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| 64601. |
10.Show that i) tan, θ + tane\tan ^{2} \theta+\tan ^{4} \theta=\log ^{4} \theta-\sec ^{2} \thetaii) (cosec θ-ote?1-cos θ1+ cos6 (P:S |
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| 64602. |
construct a parallel line from point M outside the line PQ |
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Answer» can you give your👉👤 WhatsApp no. I like you very much agar math me koi bhi question me problem ho to ham se puchh sake hai. I am expert in math. WhatsApp no. wala baat galti se likha gaya tha. sorry😔😓😩 for that delete it .right now |
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| 64603. |
MFind the heightA round balloon of radius r subtends an angle otthe eye of the observer while the angle of the elevationof its cenballoon is r sin/3 cosec α/2tre isß. Prove that the height of the centre thehove the |
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| 64604. |
Coto |
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| 64605. |
d. 3b. 1Maximum nos of zeros in polynomial ax2 bx c.b. 1a. 2c. 4a. 2c. 4d. 3 |
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Answer» Multiply both side by a. a^2.x^2+abx+ac=0 (ax)^2+2×ax×b/2+(b/2)^2-b^2/4+ac=0 (ax+b/2)^2=(b^2–4ac)/4 ax+b/2=+/-{(b^2–4ac)^1/2}/2 ax=-b/2+/-{(b^2–4ac)^1/2}/2 x=[-b+/-(b^2–4ac)^1/2]/2a , So the no of zeroes = 2 Like my answer if you find it useful! |
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| 64606. |
a*((c*((b*sqrt(a^(-2)))*(b^(-2))^(1/3)))*(c^(-2))^(1/3)) |
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Answer» (a^-2)^1/3*b*(b^-2)^1/3 * c * (c^-2)^1/3 * a = a^[-2/3 +1] * b^[-2/3 +1] * c^[-2/3 +1] = a^1/3 * b^1/3 * c^1/3 = (abc)^1/3 |
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| 64607. |
((Sino teases (fano t coto) = Secot touch |
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Answer» (sinA+cosA)(tanA+cotA)=(sinA+cosA)(sinA/cosA+cosA/sinA)=(sinA+cosA)(sin^2A+cos^2A/sinAcosA)=sinA/sinAcosA+cosA/sinAcosA= 1/cosA+1/sinA = secA+cosecA (Sinx+ CosA)(TanA+CotA)= ( SinA+CosA)( SinA/ cosA+ cosA/ sinA)=(Sin A + CosA)(SinA^2+ CosA^2)/sinAcosA=( SinA+ cosA) 1/ sinAcosA=secA+ CosecA |
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| 64608. |
Example 9 In Fig. 6.43, the line segmentXY is parallel to side AC of ΔABC and itdivides the triangle into two parts of equalareas. Find the ratio AX/AB |
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| 64609. |
5. In Fig.6.17,POO is a line. Ray OR is perpendicularto line PQ. OS is another ray lying between raysOP and OR. Prove thatd XY is roduced |
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| 64610. |
In Fig. 6.17, POQ is a line. Ray OR is perpendicularto line PQ OS is another ray lying between raysOP and OR. Prove that5.Z ROS( Q0S- Z POS). |
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| 64611. |
Draw a line segment XY of length 7.2 cm. Cutoff XP equal to 5.2 cm from it. Measure thelength of PY with a ruler. |
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Answer» here from 0 to the green line is 5.2cm and from 0 to the red line is 7.2 cm , so,. the length py = 7.2-5.2 = 2.0units. |
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| 64612. |
In the given figure, the line segment XY is parallel to the side AC of A4BC and itAXdivides the triangle into two parts of equal area. Find the ratioBY C |
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| 64613. |
In the given figure, PA LAB, 9B LAB and PA 9B.Prove that ΔΟΑΡ ΔΟΒ9.Is OA OB? |
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| 64614. |
A sector is cut from a circle of radius 21cm. the angle of the sector is 150°. Find the length of the arc andthe area of the sector. |
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Answer» thanks |
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| 64615. |
he equation of the line PQ is 3y -3x + 7-s 3y 3x+ 70.a Write down the slope of the line PQ.Calculate the angle that the line PQ makes with the positive direction oft-axis |
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| 64616. |
In the given figure, PA and PB are tangents such that PA= 8cm and APB = 60 then the length of tangent PB will be |
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Answer» samjh nahi aaya because in a equilateral triangle each angle is of 60° all sides will be equal |
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| 64617. |
In the given figure, PA and PB are tangents to a circle from an external point P such thatPA =4 cm and angleBAC= 135°. Find the length of the chord AB. |
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| 64618. |
In the given figure PA, OB and RC each isperpendicular to AC such that PA = x,RC-y, QB-z, AB-a and BC = b.Prove that+[CBSE 2015] |
