InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 3501. |
22. Derive formula for area of equilateral triangle using Heron's formula |
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| 3502. |
e area of an equilateral triangle of side "a" units.22.Using Heron's formula, find th |
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| 3503. |
Now using Heron's formula, you verify this fact by finding the areas of other triangles discussed earlier viz.(i) equilateral triangle with side 10 cm.(i) isosceles triangle with unequal side as 8 cm and each equal side as 5 cm. |
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Answer» The question you have submitted is incomplete but this could be the answer. |
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| 3504. |
15. One side of an equilateral triangle measures 8 cm.Find its area using Heron's formula. What is itsaltitude ? |
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Answer» Equilateral triangle (a=b=c=8)Heron's formula,s=a+b+c/2=8+8+8/2=24/2=12 Area=√(s(s-a)(s-b)(s-c)√(12(12-8)(12-8)(12-8))√(12)4*4*4√(3*4*4*4*4=16√3cm² Also,Area of triangle=(1/2)*base*altitude16√3=(1/2)8*altitudealtitude=4√3cm thanku |
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| 3505. |
l) Perimeter of an equilateral triangle |
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Answer» Perimeter of equilateral traingle is 3× side |
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| 3506. |
6.The hypotenuse of a right angled isosceles triangle is 16root2 mind its area. |
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Answer» 1 solution from ith diagram |
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| 3507. |
What will be the other angles of a right-angled isosceles triangle ?(b) Can you draw an obtuse-angled isosceles triangle ?1. (a |
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Answer» a)The first angle of the triangle is 90 degree as it is right-angled As the triangle is isosceles, the other angles are 45 degree as its two opposite sides are equal. b) |
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| 3508. |
Each acute angle of a right-angled isosceles triangle is(a) 30°5°(d) 60 |
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Answer» in right angled triangle one angle is 90 and other two angle are equal let them be xso x+x+90= 1802x = 90x = 45b) is correct option |
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| 3509. |
LAERCISE 13 (C)What will be the other angles of a right-angled isosceles triangle ?Can you draw an obtuse-angled isosceles triangle ?,(e)b) |
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Answer» a)The first angle of the triangle is 90 degree as it is right-angled As the triangle is isosceles, the other angles are 45 degree as its two opposite sides are equal. b) |
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| 3510. |
The hypotenuse of a right angled isosceles triangle is 16v2 m, find its area. |
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Answer» Since the hypotenuse of the right isosceles triangle is 16√2. the the legs of the triangle (represented byaain the illustration) are16units each.The area of a right isosceles triangle can be obtained from this formula:A=a^2/2Substituting:A=16^2/2⇒256/2⇒128squareunits. |
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| 3511. |
4y xty+l' 2 |
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| 3512. |
Write the equation of "The sum of nine times q and 6 is 24" |
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| 3513. |
A two-digit number is formed by eithersubtracting 17 from nine times the sum of thedigits or by adding 21 to thirteen times thedifference of the digits. Then the number is |
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| 3514. |
3. Write equations for the following statements:(a) The sum of nine times a and 6 is 24.(b) A number b divided by 7 gives 5.(c) If 12 is taken away from five times y, you get 40 |
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Answer» a) 9a+6=24 b) b/7=5 c) 5y-12=40 |
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| 3515. |
03-4 men is nine time as old as his son Attenine years, he will te only Hree timesa) oldw his son. How old is gach note |
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Answer» 27 is the right answer 27 is the right answer |
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| 3516. |
