(-3) = limx→-3 f(x)hence function Is continuous at x = -3 Now at x = 5f(x) = f(5) = 5(5)-3= 22also lim x→5 f(x) = lim x→5 5x-3= 5(5) - 3 => 22 Thus f(5) = lim x→5 f(x)hence function is continuous at x = 5 |
|
| 31. |
TH AB and CD are parallel find themeasure of a+y. |
|
Answer» Its answer is x+y=40+36=76 76 is the correct answer |
|
| 32. |
1. In th75"e ngure given alongside, find the measure o45" |
| Answer» | |
| 33. |
Directions:Ineachquestion 1 to 16 below, therederce12,are certain numbers arranged in a peculiar manner7around a figure are given. You have to find amissing number in place of question mark, fromthe given four alternatives below the question.Write its number in the answer-sheet against thecorresponding question number.1.64834C PE V1)40 2) 60 3) 67 4)78 |
|
Answer» t+v+Y=6720+22+25=67 |
|
| 34. |
Which answer figure includes all the components givethe question figure?Question Figure:Answer Figures: |
|
Answer» figure a is the answer |
|
| 35. |
sin 30° + tan 45° - cosec 60° /sec 30 + cos 60° cot 45° |
| Answer» | |
| 36. |
(a) Define closed set in a metric space |
| Answer» | |
| 37. |
) sin 30° + tan 45° — cosec 60°नsec 30° + cos 60° + cot 45° |
| Answer» | |
| 38. |
) sin 30° + tan 45° - cosec 60°sec 30° + cos 60° + cot 45° |
| Answer» | |
| 39. |
\left[\frac{\tan 30^{\circ} \cdot \sin 60^{\circ} \cdot \csc 30^{\circ}}{\sec \theta^{\circ} \cdot \cot 60^{\circ} \cdot \cos 30^{\circ}}\right]^{4} |
| Answer» | |
| 40. |
, 1 + 3819 -- 410 __ (1 + 28100: (1 â-sinÂŽ |
|
Answer» hit like if you find it useful |
|
| 41. |
Tequired to proveEXERCISE 841. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. |
| Answer» | |
| 42. |
Without using trigonometric table evaluate the following:\frac{\sin 50^{\circ}}{\cos 40^{\circ}}+\frac{\operatorname{Cosec} 40^{\circ}}{\sec 50^{\circ}}-4 \cos 50^{\circ} \csc 40^{\circ} |
|
Answer» sin 50° = sin( 90 - 40 ) = cos 50 ° Cosec 40 = Cosec ( 90 - 50 ) = sec 40° cos 50 = cos ( 90 - 40 ) = sin 40° sin 40 Cosec 40 = 1 ------------------------------------------- sin 50 / cos40 + Cosec 40 / sec50 - 4cos50cosec40 = cos 40 / cos 40 + sec 50/ sec 50 - 4sin 40 Cosec 40 = 1 + 1 - 4 = -2 |
|
| 43. |
Plot the following points on a graph sheet. Verify if they lie on a line(a) A(4, 0), B(4, 2), C(4, 6). D(4, 2:5) |
| Answer» | |
| 44. |
The following are the number of books issued in aschool library during a week:105, 216, 322, 167, 273, 405 and 346.dav |
| Answer» | |
| 45. |
19. Without using trigonometric table, evaluate the following:со с 39 + 2 tan 170.tan 33°.tan 60 .tan 52°.tan 73°-3(sir? 31° + sin' 59 )sec 51° /3 |
| Answer» | |
| 46. |
917. Without using trigonometric table evaluate:sin62 2tan73°cos28° cotl7o- 2cos2 45OR |
|
Answer» sinx=cos(90-x)sin62=cos(90-62)=cos28tanx=cot(90-x)tan73=cot(90-73)=cot=17It means1+2-1=2 |
|
| 47. |
. Without using trigonometric tables, evaluatec\frac{\cos ^{2} 20^{\circ}+\cos ^{2} 70^{\circ}}{\sec ^{2} 50^{\circ}-\cot ^{2} 40^{\circ}} \times 2 \sec ^{2} 60^{\circ} |
|
Answer» bhai clear samajh mein nhi a rha hai |
|
| 48. |
Without using tables, evaluate:sin 31 sec 59° + cot 59° cot 31°4 tan 60° sec 30° +8 sina 30° - tan2 45° |
|
Answer» 10 is the right answer |
|
| 49. |
EXERCISE 84metric ratios sin A, sec A and tan A in terms of cot A. |
|
Answer» part 2 |
|
| 50. |
Express hWrite all the other trigono-metric ratios of angle A terms of sec A. |
| Answer» | |