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Answer» InΔPAC andΔQBC∠PCA =∠QCB∠PAC =∠QBC ΔPAC congurent toΔQBCPA/QB = AC/BCx/y = AB/BCy/x = BC/AC InΔRCA andΔQBA∠RAC =∠QAB∠RCA =∠QBAΔRCA is congruent toΔQBARC/QB = AC/AB z/y= AC/ABy/z= AB/AC adding both eqy/z + y/z = BC + AC/ AC = 1 y/z + y/z = 1 multiplying both sides by y 1/x + 1/z = 1/y |
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| 64619. |
2. In the given figure, PA and PB aretwo tangents drawn from an externalpoint P to a circle with centre C andCradius 4 cm, if PA丄PB, then findthe length of each tangent. |
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| 64620. |
4, Evaluate: (i) (5-1-82) / ( 2.3 Ă 10" )The size of a plant cell is 0.00001275 m express it in andunt fiom |
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| 64621. |
ertices or a square.6. Show that the points A(1, 2,3), B(-1,-2,-1), C(2, 3, 2) and D(4,7,6) are thevertices of a parallelogram. Show that ABCD is not a rectangle. |
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| 64622. |
2Show thatthatItit casocas o= casec o + coroShow=cosec ot coto.1 - Caso |
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| 64623. |
ler zole 2.10the area of the following4 cm5 cmRaca |
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| 64624. |
किक लक न e SRo 3/% et uL\' g P,\we*ksd Sec o +ToiBD |
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Answer» SecФ = x + 1/(4x) sec²Ф = x² + 1/(16 x²) + 1/2Tan²Ф = x² + 1/(16 x²) - 1/2 as sec² - tan² = 1 = (x - 1/(4x) )²tanФ = + (x - 1/(4x)) or - (x - 1/(4x) ) secФ + tanФ = 2x or 1/(4x) + 1/(4x) = 1/(2x) |
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| 64625. |
2. Find the area of a quadrilateral ABCD in which AB 3 cm, BC4 cm, CD -4 cm,DA 5 cm and AC 5 cm. |
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| 64626. |
2. Find the area of a quadrilateral ABCD in which AB 3 cm, BC4cm, CDDA 5 cm and AC 5 cm. |
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| 64627. |
OL (p)09 (a)08/ĺ |
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Answer» Numbers = 10x and 10y Where x and y are prime to each other. ∴∴LCM = 10xy =>10xy= 120 =>xy=12 Possible pair = (3, 4) ∴∴Sum of numbers =10×3+10×4=70 [As x and y are prime to each other] hit like if you find it useful thanks |
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| 64628. |
5. Can the angles 110°. 80°. 70°and 95" be the angles of a quadrilateral?6. Al7. In a quadrilatcral A RCR R- 1309Il the angles of a quadrilateral are equal. What special name is given to this quadrilateral? |
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Answer» 5) 𝑵𝒐 𝑬𝒙𝒑𝒍𝒂𝒏𝒂𝒕𝒊𝒐𝒏:As the sum of the angles mentioned that is 110°, 80°, 70° and 95° don't add up to a sum of 360° degree, hence, we can say that the mentioned angles cannot be the angles of a quadrilateral. 6) 𝑺𝒒𝒖𝒂𝒓𝒆 𝒐𝒓 𝑹𝒆𝒄𝒕𝒂𝒏𝒈𝒍𝒆 𝑬𝒙𝒑𝒍𝒂𝒏𝒂𝒕𝒊𝒐𝒏:If all the angles of the quadrilateral are equal, then we can say that the special name that can be given to this type of quadrilateral will be a square or a rectangle. |
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| 64629. |
Construct the perpendicular bisector of a line segment XY-6.5 cm. |
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| 64630. |
Draw the perpendicular bisector of line PQ whose length is5.6 cm. |
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| 64631. |
ABCD is a cyclic quadrilateral (see Fig. 3.7).Find the angles of the cyclic quadrilateral. |
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| 64632. |
We have done various punciCan you find a pattern for each of the following? If yes, complete them:(a) 7, 3,-1,-5.- |
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Answer» the complete pattern would be 7,3,-1,-5,9,5,1 may be the Patten is 9,5,1 7-4 = 33-4 = -1-1-4 = -5-5-4 = -9-9-4 = -13-13-4 = -17hence, the answer is -9, -13, -17 7 , 3 , -1 , -5 , -9 , -13 , -17 . |
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| 64633. |
In the given figure PA. QB and RC each isperpendicular to AC such that PA-X,RC=y, QB = Z, AB = a and BC = b.Prove that[CBSE 2015 |
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Answer» InΔPAC andΔQBC∠PCA =∠QCB∠PAC =∠QBC ΔPAC congurent toΔQBCPA/QB = AC/BCx/y = AB/BCy/x = BC/AC InΔRCA andΔQBA∠RAC =∠QAB∠RCA =∠QBAΔRCA is congruent toΔQBARC/QB = AC/AB z/y= AC/ABy/z= AB/AC adding both eqy/z + y/z = BC + AC/ AC = 1 y/z + y/z = 1 multiplying both sides by y 1/x + 1/z = 1/y |
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| 64634. |
Q16. A circle is completely divided into n sectors in such a way that the angles of the sectorsare in arithmetic progression. If the smallest-of these angles is 8° and the largest 72calculate n and the angle in the fourth sector. |
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| 64635. |
