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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.
| 21451. |
If cos(a+b)=0, show that sin (a-b)=cos 2b |
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Answer» Cos(a+b)=0Cosa+cosb=0 Cosa= -cosbWe take rhsSin(a-b)Sina-sinbCos(90-a) -cos(90-b)Cos90-cosa -cos90+cosb-cosa+cosb-(-cosb) + cosbCosb+ cosbCos(b+b)Cos2b prooved Cos(a+b)= 0 (a+b)= 90a=(90-b)Sin(a-b)= sin ( 90-2b)Since, sin (A-B)= sinA* cosB - cosA* sinBSin(90-2b)= sin90*cos2b - cos90 -sin2b1*cos2b -0*sin2bHence answer is cos2b...... Thank you?? |
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| 21452. |
Y= -1cube -4 multiply1 |
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| 21453. |
Find The HCF Of K, 2k,3k,and 5k, where k is a positive integer |
| Answer» The HCF of k,2k,3k,4k and 5k will be k as the following no.s are consecutive and only k is a common factor as all numbers are multiplied by it. | |
| 21454. |
How can prove? two similar triangles have also congruent triangle |
| Answer» By SSS(Side side side) or AAA(Angle angle angle) criteria | |
| 21455. |
What are included in chapter Real numbers |
| Answer» Mtlb creal numbers chapter me kya he (formula, sign\'s, etc) | |
| 21456. |
99×. |
| Answer» 0 | |
| 21457. |
Solve for x: 1/2a+b+2a=1/2a+1/b+1/2x. |
| Answer» 1/2a+b+x=1/2a +1/b +1/x correct question, ye hai, ye mere e am me aya tha......, and answer hai x=-2a, -b........ | |
| 21458. |
Solve the equation 1/x+1+2/x+2+4/x+4,x is not equal -1,-2,-4? |
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Answer» Solve equation by simply by taking lcm then find only value of x You can solve complete question Thanks Please help Don\'t know |
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| 21459. |
Prove that sum of squares of diagonals of parallelogram are equal to sum of squares of its sides |
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Answer» Here ,a short ans for this question we have to prove that ab2+bc2+cd2+da2=ac2+bd2 since In parallelogram ABCD, AB = CD, BC = ADDraw perpendiculars from C and D on AB as shown.In right angled ΔAEC, AC2\xa0= AE2\xa0+ CE2\xa0[By Pythagoras theorem]⇒ AC2\xa0= (AB + BE)2\xa0+ CE2⇒ AC2\xa0= AB2\xa0+ BE2\xa0+ 2 AB × BE + CE2 → (1)From the figure CD = EF (Since CDFE is a rectangle)But CD= AB⇒ AB = CD = EFAlso CE = DF (Distance between two parallel lines)ΔAFD ≅ ΔBEC (RHS congruence rule)⇒ AF = BEConsider right angled ΔDFBBD2\xa0= BF2\xa0+ DF2\xa0[By Pythagoras theorem] = (EF – BE)2\xa0+ CE2 [Since DF = CE] = (AB – BE)2\xa0+ CE2 [Since EF = AB]\xa0⇒ BD2\xa0= AB2\xa0+ BE2\xa0– 2 AB × BE + CE2 → (2)Add (1) and (2), we getAC2\xa0+ BD2\xa0= (AB2\xa0+ BE2\xa0+ 2 AB × BE + CE2) + (AB2\xa0+ BE2\xa0– 2 AB × BE + CE2) = 2AB2\xa0+ 2BE2\xa0+ 2CE2 AC2\xa0+ BD2\xa0= 2AB2\xa0+ 2(BE2\xa0+ CE2) → (3)From right angled ΔBEC, BC2\xa0= BE2\xa0+ CE2\xa0[By Pythagoras theorem]Hence equation (3) becomes, AC2\xa0+ BD2\xa0= 2AB2\xa0+ 2BC2 = AB2\xa0+ AB2\xa0+ BC2\xa0+ BC2 = AB2\xa0+ CD2\xa0+ BC2\xa0+ AD2∴ AC2\xa0+ BD2\xa0= AB2\xa0+ BC2\xa0+ CD2\xa0+ AD2Thus the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.Thank you? |
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| 21460. |
If one root of the quadiatic equation 6xsquare -x-k=0 is 2/3 , this find the value of k |
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Answer» 8/3-2/3=2 hota hain bhai Sorry the answer is 2 K= 2 6×2/3×2/3-2/3-k=0. 8/3-2/3-k=0. 7/3-k=0. K=7/3 2 |
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| 21461. |
determine the ratio in which the line 3 X + Y =9 line segment joining the point (1,3)and (2,7). |