sum of the digits of a two-digit number is 9. Also, nine times this number isnwice the number obtained by reversing the order of the digits Find the numbst |
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| 3517. |
29. An oil funnel made of tin sheet consists of a 10 cmlong cylindrical portion attached to a frustum of acone. If the total height is 22 cm, diameter of thecylindrical portion is 8 cm and the diameter of thetop of the funnel is 18 cm, find the area of the tinsheet required to make the funnel. |
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| 3518. |
. An oil funnel made of tin sheet consists of a10 cm long cylindrical portion attached to afrustum of a cone. Ifthe total height is 22 cm,diameter of the cylindrical portion is 8 cm andthe diameter of the top of the funnel is 18 cnmfind the area of the tin sheet required to makethe funnel (see Fig. 15.25). |
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Answer» Send in detail Thx |
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| 3519. |
21. An oil funnel made of tin sheet consists of a10 cm long cylindrical portion attached to afrustum of a cone. If the total height is 22 cm,diameter of the cylindrical portion is 8 cm andthe diameter of the top of the funnel is 18 cm,find the area of the tin sheet required to makethe funnel |
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| 3520. |
5. An oil funnel made of tin sheet consists of a10 cm long cylindrical portion attached to afrustum of a cone. If the total height is 22 cm,diameter of the cylindrical portion is 8 cm andthe diameter of the top of the funnel is 18 cmfind the area of the tin sheet required to makethe funnel (see Fig. 13.25). |
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| 3521. |
deepAn oil funnel made of tin sheet consists of a10 cm long cylindrical portion attached to afrustum of a cone. If the total height is 22 cm,diameter of the cylindrical portion is 8 cm andthe diameter of the top of the funnel is 18 cm,find the area of the tin sheet required to makethe funnel (see Fig. 13.25).18 cm22 cm10 cm8 cmFig. 13.25 |
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| 3522. |
An oil funnel made of tin sheet consists of a10 cm long cylindrical portion attached to afrustum of a cone. If the total height is 22 cm,diameter of the cylindrical portion is 8 cm andthe diameter of the top of the funnel is 18 cmfind the area of the tin sheet required to makethe funnel (see Fig. 13.25) |
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| 3523. |
)Anoilfunnel made of tin sheet consists of a 10 cmlong cylindrical portion attached to a frustum of acone. If total height is 22 cm, diameter of thecylinderical portion is 8 cm and the diameter oftop of the funnel is 18 cm. Find area of the tinsheet required to make the funnel.6 |
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| 3524. |
d. 46. If xty 18 and x-y 2. Find the value of x and ya 6 4 |
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| 3525. |
12 cm, find its breadtn. wmcl mgt16. A godown is 50 m long, 40 m broad and 10 m high. Find the cost of whitewashing its fouwalls and ceiling at20 per square metre2 Th o hreadth and height of the room are 10mΕΧΑ |
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| 3526. |
4. A policeman fire 6 bullets on a dacoit. The probability that the dacoit will be killed by abullet is 0.6. What is the probability that dacoit is still alive. |
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Answer» prabability is 1-0.6=0.4 |
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| 3527. |
14. A room is 5 m 40 cm long and 4 m 50 cm broad. Its area is(b) 24.3 m2(a) 23.4 m2(c) 25 m2(d) 98.01 m2 |
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| 3528. |
1. Fire the perfect square members between (1) 30 and 40 (1) 50 and 60 |
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Answer» since 1 x 1= 12 x 2 = 43 x 3 = 94 x 4 = 165 x 5= 256 x 6 = 367 x 7 = 49 Therefore 36 is the perfect square between 30 and 40.Since 7 x 7 = 49 and 8 x 8 = 64, therefore there is no perfect square between 50 and 60 square root=30x30=900, 31x31=961; 32x32=1024, 33x33=1089; 34x34=1156; 35x35=1225; 36x36=1296; 37x37=1369; 38x38=1444; 39x39=1521; 40x40=1600 50 to 60; 50x50=2500;51×51=2601, 52x52=2704;, 53x53=2809; 54x54=2916; 55x55=3025; 56x56=3136, 57x57=3249; 58x58=3364, 59x59=3481; 60x60=3600 |
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| 3529. |
Mary wants to frame a picture 40 cm long and 25 cm broad. What length ofstick does she need? |