20. In the given figure, each one of PA, QB and PRC is perpendicular to AC. If AP x, QB z,RCy, AB a and BC b, show thatx1+1 1. |
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| 64636. |
Exercise - 1Construct Δ ABC in which AB-5.5 cm, BC-65 cm and CA-7.5cm. |
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Answer» Draw a line segment CA of the length given.With C as the centre and radius 6.5 draw an arc.With A as the centre and radius 5.5 draw an arc to cut the previous arc of BJoin AB and AC then ABC is formed |
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| 64637. |
9.The length of a rectangular room exceeds its breadth by 4m. if the length isincreased by 6m and breadth by 4m, there would be no change in the area. Find thelength and breadth of the room.10, when 75% of a number is added to 75, the result is the number again. Find thenumber.11.A lady went to a bank with 1,00,000. She asked the cashier to give her 500 and2 1,000 currency notes in return. She got 175 currency notes in all. Find the numberof each kind of currency notes.12. After 12 years, kKanwar shall be 3 times as old as he was 4 years ago. Find hispresent age. |
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| 64638. |
Δ ABC in which AB-0 cm, /400Δ POR in which P0-5.5 cm, OR-65 cm, LO- |
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| 64639. |
Construct AABC with BC7.5 cm, AC5 cm and mecs-60 |
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Answer» tnq soo much I have struggled to find out this solution........ |
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| 64640. |
5. Construct a AABC in which AB 3.8 cm, ZA -60° and AC -5 em. |
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| 64641. |
Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 65 cm. Findthe area of the parallelogram. |
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| 64642. |
walller fiom theihich ofthe following can be the sides of a right25cm.65 cm, 6 cm.2con. 2cm. 5cm.1,5 om, Don.2.5 cm. |
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Answer» thanks |
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| 64643. |
1. Construct a AABC in which BC=36 cm. AB-5 cm and AC=5.4 cm. Draw theperpendicular bisector of the side BC. |
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| 64644. |
g. In the figure (12.25), QX and RX are the bisectors of the anglesQ and R respectively of the triangles PQR. If XS LQR andXT L PQ. Prove that8T.(ü) PX bisects the angle P |
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Answer» Solution:Angle XSQ = 90°Angle XTQ = 90°QX = QX (This is the common side)Since QX bisects Q the angle is equally split between the triangles)So, XQS = TQXSo,Δ XTQ is congruent toΔ XSQXS = XT (According toCPCT) ...(1)Draw XW perpendicular to PRSimilarly, we can prove thatΔ XSR is congruent toΔ XWR.So, XS = XW ... (2)So, from (1) and (2)now in PXT and PXW, PTX = PWX, PX is common and XT = XW.BY R.H.S. both triangles are congruent, XPT = XPW and PX bisects the angle P. Hence proved |
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| 64645. |
7. Construct a quadrilateral XYZT in which XY = XZ = 5.7 cm, YZ-4.5 cm, ZX = 4.6 cm aXT = 5 cm. |
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| 64646. |
The length of a room is 3 times its height and breadth is 14 times its height. The cost of whitewashingthe walls at the rate ofäš1.50 per sq. m is? 216. Find the dimensions of the room. |
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Answer» Area of walls=Curved surface area of cuboid=2(l+b)h=2(3h+3h/2)h=2(8h/2)h=8h² Cost of 1m²=1.50RsArea covered in 216Rs=216/1.5=144m² 144=8h²h²=18h=3√2 |
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| 64647. |
4.In the given fig. XY2T is a rectangle and aa rhombus " where vertices are mid paire andthe side of the rectangle . If XY = 10 cmthen theXT = 8 cm,length of perpenderdrawn from a do Da is.Lars Mon 7yesof perpendicular |
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Answer» jdjsvdjdjdhdbdbbdndjdjdjdjdndnsns NC vsbsnsbsbsbsdjjsjsjsjsjsjsjsnsnssnsnsnsnsnsn 40/√41 is the correct answer of the given question 40/√41 is the correct answer 40/41 is the correct answer of the given question |
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| 64648. |
0G+ Xy(H |
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| 64649. |
2. In the given figure, BA II QR and CA ll SR. Prove thatQB SCBP CP |
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| 64650. |
Find the height of the trapezium, the sum of the lengths of whose bases is 50 cm, and whose area is500 cm |
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Answer» Area of trapezium is given by:½(sum of the two parallel sides)x height so,½x 50 x h = 500h= 20 cm |
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