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Answer» Let the ratio be k:1Applying section formula,x = (2k+1/k+1) , and ,y = (7k+3/k+1)Therefore , 3x + y = 93(2k+1/k+1) + (7k+3/k+1) = 9(6k+3/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 913k+6/k+1 = 913k+6 = 9k+94k = 3k = 3/4Therefore, the required ratio = 3:4 Let it divides it in the ratio m:n and coordinates of intersection is x,y Now find x and y in terms of m and n by the help of section form. and then put the val. on the line seg. you will get the ratio.????????????????????? Sol. It 3:4 |
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| 21462. |
{(Msin+nsin)÷(msin-nsin)}+{(msin+nsin)÷(msin-nsin)}={2(m^4+n^4)}÷(m^4-n^4) |
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| 21463. |
What is the common difference of |
| Answer» The common difference is the difference between two numbers in an arithmetic sequence. Thank you?? | |
| 21464. |
Sir median nikalte samay cf kaise pata karege |
| Answer» Addition of all frequency | |
| 21465. |
Factorise ~ x^2 - 2√5x + 3 |
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Answer» Its possible as it was given in the book Not possible |
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| 21466. |
Plz tell me imp. Ques of chapter 13of maths |
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Answer» Example dekh lena us me se bhut se imp. Question he In which we have to find the the volume,area,t.s.a.,c.s.a. of combination of shapes |
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| 21467. |
Mean formula? |
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Answer» Mean = a + (sigma fdi\'/sigma f) x h Sigma fixi/sigma fi |
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| 21468. |
Tommorow I\'m having mathematics pre board exam so please help me to study |
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Answer» Radius is always perpendicular to tangent at the point of contact Can you explain theorem 1in circles lesson And, if yu have any doubt yu can ask here.....? Its, maths, just go through all the formulas, and practice the problems which are hard fr yu........? |
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| 21469. |
The circumference of a circle exceed its diameter by 180cm .what is radius of its |
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Answer» 42cm Given that, Circumfrence=diameter+180 2πr=2r+180 2(πr)=2(r+90) πr=r+90 πr-r =90 r(π-1)=90 r(22/7-1)=90 r(22-7/7)=90 r(15/7)=90 r=90×7/15 r=630/15 r=42 17.14 |
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| 21470. |
The perimeter of a right triangle is 60cm.its hypotenus is 25cm. Fund area of triangle. |
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Answer» Peeimeter = 60 cmHyp.= 25 cmThe remaning side must be 60- 25 = 35 cmLet one side be x The third side be 35 - xBy pythagoras therom Hyp.ka 2 = base ka 2 +. Perpendicular ka 2 25 ka 2 = x ka 2 +. 35 - x ka 2 625 = x^ 2 + x ka 2 - 70x + 12252x ka 2 - 70x + 60 = 02x (x - 20) - 30 ( x- 20) = 0(x- 20) (2x - 30) = 0x- 20 = 0x = 202x - 30 = 0 2x = 30x = 15So one of side is 20 cm and 15 cmIf one side is 20 Then other side 35 - 20 = 15 cmIf it is measured is 15 Then othet side 35 - 15 = 20 Therefore Ar. Of ∆1/2 × height × base1/ 2 × 20 × 15150 cm ka 2 Here is your answer Aur vo power he Ka 2. Wala Height =15 .......base =20So, area will be 150 square cm |
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| 21471. |
Given that √2 is irrational,prove that (5+3√2) is an irrational no. |
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Answer» Let 5 + 3 √2 be a rational number= 5+3√2 = a= 3√2 = a-5= √2 = a-5/3Now, here a-5 / 3 is a rational number.Therefore root 2 is also a rational number.But also we know that root 2 is an irrational number.So our assumption was wrong,Therefore 5 + 3 root 2 is an irrational numberHence proved✓ Bro in dono question ko sath me prove karna he ya alag alaf |
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| 21472. |
How to solve 1.1 |
