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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.
| 3401. |
6. The volume of a cuboid is 14400 cm3 and its height is 15 cm. The cross-section of the cuboidis a rectangle having its sides in the ratio 5 3. Find the perimeter of the cross-section.n it with gravel 14 cm deep at the |
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Answer» Volume of a Cuboid = length* width*height let length of a cuboid = 5x cm & width= 3x cm,Volume of a cuboid = 14400 cm3,Height=15cm substituting in formula, 14400 = 15*5x*3x 14400=x2 15*15 taking square root on both sides, we get 120/15 =x 8= x so length of a cuboid ( rectangula) =5*8=40cm width of a cuboid (rectangular)=3*8 =24 cm Perimeter of a cross section= 2(l+w) = 2(40+24)=2(64)=128cm |
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| 3402. |
ulmung vertically upward.)A simple pendulum of length 40cm subtends 60 at the vertex in one full oscillation. Whatwill be the shortest distance between the initial position and the final position of the bob?(between the extreme ends) |
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| 3403. |
1ung the factor theorem.JLIU e given expressUse factor theorem to factorise the following polynomials completely :(i) r3 + 2x2 – 5x – 6TT(i) 73 13 10express2016 |
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Answer» You can use factor theorem.f(x) = x^3+2x^2-5x-6f(-1) = -1+2+5-6 = 0So, x+1 is a factor Use synthetic division,x^3+2x^2-5x-6 = (x+1)(x^2+x-6) = (x+1)(x-2)(x+3) = 0 So, the solution is x = -1, 2, -3 |
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| 3404. |
IN OUE5. "C = "C) => a = b or a =n-Theorem 6 "C, +" C -1 = n+IC,n |
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| 3405. |
1(Converse of Theorem 6) The line drawn through the centre of acircle to bisect a chord is perpendicular to the chord. |
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Answer» join the ends of chords with centre and prove it congruent by using sss criteria and by cpct prove that 90 |
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| 3406. |
THEOREM 6 If three or more parallel lines are intersected by two transversals, prove that theintercepts made by them on the transversals are proportional. |
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Answer» Let the three parallel straight lines AB, CD, EF make equal intercepts KL and LM from the transversal IJ, that is KL = LM.The intercepts made by these three parallel lines on the transversal XY are PQ and QR.Construction:Through Q, a straight line is drawn parallel to IJ to intersect AB and EF at U and V respectively. Proof:For quadrilateral KLQU,KU∥LQ [∵, AB∥CD] and KL∥UQ [By construction]∴KLQU is a parallelogram.∴KL = UQSimilarly, from quadrilateral LMVQ, we get LM = QV.But it is given that KL = LM.∴UQ = QV.Now, from△UPQ and△QVR, we get∠PUQ = alternate∠QVR [∵AB∥EF, UV is the transversal]∠PQU = vertically opposite∠VQRUQ = QV [Proved before]∴△UPQ≅△VRQ [By A-A-S condition of congruence]∴PQ = QR [Corresponding sides of two congruent triangles]Thus the theorem is proved for three parallel straight line. Given, KL = LM = MNTo prove, PQ = QR = RS.By drawing a straight line through Q, parallel to IJ, we have proved that PO = QR.Again, a straight line is drawn through R parallel to IJ to intersect CD and GH at Z and W a respectively.As before, if can be proved that QR = RS.∴PQ = QR = RSIn this way, the theorem can be proved for any number of parallel straight lines greater than 3.Remark:From figure 2, we get:KL = LM = MN implies PQ = QR =RS.∴L is the mid point of KM.That is, KM = 2KL.∴KMKL=21or,KMMN=21 [∵KL = MN],∴KM : MN = 2 : 1Similarly from PQ = QR = RS, we get PR : RS = 2: 1So, it can be said: If three parallel straight lines make two intercepts from a transversal in the ratio 2 :1, then those three parallel straight lines will make two intercepts from transversal in the ratio 2 : 1. |
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| 3407. |
In figure, AB = AC and <3-5go, then find the value of LA.If triicnecessary thatIf three sidesnottriangles be congrTheorem 6. Si |
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| 3408. |
1. Mll up the following blanks.(i) If the alternate angles are equal, the two straight lines are(ii) If a transversal line cuts two parallel lines, the corresponding angles are(iii) If one of the angles of a pair of alternate angles is 127°, the other angle is(iv) If one angle of a pair of interior angles is 87.5°, the second angle is(v) If three straight lines intersect at one point, then straight lines are_manto that |
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Answer» parallel ,equal,53°, the answer isparallel,equal,= 180 - 127 = 53 |
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| 3409. |
Two isosceles triangles have equal vertical angles and their areas16: 25. Find the ratio of their corresponding heights. |
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| 3410. |
6.State fundamental Theorem of Arithmetic. |
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Answer» Thefundamental theorem of arithmetic(FTA), also called the unique factorizationtheoremor the unique-prime-factorizationthoerm,statesthat every integer greater than 1 either is prime itself or is the product of a unique combination of prime numbers. |
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| 3411. |
heorem 6.3:corresponding sides are in the same ratio (or proportion) and hence the two6.3 : If in two triangles, corresponding angles are equal, then theirngles are similar |
