81279 + Interview Questions in Mathematics QA in Mathematics

1.	Show that the line segment joining the midpoints of a pair of oppositesides of a parallelogram divides it into two equal parallelograms.AMPLE 1
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2.	6.EXAMPLE 12In the adjoining figure, PORS and PABC aretwo parallelograms of equal area. Prove thatQC\|\| BR.Let BC and QR intersect at O.Join BQ, QC, CR and RB.OLUTION
Answer» Let QR and BC intersect at O.Join CQ, QB, BR and RC.ar(//gm PQRS) = ar(//gm PABC)⇒ ar(//gm PQOC) + ar(//gm CORS) = ar(//gm PQOC ) + ar(//gm QABO)⇒ ar(//gm CORS) = ar(//gm QABO)⇒1/2 ar(//gm CORS) = 1/2 ar(//gm QABO)⇒ar (ΔCOR) = ar (ΔQOB)⇒ar (ΔCOR) + ar (ΔCQO) = ar (ΔQOB) + ar (ΔCQO)⇒ar (ΔCQR) = ar (ΔCQB) ΔCQR and ΔCQB are on the same base CQ and have equal areas. Therefore, ΔCQR and ΔCQB lie between the same parallels QC and BR.Hence, QC // BR

2.

6.EXAMPLE 12In the adjoining figure, PORS and PABC aretwo parallelograms of equal area. Prove thatQC|| BR.Let BC and QR intersect at O.Join BQ, QC, CR and RB.OLUTION

Answer»

Let QR and BC intersect at O.Join CQ, QB, BR and RC.ar(//gm PQRS) = ar(//gm PABC)⇒ ar(//gm PQOC) + ar(//gm CORS) = ar(//gm PQOC ) + ar(//gm QABO)⇒ ar(//gm CORS) = ar(//gm QABO)⇒1/2 ar(//gm CORS) = 1/2 ar(//gm QABO)⇒ar (ΔCOR) = ar (ΔQOB)⇒ar (ΔCOR) + ar (ΔCQO) = ar (ΔQOB) + ar (ΔCQO)⇒ar (ΔCQR) = ar (ΔCQB)

ΔCQR and ΔCQB are on the same base CQ and have equal areas.

Therefore, ΔCQR and ΔCQB lie between the same parallels QC and BR.Hence, QC // BR

Discussion

3.	PLE 12ABCD is allgm.In the adjoining figure, PQRS and PABC aretwo parallelograms of equal area. Prove thatQC \|\| BR.Let BC and QR intersect at O.Join BQ.QC,CR and RB.ON
Answer» Let QR and BC intersect at O.Join CQ, QB, BR and RC.ar(//gm PQRS) = ar(//gm PABC)⇒ ar(//gm PQOC) + ar(//gm CORS) = ar(//gm PQOC ) + ar(//gm QABO)⇒ ar(//gm CORS) = ar(//gm QABO)⇒1/2 ar(//gm CORS) = 1/2 ar(//gm QABO)⇒ar (ΔCOR) = ar (ΔQOB)⇒ar (ΔCOR) + ar (ΔCQO) = ar (ΔQOB) + ar (ΔCQO)⇒ar (ΔCQR) = ar (ΔCQB) ΔCQR and ΔCQB are on the same base CQ and have equal areas. Therefore, ΔCQR and ΔCQB lie between the same parallels QC and BR.Hence, QC // BR

3.

PLE 12ABCD is allgm.In the adjoining figure, PQRS and PABC aretwo parallelograms of equal area. Prove thatQC || BR.Let BC and QR intersect at O.Join BQ.QC,CR and RB.ON

Answer»

Let QR and BC intersect at O.Join CQ, QB, BR and RC.ar(//gm PQRS) = ar(//gm PABC)⇒ ar(//gm PQOC) + ar(//gm CORS) = ar(//gm PQOC ) + ar(//gm QABO)⇒ ar(//gm CORS) = ar(//gm QABO)⇒1/2 ar(//gm CORS) = 1/2 ar(//gm QABO)⇒ar (ΔCOR) = ar (ΔQOB)⇒ar (ΔCOR) + ar (ΔCQO) = ar (ΔQOB) + ar (ΔCQO)⇒ar (ΔCQR) = ar (ΔCQB)

ΔCQR and ΔCQB are on the same base CQ and have equal areas.