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Answer» Which question ? Exercise 1.1 is so easy... Yu can take help of this app,it also contains ncert solutions.............? |
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| 21473. |
In a parallelogram one angle is 4/5 of adjacent angle.determine the angles of parallelogram |
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Answer» et the first angle be x and the second angle be y.Then x = 4y/55x = 4y\xa05x - 4y = 0 ......(1)Also x + y = 180° .......(2)Multiply eq (2) by 5Then 5x + 5y = 900° ......(3)(3) - (1) we get9y = 900°y = 100°Put this value in eq (2)x + 100° = 180°x = 180° - 100°x = 80°Therefore, the angles are 80°, 100°, 80°, 100° because in a parallelogram opposite angles are equal. Solution:Let one angle be\xa0Other angle =\xa0But sum of adjacent angles in a parallelogram is\xa0\xa0\xa0\xa0\xa0\xa0\xa0Hence the angles of the parallelogram are |
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| 21474. |
Prove the no is irrational no √2 |
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Answer» Let us take √2 is rational We can take x and y √2 = x/y Suppose x and s have a common factor other than 1. Then you have to divide by the common factor √2 = a/ b, where a and b are coprime.So b √2 = aOn sq. Both side 2b ka 2 = a ka 22 divide a ka 2.So we take another integer c.a = 2cWe get 2b ka 2 = 4c ka 2 b ka 2 = 2c ka 2That means 2 divide b ka 2 and so 2 divides b. Therefore a and b have at least 2 as a common factor.This contradiction has arisen because of our incorrect assumption that √ 2 is rational.So, we conclude that √2 is irrational. See in NCERT |
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| 21475. |
Note on Function and Polynomials |
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| 21476. |
2/√x+3/√y=2, 4/√x-9/√y=1 |
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| 21477. |
Check whether X + 2 whole cube equal x cube + 5 is a quadratic equation |
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| 21478. |
One zero of the polynomial 3x3+ 16x2+15x-18is2/3 find the other zero of polynomial |
| Answer» 2/3 is a zero of polynomialThen,x=2/3 . 3x=2 . 3x-2=0 is a factor Divide the polynomial by 3x-2Factorise the remainder and find the zeroes | |
| 21479. |
how to i learn maths ?? |
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Answer» You can\'t learn maths or anyone cannot learn maths it is not possible....... You have to do practice and hard practice for it.... ☺️☺️ We cannot learn math it only wants practise and practise Maths is not be learn by anyone because it want practise and only practise |
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| 21480. |
Ncert exemplar solutions |
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| 21481. |
If p(e)=5×10-2 then find p(e bar) |
| Answer» Given ,p(e)=5×10-2 = 5/100therefore,P(E)=0.05\xa0P(E) + P(Not E) = 1⇒ 0.05 + P(Not E) = 1∴ P(Not E) = 1 – 0.05 = 0.95 | |
| 21482. |
If tanA+sinA=m and tanA - sinA =n, show that m^2−n^2= 4√mn |
| Answer» Lhs(tan A+sin A )(tan A-sin A) _(tanA+sin A)(tan A-sin A)=(2tan A)(2sin A)=4tan A sin ARhs 4√(tanA+sin A)(tanA-sinA)4√tan Square A-sin square A4√tan square A_sin square A4√sin square A/cos square A_sin square A4√sin square A (1/cos square A-1)4√sin square A (sec square A-1)4√sin square A tan square A4 sin A tan AHence proved | |
| 21483. |
If P(e)=5×10-2 then find P(e) |
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Answer» 48 48.....?? |
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| 21484. |
Which term of the AP 3,15,27,39.....will be 120 more than its 21st term |
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Answer» a=3d=15-3 =12A21 = a+20d =3+20×12 =3+240 =243An=243+120 =363An=a+(n-1)d363=3+(n-1)12363-3=12n-12360+12=12n372=12n372/12=n31=n Ans=31 31 st term |
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| 21485. |