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| 3412. |
OPORS is a rectangle having length 15 cm andbreadth 10 cm. A semicircle with diameter 7 cm iscut as shown in the figure. What is the perimeter ofthe figure?0 |
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| 3413. |
to construct a triangle similar to triangleABC in which BC=4.5cm,B=45°and C=60°, using scale factor of 3/7,BC will be divided in the ratio(a) 3:4 (b)4:7 (c)3:10 (d)3:7 |
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| 3414. |
Theorem 6.4 : If in two triangles, sides of one triangle are proportional to(te., in the same ratio of) the sides of the other triangle, then their correspondingangles are equal and hence the two triangles are similiar |
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| 3415. |
322. Show that the area of an equilateral triangle isx2 where x is side4of the triangle. |
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Answer» thank you😊☺️ |
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| 3416. |
d) 26.2 feet7. How many solutions are there to thesystem of equations below?-3x +3y 4(a) One solution(b) Two solutions(c) Infinite solutions(d) No solutions |
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Answer» hit like if you find it useful |
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| 3417. |
(m))What is scale factor? |
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Answer» A scale factor is a number which scales, or multiplies, some quantity. In the field of measurements, the scale factor of an instrument is sometimes referred to as sensitivity. The ratio of any two corresponding lengths in two similar geometric figures is also called a scale factor. To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides. If you begin with the smaller figure, your scale factor will be less than one. If you begin with the larger figure, your scale factor will be greater than one. |
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| 3418. |
(C) rdIf the graph of two linear equations in two variables is intersecting lines, then the number of solutions311s(A) Only one(C) Infinite solutions(B) No solution(D) of these |
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Answer» the correct option is (A) .. that is only one solution like if u go the answer ..to let me know my answer was useful..thnks |
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| 3419. |
If two linear equations in two variables have infinite solutions, then their graphs will be |
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Answer» in graph line will have coincident lines the graph will have co-incident lines |
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| 3420. |
If two linear equations in two variables have infinite solutions, then their graphs will bentarsecting lines |
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Answer» their graphs will be parallel in shape they will not intersect each other |
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| 3421. |
1.Forwhatvaluesofa,b the linear equations 2x+3y-7, (a-b)x+ (a-b)y- 3a+b-2 areinfinite solutions? |
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Answer» tq sir |
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| 3422. |
Does the following have one solution, no solution, infinite solutions? How do you know? - 2(4+x)=2x-8 |
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| 3423. |
Q-3For what value of k, will the following system of equations have infinite solutions?2x + 3y = 4;(k+2)x + y = 3k +2Lt |
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| 3424. |
IF the graph of two linear equations in two variables is intersecting lines, then the number of soluticis-(A) Only one(B) No solution(C) Infinite solutions(D) of these |
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| 3425. |
12. For what value of k,the following pair of linear equations has infinite number of solutions |
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| 3426. |
Area of an equilateral triangle measures /3 times as the perimeter of equilateral triangleFind the area of the triangle.7If each side of a triangle is doubled, then find the ratio of area of the new triangle thus |
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| 3427. |
2. A side of an equilateral triangle is 20 cm long. Asecond equilateral triangle is inscribed in it by joiningthe mid-points of the sides of the first triangle. Theprocess is continued as shown in the accompanyingdiagram. Find the perimeter of the sixth inscribedequilateral triangle. |
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| 3428. |
Prove that: 2cOS COSCOScos02cosTS⌠131313 |
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Answer» 2cos pi/13 cos 9pi/13+ cos 3pi/13 +cos 5pi/13 =cos 10 pi/13 +cos 8 pi/13 +cos 3pi/13 +cos 5pi/13 =cos 10 pi/13 +cos 3pi/13 +cos 8pi/13 +cos 5pi/13 =2 cos pi/2 .cos 7 pi/26 +2 cos pi/2 .cos 3 pi /26 =2 (0)cos 7 pi /26 + 2(0) cos 3pi/26 =0 =R.H.S. |
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| 3429. |
UCH Iung6. Construct an equilateral triangle havingot an equilateral triangle having its perimeter 15 cm7. Construct a triangle ABC in which AB-2 ... |