Therefore, ΔCQR and ΔCQB lie between the same parallels QC and BR.Hence, QC // BR

Discussion

4.	2. Two angles measures a -60° and 1230 - 2a. If each one is opposite to equal sides of an isoscelestriangle, then find the value of a.-12-
Answer» 123-12033 is the right option

Discussion

5.	10. The base of an isosceles triangle measures 80 cm and its area is 360 cmFind the perimeter of the triangle.
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6.	12. Find the area of a rectangular plot one side ofwhich measures 48 m and the diagonal is 50 m
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7.	he sides of an isosceles triangle are in the ratio:5:4. The perimeter of the triangle is 196 cmFind the measures of all the sides of the triangle
Answer» Let the ratio be x So, sides are 5x, 5x, 4x According to question, 5x + 5x + 4x = 196 14x = 196 x = 196/14 = 14 So, sides are 70, 70, and 56

7.

he sides of an isosceles triangle are in the ratio:5:4. The perimeter of the triangle is 196 cmFind the measures of all the sides of the triangle

Answer»

Let the ratio be x

So, sides are 5x, 5x, 4x

According to question,

5x + 5x + 4x = 196

14x = 196

x = 196/14 = 14

So, sides are 70, 70, and 56

Discussion

8.	Prove that the parallelograms on equal (or same) bases and between the same parallelsare equal in area.
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Discussion

9.	Ifany two sides ofa triangle are produced beyond its base and the exterior angles thus obtainedbisected, then these bisectors will include an angle equal to-the sum of the base angleshalf the difference of the base angleb) sum of the base anglesd) difference of the base angles
Answer» so, the correct answer is option A.. see the example below.

Discussion

10.	1. A plot of magnetic flux (0) versus current (/) is shown in the figure for two1inductors A and B. Which of the two has larger value of self inductance?2. Define mutual inductance. Give its Sl units
Answer» We know self inductance L= Magnetic flux / I .. given plot is of magnetic flux versus I . Therefore the slope will be equal to L (self inductance) . Since slope of A is more than B => A has higher value of self inductance.

Discussion

11.	3.l ne sum or two integers is 28. If one ıntger s, linu te one4. The sum of two integers is -56. If one integer is -42, find the other
Answer» If you do -56+42, the answer is -14, which is the answer to the problem.

Discussion

12.	6. What is the value of y so that the line through (3, y) and (2,7) is parallel to the line through(1, 4) and (0, 6)?7. What can be said regarding a line if its slope is(i) zero(ii) positive(ii) negative?lal to tha lineininine (7-11 and (0.3).
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13.	EXERCISE 7.2cube root of each of the following numbers by prime factorisation ne6415625175616(i) 512(vi) 13824(x) 91125im) 10648(vi) 110592(iv)(iii) 46
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14.	he perpendicular to the line segment XY. Let PO and XY intersect ace ne segment 1 etrThe letter Z.(vi)Let PQis the measure of PAY?Let PO and XY intersect at point A. What
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15.	5. A certain sum of money was acsum of money was deposited for 5 years. Simple interest at nerate of 12% per annum was paid. Calculate the sum deposited,interest received by the depositor is 12,000.यदि
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16.	thetinifL.ne13k2-0 (this is13k 2213EXERCISE-6.2Find three different solutions of the each of the following equationsii) y 6xv) 10x + lly-21 vi)xy-iii) 2x -y) 3x+4y 7iv) 13x 12y 25
Answer» 2.y=6x x=0y=0 x=1y=6 x=2y=12 x=-1y=-6

16.

thetinifL.ne13k2-0 (this is13k 2213EXERCISE-6.2Find three different solutions of the each of the following equationsii) y 6xv) 10x + lly-21 vi)xy-iii) 2x -y) 3x+4y 7iv) 13x 12y 25

Answer»