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Answer» the perimeter of this this frame would be the answer so it is a rectangle then the perimeter of a rectangle is 2(l+b)2(40+25)130 cm |
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| 3530. |
16.50of which is 100 m and the breadllle covered by him.Mary wants to frame a picture 40 cm long and 25 cm broad. Wstick does she need ?hat length of woAca:5 m 20 cm long and 3 m 20 cm broch of tan |
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| 3531. |
olume of a wall, 5 times as high as it is broad and 8 times as long as its high is 12.8 m2breadth of wall is(A) 30 cm(C) 22.5 cm(B) 40 cm(D) 25 cm |
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| 3532. |
What is the volume of a storage tank 15 m 5 cm long, 12 m 50 cm wide and 7m 40 cm high in m? |
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Answer» l x h x h; L=15 m 5 CM =15.05m, b=12 m 50cm=12.50 m, h=7m 40cm/7.40 m;;V=LXBXH=15.05X 12.50 X 7.40=1392.125 m^3 |
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| 3533. |
4 m 50 cm,Find the area of the floor of aHow many24 cn long and 15 cm wideisquare room in square metres WhosE LIbricks will be required to lay a path 120 m long and 2.4 m broad # a brick8.9. |
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| 3534. |
Draw neat labelled diagram of eukaryotic animal cell |
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| 3535. |
(2) To prove the converse of basic proportionality theorem, do the followingactivity(i) Draw neat labelled figure.(ii) Write : Given and To prove. |
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Answer» 2 |
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| 3536. |
(ii) 3x-5y 206x-10y 40 |
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Answer» these equations cannot be solved Multiplaying 1st eqn by 618x-30y=120Multiplaying eqn 2nd by 318x-30y=120Both eqn are same. Therefore Infinite ans can be found.... |
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| 3537. |
Q8. Determine the value of c for which the following system of linear equations has no solution.Cx+3y 312x-су-6 |
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| 3538. |
ii)3x-5y = 206x-10y = 40 |
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Answer» 3x - 5y = 20 and 6x - 10y =40 x = 20 + 5y /3 .............1 6x - 10y = 40 now put .........1 in 6x - 10y = 40 6(20+5y/3) - 10y =40 2(20+5y) - 10y = 40 40+10y - 10y =40 40 = 40 0 infinite many solutions |
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| 3539. |
Draw the graph of each of the following linear equations.i)2y-x+1 i)-xty 6 ii) 3x +5y-15 i)3 |
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| 3540. |
2) The weight of a man is four times the weight of a child. Write an equation intwo variables for this situation. |
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Answer» Let weight of child be x and weight of man be y So, according to question y = 4x |
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| 3541. |
Solve the following questions. (Any one)If your age is 13 years and your friend is 15 years old, then write a word puzzle to formtwo linear equations. Frame two linear equations and verify your equations with yourgiven age by solving equations.nt and the numher of students a |
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Answer» Sum of ages is 28 and difference is 2. Find the ages of the two persons. x+y = 28y-x = 2=> x=13 years old. |
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| 3542. |
(2) Prove that corresponding medians of two similar triangles are proportional to thecorresponding sides of the triangle. |
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Answer» Triangles. If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. ... Lastly, if two triangles are known to be similar then the measures of the corresponding angle bisectors or the corresponding medians are proportional to the measures of the corresponding sides |
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| 3543. |
zn. Solve the following system of linear equations graphicallyan. Solve the following system of linear equations graphically4z - 5y 20 0 3x+5y 15-0Determine the vertices of the triangle formed by the lines, representing the[CBSE 2004]above equations and the y-axis. |
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| 3544. |
apho a linear equationsDraw the graphs of the equationsx 2 and y 3.Ex. |
