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| 67551. |
2T,Q.14 Prove thatcos 2 x + cos 2 (x+ä¸)+cos 2 (x-ä¸) = 3 |
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Answer» i) By double angle identity, cos²θ = {1 + cos(2θ)}/2 Using this, cos²x = {1 + cos(2x)}/2cos²(x + π/3) = {1 + cos(2x + 2π/3)}/2 and cos²(x - π/3) = {1 + cos(2x - 2π/3)}/2 ii) Hence, left side of the given one is: = {1 + cos(2x)}/2 + {1 + cos(2x + 2π/3)}/2 + {1 + cos(2x - 2π/3)}/2 = (3/2) + (1/2)[cos(2x) + cos(2x + 2π/3) + cos(2x - 2π/3)] = (3/2) + (1/2)[cos(2x) + 2cos(2x)*cos(2π/3)][Since cos(A+B) + cos(A-B) = 2cosA*cosB] = (3/2) + (1/2)[cos(2x) - cos(2x)] [Since cos(2π/3) = -1/2] = 3/2 = Right side |
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| 67552. |
If cos α + cos β-sin α + sin β, then prove that cos 2a + cos 2β--2 cos (α +β).0NCERT EXEM |
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| 67553. |
lfsin A = 2 and cos B-9 , where 0 < A < 프, 0 < B < find the values of( sin (A+B) (i) sin (A-B) (ii) cos (A+ B) (v) cos (A-B).54172cus (A +EB |
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Answer» Sin(A+B) = SinAcosB + CosAsinB |
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| 67554. |
7. The ages in years of 10 teachers of a schoolare: 32, 41, 28, 54, 35, 26, 23, 33, 38 and 40.What is the range of the ages of the teachers? |
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Answer» age in the increasing order:23,26,28,32,33,35,38,40,41,54 range: 23-54 |
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| 67555. |
in figure , a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are the lengths 4 cm &3 cm. if areas of ∆ABC=21 cm²,then find the lengths of sides AB and AC. |
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| 67556. |
CUScos 45osec 30° cosec 30° |
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Answer» hit like if you find it useful |
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| 67557. |
Prove ihat 2 Cos A cus A |
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| 67558. |
2. Write the number names of the given numbers.a. 56C. 98b. 67d. 20 |
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Answer» a. Fifty sixb. Sixty sevenc. Ninty eightd. Twenty |
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| 67559. |
A cirele macentre of the circle iskes intercepts of lengths a and b on x-axis aad y -axis respectively. Then the locus of theA)4a + b4 |
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Answer» Thx Alot for tellingI just want to know how that eqn came--X^2 - y^2=....... |
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| 67560. |
newton raphson method |
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Answer» Newton-Raphson Method:If you've ever tried to find a root of a complicated function algebraically, you may have had some difficulty. Using some basic concepts of calculus, we have ways of numerically evaluating roots of complicated functions. Commonly, we use the Newton-Raphson method. This iterative process follows a set guideline to approximate one root, considering the function, its derivative, and an initial x-value.You may remember from algebra that a root of a function is a zero of the function. This means that at the "root" the function equals zero. We can find these roots of a simple function such as: f(x) = x2-4 simply by setting the function to zero, and solving: f(x) = x2-4 = 0(x+2)(x-2) = 0x = 2 or x = -2 The Newton-Raphson method uses an iterative process to approach one root of a function. The specific root that the process locates depends on the initial, arbitrarily chosen x-value. |
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| 67561. |
18. P, Q & Rare respectively, the mid points of sides BC, CA & AB of a triangle ABC. PR & BQmeet at XăCR & PQ meet at Y. Prove that XY--BCéŁ |
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Answer» Given ABC is a Triangle. P is the m.p of BC Q is the m.p of CA R is the m.p of AB To prove XY = BC Proof In ΔABC R is the midpoint of AB. Q is the midpoint of AC. ∴ By Midpoint Theorem, RQ║BC RQ║BP → 1 [Parts of Parallel lines] RQ = BC → 2 Since P is the midpoint of BC, RQ = BP → 3 From 1 and 3, BPQR is a Parallelogram.BQ and PR intersect at X Similarly, PCQR is a Parallelogram.PQ and CR intersect at Y. X and Y are Midpoints of sides PR and PQ respectively. In ΔPQR X is the midpoint of PR Y is the midpoint of PQ ∴ By Midpoint Theorem, XY = RQ From 3, XY = + BC XY = 1/4BC |