2.y=6x

x=0y=0

x=1y=6

x=2y=12

x=-1y=-6

Discussion

17.	4. An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio2: 3. Find the angles of the triangle.
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18.	Two angles of a triangle are in the ratio 2:3 and third angle is 60°. Find the other two angles of thetriangle1.
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19.	Two angles of a triangle are in the ratioof the triangle.1:2anditsthirdangleis60Findtheothertwoangles
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20.	A rectangular banana plot measures 110 m by 90 m. The gate to the gar2 m wide. How many posts, 2 m apart, will be needed to fence this plot?den is
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21.	Fach of the equal sides of an isosceles triangle measures 2 cm more thanits height, and the base of the triangle measures 12 cm. Find the area ofthe triangle.18.
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22.	11. Find the sum of n terms of the sequence fa,), where a5-6n, ne N
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23.	(1) a number lying betweenne card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting(i) aking of red colour(iv) the jack of hearts(ii) a face card(v) a spade(ii) a red face card(vi) the queen of diamonds
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24.	sudesh is twice as old as seema . if 6 year is subtracted from Seema's age and four years are added to sudesh's age ,sudesh will be four times seema's age . how old they were three years ago ?
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25.	meeraa's mother is four times as old as meera.After five year,her mother will be three times as old as she will be then.what are their present ages
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26.	Find which of the following can be the measures of three anglestriangle.(a) 35, 80, 65°(b) 15, 75 90(c) 70, 70, 70(d) 45, 59, 81°angle with two right angles? Give reasons.
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27.	ove thatangle and the external bisector of the other base angle ofatheangleberweeninternalbisedtรณr8fBReEDLLtriangle is equal to one-half of the vertical angle.
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28.	(II)its(ii) the volume of its material whose thickness is 5 mm.sarface area of the eun4. Two cubes, each of volume 512 cm2 are joined end to end. Pind thecuboid.
Answer» Volume of one cube=512 cm³a³=512 cm³a=8 cm Length of resulting cuboid= 16 cmBreadth of resulting cuboid=8 cmHeight of resulting cuboid= 8 cm Surface area of the resulting cuboid=2(lb+bh+hl)=2(168+88+8*16) cm²=2(128+64+128) cm²=2(320) cm²=640 cm²

28.

(II)its(ii) the volume of its material whose thickness is 5 mm.sarface area of the eun4. Two cubes, each of volume 512 cm2 are joined end to end. Pind thecuboid.

Answer»

Volume of one cube=512 cm³a³=512 cm³a=8 cm

Length of resulting cuboid= 16 cmBreadth of resulting cuboid=8 cmHeight of resulting cuboid= 8 cm

Surface area of the resulting cuboid=2(lb+bh+hl)=2(16*8+8*8+8*16) cm²=2(128+64+128) cm²=2(320) cm²=640 cm²

Discussion

29.	XYǐs a line parallel to side BC ofa triangle ABernEllACand CFand F respectively, show thatAB meet XY at E
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30.	n hemeasure of each angle.One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the remainithe measures of the three angles of the triangleng two angles is 2: 1, fim4
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31.	* An exterior angle of a triangle measures 110 and its interior opposite angles are in the ratio
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32.	naca" angles ofa triangle ABC, show that sin(B2C)-cos2
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33.	The coordinates of the vertices ofA ABC are A(4, 1), B (-3, 2) and C (0, k) Given thatarea of triangle ABC is 12 unit', find the value of k.
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34.	25.Draw a triangle ABC with side BC = 6 cm, AB-5 cm andABC-60°.Then construca triangle whose sides areof the corresponding sides of the triangle ABC.les4
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35.	हों।Construct a triangle to a given triangle ABC witits sides equal to of the corresponding sidof the triangle ABC.बेन्दुओं A(2,-2) और B-7, 4) को जोड़ने वाले रेखाखण्डम-त्रिभाजित करने वाले बिन्दुओं के निर्देशांक ज्ञात कीजिए।nd the co-ordinates of the points of trisectice line segment joining the points A(2,-2)74)के प्रकार सेली गई ८० पत्तों की एक गली में से
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Discussion

36.	4. The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find the other two sidand the area of the triangle.
Answer» p+b+h=60b+p=34by hit nd trial b=10and p=24 area of triangle = 120 cm²

36.

4. The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find the other two sidand the area of the triangle.

Answer»