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Answer» Equilateral Triangle: 1. All sides of a triangle are equal. 2. Each angle of a triangle is of 600. STEP: 1. Draw a line AB of 15 cm. 2. At point A draw an angle CAB of600 3. At point Bdraw an angle DBA of600 4. Draw the angle bisector of∠CAB and ∠DBA, both the angle bisector intersect each other at P. 5. Draw the perpendicular bisector of AP and BP, it intesect AB at Q and R respectively. 6. Join PQ and PR. HenceΔPQR is the required triangle. |
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| 3430. |
(sin θ-2cos θ)-12(tan 0- cot 0)713. If sec θ, show that |
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| 3431. |
In an equilateral triangle with side a, prove that-aArea of an equilateral triangle4 |
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| 3432. |
1. ay = (xy- cosx) dx |
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| 3433. |
5sin A - 2cos A(b), If 13 sin A =5 and A is acute then find the value oftan A |
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Answer» sin A = 5/13cos A = (1 - sin^2 A)^1/2 = (1 - 25/169)^1/2 = [(169 - 25)/169]^1/2 = (144/169)^1/2 = 12/13tan A = sin A/cos A = 5/13 / 12/13 = 5/12 Therefore,Value of 5sin A - 2cos A/tan A= (5*5/13 - 2*12/13)/(5/12)= (25/13 - 24/13)/(5/12)= (1/13)/(5/12)= 12/65
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| 3434. |
Construct an equilateral triangle similar to the equilateral triangle of side 4cm with a scale factor 4/3. |
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Answer» Please refer to this similar solution! |
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| 3435. |
the sum of three times a number and 11 is 32 .Find the number |
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Answer» Let the number is nAs per given condition3n + 11 = 323n = 32 - 113n = 21n = 7 Number is 7 |
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| 3436. |
The sum of three times a number and 11 is 32. Find the number |
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Answer» Suppose that number is xthen3x+11= 32( according to the question)3x= 21x= 7Number is 7 Please like this solution 👎👎👎👎 |
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| 3437. |
If 11 is subtracted from 4 times a number, the result is 89. Find the number. |
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Answer» 11*4=44 Then no.. 89-44=45 11×4=44 then substract number 89-44=45. 45 is the best answer. 11×4=4489-44=45is a correct answer 11*4=44then no.. 89-44=45 45 is the correct answer of the given question let the no be x4x-11=894x=89+114x=100x=100/4x=25 133 is the Correct Answer. . . 11×4=4489+44=133After that if we subtract 44 - 133 = 89 |
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| 3438. |
104. The sum of three times a number and 11 is 32. Find the number. |
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Answer» Let the number be x.3x + 11 = 32 3x = 32 - 11 3x = 21 x = 7 let the no. be x3x+11=323x=32-113x=21x=21/3x=7 |
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| 3439. |
2. The ratio of the prices of a bicycle and a motorbike is 8: 75. If the priceof the cycle is 4800, what is the price of the motorbike?(1) 54,000 (2) * 45.000(3) 48,000 (4) * 84,000 |
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Answer» 75*600=45000 answer 2 is correct price of bicycle/price of motorbike = 8/754800/ price of motorbike = 8/75price of motorbike = 4800*75/8 = 600*75 = 45000(2) is the answer. Hope it helped.Mark as best if u like. |
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| 3440. |
If 11 is subtracted from 4 times a number, the result is 89. Find the number |
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| 3441. |
1. If 11 is subtracted from 4 times a number, the result is 89. Find the number. |
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Answer» 4x-11=894x=100x=25The number is 25.is the best answer 4x -11 =89 x = 25 4 x 25 = 100 -11 =89 4x-11=894x=100x=25 answer. |
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| 3442. |
1. Show that the three lines with direction cosines12 -3 4 4 12 3 3 -4 1213' 13' 13' 13' 13'1·ー---一·13' 13' 13 13 are mutually perpendicular.· |
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Answer» Thnq😘 |
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| 3443. |
Show that the three lines with direction cosines12 -3 -4 4 12 3 3 4 1213 13 13' 13 13 13 13 13 13 are mutually perpendicular.1.is nerrnendicular to t |
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Answer» l m + pq +rs =0 we u do this u can get the answer |
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| 3444. |
1. Show that the three lines with direction cosines12 -3 -4 4 12 313 13' 13 13' 13' 13are mutually perpendicular.3 -4 1213' 13and |
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| 3445. |
differentiate with respect to x : if Y =√x+1/√x, prove that 2x dy/dx=√x-1/√x |
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| 3446. |
ĺ 1313 1313 |
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| 3447. |
√13-√11/√13+√11 +√13+√11/√13-√11 |
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| 3448. |
2cos coscoscos13 131313 |
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| 3449. |
9Ď13 13ST2coSCOScoS+ COS01313 |
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Answer» 2cos π/13 cos 9π/13+ cos 3π/13 +cos 5π/13 =cos 10 π/13 +cos 8 π/13 +cos 3π/13 +cos 5π/13 =cos 10 π/13 +cos 3π/13 +cos 8π/13 +cos 5π/13 =2 cos π/2 .cos 7 π/26 +2 cos π/2 .cos 3 π /26 =2 (0)cos 7 π /26 + 2(0) cos 3π/26 =0 =R.H.S. |
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| 3450. |
ĺ ĺ cosCOs+COs+cos13 131313 |
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