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| 67562. |
5.D, E and F are respectively the mid-points of the sides BC, CA and AB of a Δ ABC.Show that(i) BDEF is a parallelogram.ii)ar (BDEF) = ar (ABC)Ufar (DEF) =ar (ABC)2 |
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| 67563. |
In AABC, P, Q and R are the mid pointsof sides BC, CA and AB respectively.If AC 21 cm, BC 29 cm and) cm, find the perimeter of thequadrilateral ARP |
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| 67564. |
The angle of elevation of the top of a light house, as seen by a person onthe ground such that tan =5/12When the person moves a distance of 240 m towards the lighthouse, the angle of elevation becomes phi such that tan phi=3/4-Find the height of the lighthouse. |
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Answer» AB =height of the lighthouse AB/BD = 5/12 = h/240+ x 5(240+x) = 12h 1200+ 5x = 12 h (1) AB/BC = h/x 3x = 4h 3x/4 =h 1200+ 5x = 1(3x/4) 1200+5x = 9x 1200 = 4x 1200/4 = x 300 = x h = 3(300)/4 = 900/4 = 225mHence height is 225m |
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| 67565. |
17. In a AABC, if lines are drawnthrough A, B, Cparallel respectively tothe sides BC, CAand AB, forming ΔPQRas shown in the figure,10show that BC =-QR.2 |
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| 67566. |
6;7_Lfi frha ली (८... ८८0८4... two fangenls drawn(|||£ e entir nok ook तप(410. थ ह 0५09-44 o tndYe“flu ,/Uy\?/a\”o oooo. fun P nel |
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| 67567. |
ar (AABC)Question S. D, E and F are respectively the mid-points of the sidesBC, CA and AB of a 4ABC. Show that(i) BDEF is a parallelogram(ü) ar (DEF) ar (ABC)(iii) ar (BDEh-I-ar (ABC)) = 3 ar (ABC) |
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| 67568. |
Write the numbers names of:(a) 2136-(b) 4025-(c) 6220-(d) 7642-(e) 8427- |
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| 67569. |
Fig. 9.31Fig. 9.325. In Fig 9.33, ABC and BDE are two equilateraltriangles such that D is the mid-point of BC. IfAEintersects BC at F, show that0) ar (BDE) ar (ABC)4(i) ar (BDE) ar (BAE)(ii) ar (ABC)-2 ar (BEC)(iv) ar (BFE)-ar (AFD)F D |
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| 67570. |
D. E and F are respectively the mid-points of the sides BC, CA and AB of a A ABCShow that(o) BDEFis a parallelogram.(ii)ar (BDEFD-2 ar (ABC)(ii) ar (DEF)ar (ABC)4 |
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| 67571. |
b) A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policemanHe goes 60 m in first minute and increases his speed by Sm/minute every succeeding131minute. After how many minutes, the policeman will catch the thief ? |
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Answer» Thief has a lead of 50*2 = 100m Relative distance covered by cop in 1st min = 60-50 = 10 Relative distance covered by cop in 2nd min= 65-50 = 15 Relative distance covered by cop in 3rd min = 70 -50 = 20 10, 15, 20 ... is an AP whose sum is 100a= 10 , d = 5 Sum = 100 100 = n/2(2a + (n-1)d) = n/2(20 +(n-1)5)100= n/2(20 + 5n -5)200 = n(15 + 5n)divide by 540 = n(n + 3)n^2 + 8n - 5n - 40 =0n(n+8) - 5(n+8)= 0 >> n = 5 as it cant be negative Therefore cop catches after 5 min + 2min (when cop was at rest) = 7min |
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| 67572. |
Which of the folllowing is not an effect of gravita) Falling of an object released from a heightb) Revolutions of planetsc) Solar eclipsed) High tide and low tide |
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Answer» a) falling of an object when released from height h is effect of gravitational pull by earth. b) revolution of planets is also due to gravitational force acting as centripetal force for circular motion of planet. c) clearly their is no involvement of gravity in solar eclipse so other is the right answer. d) high tide and low tide is due to gravitational pull by moon on ocean water. |
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| 67573. |
2. Find the aled UDT(a) Length= 8 cmBreadth =3cm |
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Answer» Area of the rectangle=8×3 cm²=24 cm² |