p+b+h=60b+p=34by hit nd trial b=10and p=24

area of triangle = 120 cm²

Discussion

37.	D,E, P, are the mid points of the side BC CA and AB respectively of triangle ABC PROVE THAT BEEF IS a 11gmarea of triangle DEF =1/4 area of triangle ABCarea (11gmBDEF)=1/2 ar (triangle ABC)
Answer» Parallelogram :A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. In aparallelogram diagonal divides it into two triangles of equal areas. Mid point theorem:The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it. SOLUTION : Given:ABC is a Triangle in which the midpoints of sides BC ,CA and AB are D, E and F. To show:(i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4ar (ABC)(iii) ar (BDEF) =1/2 ar (ABC) Proof: i)Since E and F are the midpoints of AC and AB. BC\|\|FE & FE= ½ BC= BD (By mid point theorem) BD \|\| FE & BD= FE Similarly, BF\|\|DE & BF= DE Hence, BDEF is a parallelogram .[A pair of opposite sides are equal and parallel] (ii)Similarly, we can prove that FDCE & AFDE are also parallelograms. Now, BDEF is a parallelogram so its diagonal FD divides its into two Triangles of equal areas. ∴ ar(ΔBDF) = ar(ΔDEF) — (i) In Parallelogram AFDE ar(ΔAFE) = ar(ΔDEF) (EF is a diagonal) — (ii) In Parallelogram FDCE ar(ΔCDE) = ar(ΔDEF) (DE is a diagonal) — (iii) From (i), (ii) and (iii) ar(ΔBDF) = ar(ΔAFE) = ar(ΔCDE) = ar(ΔDEF).....(iv) ar(ΔBDF) + ar(ΔAFE) + ar(ΔCDE) + ar(ΔDEF) = ar(ΔABC) 4ar(ΔDEF) = ar(ΔABC)(From eq iv) ar(∆DEF) = 1/4 ar(∆ABC)........(v) (iii)Area (parallelogram BDEF) = ar(ΔDEF) + ar(ΔBDF)ar(parallelogram BDEF) = ar(ΔDEF) + ar(ΔDEF) ar(parallelogram BDEF) = 2×ar(ΔDEF)(From eq iv) ar(parallelogram BDEF) = 2× 1/4 ar(ΔABC)(From eq v) ar(parallelogram BDEF) = 1/2 ar(ΔABC

37.

D,E, P, are the mid points of the side BC CA and AB respectively of triangle ABC PROVE THAT BEEF IS a 11gmarea of triangle DEF =1/4 area of triangle ABCarea (11gmBDEF)=1/2 ar (triangle ABC)

Answer»

Parallelogram :A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram.

In aparallelogram diagonal divides it into two triangles of equal areas.

Mid point theorem:The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it.

SOLUTION :

Given:ABC is a Triangle in which the midpoints of sides BC ,CA and AB are D, E and F.

To show:(i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4ar (ABC)(iii) ar (BDEF) =1/2 ar (ABC)

Proof: i)Since E and F are the midpoints of AC and AB.

BC||FE & FE= ½ BC= BD

(By mid point theorem)

BD || FE & BD= FE

Similarly, BF||DE & BF= DE

Hence, BDEF is a parallelogram

.[A pair of opposite sides are equal and parallel]

(ii)Similarly, we can prove that FDCE & AFDE are also parallelograms.

Now, BDEF is a parallelogram so its diagonal FD divides its into two Triangles of equal areas.

∴ ar(ΔBDF) = ar(ΔDEF) — (i)

In Parallelogram AFDE

ar(ΔAFE) = ar(ΔDEF) (EF is a diagonal) — (ii)

In Parallelogram FDCE

ar(ΔCDE) = ar(ΔDEF) (DE is a diagonal) — (iii)

From (i), (ii) and (iii)

ar(ΔBDF) = ar(ΔAFE) = ar(ΔCDE) = ar(ΔDEF).....(iv)

ar(ΔBDF) + ar(ΔAFE) + ar(ΔCDE) + ar(ΔDEF) = ar(ΔABC)

4ar(ΔDEF) = ar(ΔABC)(From eq iv)

ar(∆DEF) = 1/4 ar(∆ABC)........(v)

(iii)Area (parallelogram BDEF) = ar(ΔDEF) + ar(ΔBDF)ar(parallelogram BDEF) = ar(ΔDEF) + ar(ΔDEF)

ar(parallelogram BDEF) = 2×ar(ΔDEF)(From eq iv)

ar(parallelogram BDEF) = 2× 1/4

ar(ΔABC)(From eq v)

ar(parallelogram BDEF) = 1/2 ar(ΔABC

Discussion

38.	11. Find the sum of x +y+z in the following figuresa.b.C.350 6049°5212. Find the sum of a+b+c+d in the following fiun
Answer» a) x+50=180 so x=130 y+70=180 so y=110 z+60=180 so z=120x+y+z=130+110+120=360b) x+90=180 so x=90 y+35=180 so y=145 z+55=180 so z=125x+y+z=90+145+125=360c) x+49=180 so x=131 y+52=180 so y=128 z+79=180 so z=101x+y+z=131+101+128=360