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Answer» red line is x = 2blue line is y = -3 |
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| 3545. |
7. The pair of linear equations 2x + 3y + 4 = 0and 4x + 3y + 2 = 0 hasI 11) Unique solutions2) Infinitely many solutionsNo solution 4) Solutions8. Linear equations is two variable amongthe following isI 1 |
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Answer» (4) Solution hai mere dost unique solution is the awnser |
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| 3546. |
EXERCISE 3.61. Solve the following pairs of equations by reducing them to a pair of linear equations11133x2y 6of |
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Answer» 3y+2x=12xy........(1)2y+3x=13xy........(2)multiply (1)by 2and (2) by 36y+4x=24xy6y+9x=39xy5x=15xy1/3=yput y=1/3 in (1)2+4x=8x2=4x1/2=x |
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| 3547. |
VPILUUICILEThe given graph represents a pair of linear equations in two variablesWrite how many solutions these pair of equations have.AO, |
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Answer» unique solution intersection lines consistent this is an unique solution because lines are intersection consistant |
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| 3548. |
do.If (a + b)(b + c): (c + a) :: 6:7:8& a + b + c = 14 then find c-?(b) 6(c) 8(d) 7 |
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Answer» 7 is your answer because 6 is aand b is your 8 so c is your 7 a+b+c=14. c=7ddddddddddd answer 6. hoga this question's answer is seven this question answer is seven. seven is a right answer answer 7 hoga....,. .... 7 is the correct answer c is the correct answer......... d is the correct answer..... a+b+c=14 c=7ddddddddddd A+B+C=14 c=7DDDDDDDDD 8 it is a write answer 7 answer correct gai the answer of this question is 7 7 is correct it is right 8 is the exact answer for this question answer is 8 using equality formula correct answer is 7 option dddddddddddddd 7 it is a write answer The right answer is7 correct answer is 8 (c) 9 it is a write answer 7sghffhchyhgcvxcgdg ccvhffh compression between same sidethen a+b=6put this value in a+b+C=14 6+C=14 C==14-6 C=8option c Q.no. 10Ans. (b) 6 6 I don't know but sorry 7 is the correct answer 7 is the right answer Answer 7 hoga bhai sab 7DDDDDDddddddddddddddddd 4 &&&& this question, answer is sevan7 7 is the correct answer of the given question (a+b)=6(b+c)=7(c+a)=8(a+b+c)=14(a+b)+c=146+c=14c=14-6c=8 option no c hoga a b c d me (d) is the right answer ddddddddddddddddddd=7 a+b =6 and a+b+c =14 14-6 =8 thus (c) 8 your answer is C=7 this the answer is = seven the question answer is seven options number C is the correct answer please like my answer d. 7. c=4 it is a write answer a+b+c=14C=?a+b=66+c=14C=14- 6 =8 I guess... ans is 7🤔🤔🤔🤔🤔 4is right answer the question ......................8 (d) 7 is the correct answer option (d) 7 is right answer. The right answer is 7 how worst are all of you the answer is 6 a+b+c= 14 than c = 8 a+b+c=14 and a+b=6so, (a+b)+c=14 6+c=14 c=8 (ans) your answer is 7........ This is tha answar D Let (a+b) = 6x.......(I)(b+c) = 7x.......(ll)(c+a) = 8x.......(lll) (l)+(ll)+(lll) 2(a+b+c) = 21x=>2×14=21x we get=> x = 4/3 Applying x value in above Equationwe get a = 14/3, b = 10/3 and c = 18/3. for the given question answer of c=7 right answer for this question (d) 7 is the right answer 77777777777777777777777777 |
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| 3549. |
f linear equations2x 31 |
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| 3550. |
Prove that in a right angled triangle square of the hypotenuse is equal to sum of the squaresof other two sides.25.4 |
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Answer» Given: A right angled ∆ABC, right angled at B To Prove- AC²=AB²+BC² Construction: draw perpendicular BD onto the side AC . Proof: We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other. We have △ADB∼△ABC. (by AA similarity) Therefore, AD/ AB=AB/AC (In similar Triangles corresponding sides are proportional) AB²=AD×AC……..(1) Also, △BDC∼△ABC Therefore, CD/BC=BC/AC (in similar Triangles corresponding sides are proportional) Or, BC²=CD×AC……..(2) Adding the equations (1) and (2) we get, AB²+BC²=AD×AC+CD×AC AB²+BC²=AC(AD+CD) ( From the figure AD + CD = AC) AB²+BC²=AC . AC Therefore, AC²=AB²+BC² This theroem is known as Pythagoras theroem. |
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