Formula ofmode |
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Answer» Right formula L +. (f1 - f0 /. 2f1 - f2 - f0 ). *. H |
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| 21486. |
X square +(a/a+b+a+b/a)x+1=0 |
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| 21487. |
Let find hcf of 134791,6341,6339by euclid divisions |
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Answer» Putting on formula a= b.q+r This type of question have some trick to solve. |
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| 21488. |
Sec theta + tan theta = 3 then fund cosec tgeta |
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Answer» Tan theta =3-sec thetaTan=sin/cosSin/cos=3-sec thetaSin=(3-sec theta)cos theta After solving ,Sin=3cos theta - sec theta cos theta Sin=3cos theta -1/cos theta×cos thetaSin=3cos theta - 1 Cosec theta = 1/sin theta Cosec theta =1/3cos theta-1 Question is Sec theta +tan theta =3,then find cosec theta . |
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| 21489. |
the probability of occurrence of event a is denoted by p(a). so, the range of p(a) is |
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Answer» Between 0 and 1 Between 0 and 1 |
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| 21490. |
If x=2/3 and x=-3 are the roots of quadratic equation ax^2+bx+c find the values of a and b |
| Answer» Use the D=b²-4ac | |
| 21491. |
Please prove that ,sinA ÷ 1-cosA + tanA ÷ 1+cosA = secA×cosecA + cotA |
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| 21492. |
Find the length of the shadow of a 20m tall pole , on the ground when the sun elevation is 45° |
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Answer» Length of the shadow is 20 m ... Use sin 45° in it I am not getting what you are saying Can solve in detail Use tan 45°=1 and solve |
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| 21493. |
Cos0 - sin0 + 1 ÷ cos0 + sin0 - 1 = Cosec0 +cot0 |
| Answer» Cos 0 se divide kar | |
| 21494. |
Tan A+B=√3 tan A-B#1/√3 find A and B |
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Answer» Thank you so much ? TanA+B=√3TanA+B=tan 60 eq...1A+B=60.....1TanA-B=1/√3TanA-B=tan 30eq....2A-B=30.....2From eq...1A+B=60...1A-B=30....22A=90A=90/2A=45Putting...1A+B=6045+B=60B=15 |
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| 21495. |
Can\'t we plot the frequency on y axis in o give representation??? |
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Answer» Sorry but my question is can\'t we plot CF on x axis Always CF is plotted on y axis not frequency |
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| 21496. |
Cosec +cot =sec |
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| 21497. |
Prove that the tangents at the extremities of any chord make equal angle with the chord |
| Answer» \xa0Let AB be a chord of a circle with centre O, and let AP and BP be the tangents at A and B respectively. Let the two tangents AP and BP meets at P.\xa0Now Join OP. Suppose OP meets AB at C and the chord AB=AC+BC.We have to prove that\xa0{tex}\\angle P A C = \\angle P B C{/tex}In two triangles PCA and PCB, we havePA = PB\xa0[{tex} \\because{/tex}Tangents from an external point are equal]{tex}\\angle A P C = \\angle B P C{/tex}\xa0[{tex} \\because {/tex}\xa0PA and\xa0PB are equally inclined to OP]and, PC = PC [Common]So, by SAS-criterion of congruence, we obtain{tex}\\Delta P A C \\cong \\Delta P B C{/tex}{tex}\\Rightarrow \\quad \\angle P A C = \\angle P B C{/tex} | |
| 21498. |
Express sin60° geometrically |
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| 21499. |
Area of the minor segment when length of arc and radius of the circle is given????? |
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| 21500. |
Composite number what |
| Answer» Numbers which have more than 2 factors are known as composite number | |