Discussion

39.	B. 1. Without performing the actual addition and division, find the quotient when(i) the sum of 45 and 54 is divided by(ii) the sum of 37 and 73 is divided by(ii) the sum of 93 and 39 is divided by(a) 11 (b) 9(a) 10 (b) 11(a) 11 (b) 12
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40.	The sum of two numbers a and b is 15 and the sumof their reciprocals-andnumbers a and b.16.Find theis-b 10
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41.	\left. \begin{array} { l } { \text { Subtract the sum of } - 7 a ^ { 2 } - 3 a b + 4 b ^ { 2 } \text { and } } \\ { a ^ { 2 } \text { Tab from the sum of } 4 a ^ { 2 } - b ^ { 2 } \text { and } - 7 a ^ { 2 } + 7 b a } \end{array} \right.
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42.	4. Find the ratio of volumes of cylinder and cone having same base radi and sameheights.
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43.	23. A man saved 16,500 in ten years. In each year after the first he savedin the preceding year. IHow much did he save in the first year ?100 more than he did
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44.	Fig. 8.10Find the area of a triangle two sides of which are 1 8cm and 10cm and the perimete42cm.Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its aAn isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm.the area of the triangle.
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Discussion

45.	SSS Congruence Criterion of triangles meansWfhree sides of a triangle are equl.(B) Three angles of a triangle are equal.Q. Threesides of one trfiangle are equal opading sidtriangleum of the two sides of one triangle is equal to its third side.
Answer» which option?

Discussion

46.	Find the area of a triangle two sides of which are 18em and 1ocemi and the perimeser42cm
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47.	Find the area of a triangle two sides of which are 18cm and 10cm andtperimeter is 42cm.
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Discussion

48.	The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 mrespectively. The density of the metal is 8.88 gm per cm3. Find the outer surfacearea and mass of the sphere.
Answer» Diameter of sphere from outside = 12 cm Radius from outside R = 6 cm Surface area = 4 πR² = 4 (22/7) (6²) = 452.57 cm² Now, Thickness of sphere = 0.01 m = 1 cm Diameter from inside = 12 - 2 = 10 cm [ -2 is done to reduce from both sides ] Radius from inside r = 5 cm Volume of this sphere V = Volume of outside sphere - Volume of inside sphere So, V = 4/3 πR³ - 4/3 πr³ = 4/3 π (R³ - r³) V = 4/3 (22/7) (6³ - 5³) V = 4/3 (22/7) (91) V = 381.33 cm³ Now, Density = Mass / Volume Mass = Density x Volume Mass = (8.88) x (381.33) Mass = 3386.24 g = 3.38624 kg

48.

The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 mrespectively. The density of the metal is 8.88 gm per cm3. Find the outer surfacearea and mass of the sphere.

Answer»

Diameter of sphere from outside = 12 cm

Radius from outside R = 6 cm

Surface area = 4 πR²

= 4 (22/7) (6²) = 452.57 cm²

Now, Thickness of sphere = 0.01 m = 1 cm

Diameter from inside = 12 - 2 = 10 cm [ -2 is done to reduce from both sides ]

Radius from inside r = 5 cm

Volume of this sphere V = Volume of outside sphere - Volume of inside sphere

So, V = 4/3 πR³ - 4/3 πr³ = 4/3 π (R³ - r³)

V = 4/3 (22/7) (6³ - 5³)

V = 4/3 (22/7) (91)

V = 381.33 cm³

Now, Density = Mass / Volume

Mass = Density x Volume

Mass = (8.88) x (381.33)

Mass = 3386.24 g = 3.38624 kg

Discussion

49.	The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 nrespectively. The density of the metal is 8.88 gm per cm. Find the outer surfacarea and mass of the sphere.6.
Answer» Diameter of sphere from outside = 12 cm Radius from outside R = 6 cm Surface area = 4 πR² = 4 (22/7) (6²) = 452.57 cm² Now, Thickness of sphere = 0.01 m = 1 cm Diameter from inside = 12 - 2 = 10 cm [ -2 is done to reduce from both sides ] Radius from inside r = 5 cm Volume of this sphere V = Volume of outside sphere - Volume of inside sphere So, V = 4/3 πR³ - 4/3 πr³ = 4/3 π (R³ - r³) V = 4/3 (22/7) (6³ - 5³) V = 4/3 (22/7) (91) V = 381.33 cm³ Now, Density = Mass / Volume Mass = Density x Volume Mass = (8.88) x (381.33) Mass = 3386.24 g = 3.38624 kg

49.