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| 67574. |
A person observes the angle of elevation of the peak of a hill from a station to bec metres along a slope inclined at the angle β and finds the angle of elevation of the peak ofthe hill to be . Show that the height of the peak above the ground is c sin a sin (y-p)30.(sin γ-a) |
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| 67575. |
1. , IF → 8 and- is an unil seem and I 리。능belweenavel 군and |
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| 67576. |
5. I have a two digit number. The first digit is the secondmultiple of 4. When the two digits are added, the sum isthe third multiple of 4. What is my number? |
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Answer» Let the no be 10y+xy=4x......110y+x+10x+y=11011x+11y=110x+y=10.......2From 1 and 2x=2 and y=8Therefore the no is 10(8)+2=82 |
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| 67577. |
NCERT EXEMPLAR, CBSE 2015]A thief, after committing a theft runs at a uniform speed of 50 m/minute. After 2 minutesn runs to catch him. He goes 60 m in first minute and increases his speed by5 m/minute every suceeding minute. After how many minutes, the policeman will catchICBSE 2016]the thief? |
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| 67578. |
38,1.31813,18...an = at(nodसहा121 |
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| 67579. |
ercise90.00 each. How muchnod bought 8 DVDs at the rate ofdid he pay?ch |
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Answer» if each DVD costs 90 RS.then 10 DVD will cost 90 * 10 = 900 RS. |
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| 67580. |
(3) Find out two hidden words of miniinum four letters eachfrom the word 'challenge'. |
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| 67581. |
2866. The demand function of a commodity is x = 40-p),Indineelasticity of demand when p = 4Ans.. |
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| 67582. |
14. Prove that an isosceles trapezium is always cyclicICBSE 2016)and its diagonal are equal. |
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| 67583. |
(118) Vidyalankar : Std. XI - Mathematics1+7i(ix) (2-01+3i(viii)(vi) 1 +i(хі)읊을2-i 1+i'tx) 2-1.2+11-3i(x)a, b3.Express the following in the form a + ib, where a, b e R. State the values of2 +iK4+3)6.2/)((23)(2 3)4(v) (1 + i) (1 i)" (vi) 3.2i宗름 (vii) 3(vil)(2 + 3i) (2-3) (ix) 긍 름景卡(x) (1+2) (1+3) (2 + )-,1 2 3 5(x0) i(4-3)3-2(xv)3+64(xviii)(1 +3], (3-1)5+7 5+7(xv)4-31 +4-a(xvi)(2 3) (1-4i)03(xvi)(2pp(xix) 4 -1-i4.Find the value of(ii)(1-i+がs(iii) (i13" +m)5. Show that, (3i)P is a real numberand bi, then show that, ab and ba7.thon prove tht081800 |
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Answer» Please specify the question! 55%4523%58℅0868*6787868 |
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| 67584. |
ExAMPLE The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is88 m2. Find the dimensions. |
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| 67585. |
Q2. Let A | 05 α| if IA21-25, find loc!α |
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Answer» take alpha as adet ( A)= product of eigen vectorAs it is a triangular matrix eigen values are5, 5a, 5 so eigen value of A² are 25, 25a², 25so det(A²) = 25×25a²×25 = 25 so a² = 1/(25)²a = + or - 1/25so |a| = 1/25 Bhai in this question we have to find |¢| |
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| 67586. |
AOB = 64°, find LOC.he diagonals of rectangle ABCD intersect at O. If64° |
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| 67587. |
VERRE ASUU ULO LOCOTULUI58. Find three different irrational numbers between the rational numbersand11 |
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| 67588. |
ABC is a triangle in which DE I1 BC such thatar(ADEF: ar(ADEC), where F is the point of intersection of DC and BEAD-3 Prove that ΔDEF-CBF and also find the ratioDB 25 |
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Answer» and also find ar(triangle def) : ar( triangle dec) |
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| 67589. |
Std: IXMATHEMATICS1. ABCD and PORC are rectangles. Q is the midpoint of AC. Show that P is the midpointof DC and R is the midpoint of BC. Also find the ratio of ar (ABCD) and ar (PQRC) |