The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 nrespectively. The density of the metal is 8.88 gm per cm. Find the outer surfacarea and mass of the sphere.6.

Answer»

Diameter of sphere from outside = 12 cm

Radius from outside R = 6 cm

Surface area = 4 πR²

= 4 (22/7) (6²) = 452.57 cm²

Now, Thickness of sphere = 0.01 m = 1 cm

Diameter from inside = 12 - 2 = 10 cm [ -2 is done to reduce from both sides ]

Radius from inside r = 5 cm

Volume of this sphere V = Volume of outside sphere - Volume of inside sphere

So, V = 4/3 πR³ - 4/3 πr³ = 4/3 π (R³ - r³)

V = 4/3 (22/7) (6³ - 5³)

V = 4/3 (22/7) (91)

V = 381.33 cm³

Now, Density = Mass / Volume

Mass = Density x Volume

Mass = (8.88) x (381.33)

Mass = 3386.24 g = 3.38624 kg

Discussion

50.	Volume of a hollow sphere is 1152m. If the outer Tadius is 8 gm, find the innerradius of the sphere.cm, If the outer radius is 8 cm, find the inner
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Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Show that the line segment joining the midpoints of a pair of oppositesides of a parallelogram divides it into two equal parallelograms.AMPLE 1

6.EXAMPLE 12In the adjoining figure, PORS and PABC aretwo parallelograms of equal area. Prove thatQC|| BR.Let BC and QR intersect at O.Join BQ, QC, CR and RB.OLUTION

PLE 12ABCD is allgm.In the adjoining figure, PQRS and PABC aretwo parallelograms of equal area. Prove thatQC || BR.Let BC and QR intersect at O.Join BQ.QC,CR and RB.ON

2. Two angles measures a -60° and 1230 - 2a. If each one is opposite to equal sides of an isoscelestriangle, then find the value of a.-12-

10. The base of an isosceles triangle measures 80 cm and its area is 360 cmFind the perimeter of the triangle.

12. Find the area of a rectangular plot one side ofwhich measures 48 m and the diagonal is 50 m

he sides of an isosceles triangle are in the ratio:5:4. The perimeter of the triangle is 196 cmFind the measures of all the sides of the triangle

Prove that the parallelograms on equal (or same) bases and between the same parallelsare equal in area.

Ifany two sides ofa triangle are produced beyond its base and the exterior angles thus obtainedbisected, then these bisectors will include an angle equal to-the sum of the base angleshalf the difference of the base angleb) sum of the base anglesd) difference of the base angles

1. A plot of magnetic flux (0) versus current (/) is shown in the figure for two1inductors A and B. Which of the two has larger value of self inductance?2. Define mutual inductance. Give its Sl units

3.l ne sum or two integers is 28. If one ıntger s, linu te one4. The sum of two integers is -56. If one integer is -42, find the other

6. What is the value of y so that the line through (3, y) and (2,7) is parallel to the line through(1, 4) and (0, 6)?7. What can be said regarding a line if its slope is(i) zero(ii) positive(ii) negative?lal to tha lineininine (7-11 and (0.3).

EXERCISE 7.2cube root of each of the following numbers by prime factorisation ne6415625175616(i) 512(vi) 13824(x) 91125im) 10648(vi) 110592(iv)(iii) 46

he perpendicular to the line segment XY. Let PO and XY intersect ace ne segment 1 etrThe letter Z.(vi)Let PQis the measure of PAY?Let PO and XY intersect at point A. What

5. A certain sum of money was acsum of money was deposited for 5 years. Simple interest at nerate of 12% per annum was paid. Calculate the sum deposited,interest received by the depositor is 12,000.यदि

thetinifL.ne13k2-0 (this is13k 2213EXERCISE-6.2Find three different solutions of the each of the following equationsii) y 6xv) 10x + lly-21 vi)xy-iii) 2x -y) 3x+4y 7iv) 13x 12y 25

4. An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio2: 3. Find the angles of the triangle.

Two angles of a triangle are in the ratio 2:3 and third angle is 60°. Find the other two angles of thetriangle1.