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Answer» By mid pt. theromPB=1/2AD and PB is parallel to ADtherefore in triangle DACby converse of mpt DA is parallel to PB and B is half of ACtherefore P is the mid pt. of DCsimilarly in triangle CABby converse of mpt R is the mid pt. of BCRatio=1:4 since P is mpt of DC and PB is half of AD |
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| 67590. |
Mohan is 18" from either andfrom either end of a row of boys. How many boys are there in that row? |
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Answer» please please please like me and I will like you 35 is the correct answer 35 is correct answer 35 answer is the correct 35 is the correct answer 35 is the correct answer 35 is the answer of the following 35 is the correct answer 35 is the correct answer 35 is correct answer 35 is correct answer |
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| 67591. |
If two coins are tossed once, find the probability of getting:(a) One head(b) One tail(c) No head(d) No tail |
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Answer» when two coins are tossed the sample space is = {HH,HT,TH,TT} So, probability of i) getting 1 head is = 2/4 = 1/2ii) getting 1 tail is = 2/4 = 1/2iii) getting no head is = 1/4iv) getting no tail is = 1/4. |
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| 67592. |
EXAMPLE 3.17Differentiate r by first principles. |
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Answer» Differentiation of x³ is 3x². |
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| 67593. |
24. If the roots of the quadratic equation plq-rh+-px+ p-q)0 are equal, show that |
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| 67594. |
y =(n-1) log(n-1) - (RH) log Cart 1) prove that de m = log (tl)onII |
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| 67595. |
4 if the sum of first m terms of an A.P. is 2m* +3m, then what is its second term. (g |
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| 67596. |
d) 14612. The volume V, of a solid is given by the formula V (R-rh. Find the value of Vgiten that R 8, r 5, h-3 and |
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Answer» V=π(R^2-r^2)h=(22/7)(8^2-5^2)(7/2)=(11)(64-25)=11*39=429cubic unit |
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| 67597. |
The reciprocals of terms in G.P. form a GP. Inlet a, ar, ar2, .. .be a G.P. then clearly,ar aris also a G.. with the first term aand the common ratio7 |
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| 67598. |
16. In a class of 38 boys, 3 were absent. 20% of the rest did not complete their homework.How many boys have completed their homework? |
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Answer» Total boys = 38Absent boys = 3Present boys = 38-3 = 35boys didn't complete their homework = 20% of 35= 20^100 × 35= 35^5= 7 boysboys complete their homework = 35-7= 28 boys Total boys = 38Absent boys = 3Present boys = 38-3 = 35boys didn't complete their homework = 20% of 35= 20^100 × 35= 35^5= 7 boysboys complete their homework = 35-7= 28 boys Total boys=38Boys absent =3Total boys present =38-3=35boys will not complete their homework =20%of 35=20÷100×35=7boys will not do their homework Boys complete their homework =35-7=28Hence,the no. of boys who do their homework is 28 7,28 is the correct answer of the given question Let the boys who have not completed their homework be xThen,Total no. of boys=38Boys who were present=38-3=35Boys who did'nt completed their homework=20%Hence,35 - 20% of 35=x35 - 7 = x28=x |
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| 67599. |
Ina wants to serve salad at her party. Shewill need one head of lettuce for every 6guests who attend. Write an expressionshe could use for deciding how manylettuce she needs. |
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Answer» Let the number of guests be x, soNumber of lettuce=X/6 let x be no. of guestsfor 6 guests,lettuce required=1for 1 guest,lettuce =1/6therefore for x guests,no. of lettuce=x/6 |
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| 67600. |
28. If the m" term of an A.P. bei and rhe and nthterm be , show that its (mny is 1.be |
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Answer» Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved. |
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