Two angles of a triangle are in the ratioof the triangle.1:2anditsthirdangleis60Findtheothertwoangles

A rectangular banana plot measures 110 m by 90 m. The gate to the gar2 m wide. How many posts, 2 m apart, will be needed to fence this plot?den is

Fach of the equal sides of an isosceles triangle measures 2 cm more thanits height, and the base of the triangle measures 12 cm. Find the area ofthe triangle.18.

11. Find the sum of n terms of the sequence fa,), where a5-6n, ne N

(1) a number lying betweenne card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting(i) aking of red colour(iv) the jack of hearts(ii) a face card(v) a spade(ii) a red face card(vi) the queen of diamonds

sudesh is twice as old as seema . if 6 year is subtracted from Seema's age and four years are added to sudesh's age ,sudesh will be four times seema's age . how old they were three years ago ?

meeraa's mother is four times as old as meera.After five year,her mother will be three times as old as she will be then.what are their present ages

Find which of the following can be the measures of three anglestriangle.(a) 35, 80, 65°(b) 15, 75 90(c) 70, 70, 70(d) 45, 59, 81°angle with two right angles? Give reasons.

ove thatangle and the external bisector of the other base angle ofatheangleberweeninternalbisedtรณr8fBReEDLLtriangle is equal to one-half of the vertical angle.

(II)its(ii) the volume of its material whose thickness is 5 mm.sarface area of the eun4. Two cubes, each of volume 512 cm2 are joined end to end. Pind thecuboid.

XYǐs a line parallel to side BC ofa triangle ABernEllACand CFand F respectively, show thatAB meet XY at E

n hemeasure of each angle.One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the remainithe measures of the three angles of the triangleng two angles is 2: 1, fim4

* An exterior angle of a triangle measures 110 and its interior opposite angles are in the ratio

naca" angles ofa triangle ABC, show that sin(B2C)-cos2

The coordinates of the vertices ofA ABC are A(4, 1), B (-3, 2) and C (0, k) Given thatarea of triangle ABC is 12 unit', find the value of k.

25.Draw a triangle ABC with side BC = 6 cm, AB-5 cm andABC-60°.Then construca triangle whose sides areof the corresponding sides of the triangle ABC.les4

4. The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find the other two sidand the area of the triangle.

D,E, P, are the mid points of the side BC CA and AB respectively of triangle ABC PROVE THAT BEEF IS a 11gmarea of triangle DEF =1/4 area of triangle ABCarea (11gmBDEF)=1/2 ar (triangle ABC)

11. Find the sum of x +y+z in the following figuresa.b.C.350 6049°5212. Find the sum of a+b+c+d in the following fiun

B. 1. Without performing the actual addition and division, find the quotient when(i) the sum of 45 and 54 is divided by(ii) the sum of 37 and 73 is divided by(ii) the sum of 93 and 39 is divided by(a) 11 (b) 9(a) 10 (b) 11(a) 11 (b) 12

The sum of two numbers a and b is 15 and the sumof their reciprocals-andnumbers a and b.16.Find theis-b 10

\left. \begin{array} { l } { \text { Subtract the sum of } - 7 a ^ { 2 } - 3 a b + 4 b ^ { 2 } \text { and } } \\ { a ^ { 2 } \text { Tab from the sum of } 4 a ^ { 2 } - b ^ { 2 } \text { and } - 7 a ^ { 2 } + 7 b a } \end{array} \right.

4. Find the ratio of volumes of cylinder and cone having same base radi and sameheights.

23. A man saved 16,500 in ten years. In each year after the first he savedin the preceding year. IHow much did he save in the first year ?100 more than he did

Fig. 8.10Find the area of a triangle two sides of which are 1 8cm and 10cm and the perimete42cm.Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its aAn isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm.the area of the triangle.

SSS Congruence Criterion of triangles meansWfhree sides of a triangle are equl.(B) Three angles of a triangle are equal.Q. Threesides of one trfiangle are equal opading sidtriangleum of the two sides of one triangle is equal to its third side.

Find the area of a triangle two sides of which are 18em and 1ocemi and the perimeser42cm

Find the area of a triangle two sides of which are 18cm and 10cm andtperimeter is 42cm.

The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 mrespectively. The density of the metal is 8.88 gm per cm3. Find the outer surfacearea and mass of the sphere.

The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 nrespectively. The density of the metal is 8.88 gm per cm. Find the outer surfacarea and mass of the sphere.6.

Volume of a hollow sphere is 1152m. If the outer Tadius is 8 gm, find the innerradius of the sphere.cm, If the outer radius is 8 cm, find the inner