Maths questions 2069

COMPULSORY MATHS

Model Set 1

Time: 3.00 hours                                                                    Full Marks: 100

                                                                                    Pass Marks: 32

                                                ;d'x …sÚ (Group ‘A’)              [9×(2+2)=36]

1.         a.         dfg lgsfNg'xf];\ (Evaluate):

            b.       ;/n ug{'xf];\  (Simplify): 

2.         a.         xn ug{'xf];\ (Solve) :

  b.            olb Pp6f wgfTds ;ª\Vofsf] ju{af6 7 36fpFbf kl/0ffd 9 x'G5 eg] pQm ;ª\Vof kQf nufpg'xf];\ .

If 7 is subtracted from the square of a positive number, the result is 9. Find the number.  

3.         a.         olb = 400+20a, =18+2a / lbOPsf] >]0fLsf] dWos @) eP a sf] dfg lgsfNg'xf]; .                                                                            

If = 400+20a ,=18+2a, and the mean of the given series is 20, find the value of a.

b.         ;Fu} lbOPsf ;l~rt jf/Djf/tf js|jf6 dlWosf / dlWsfsf] ju{

kQf nufpg'xf];\ .  

Find the median class and value of median from the adjoining cumulative frequency curve.

4.         a.         /fd|/L lkml6Psf] 52 kQL ePsf] tf;sf] u8\8Laf6 Pp6f kQL

lgsflnPsf] 5 eg] pQm klQ /fgL  cyjf sfnf] /ªsf] PSsf kg{] ;DefJotf kQf nufpg'xf];\ . 

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting such card is queen or a black ace.

       

 b.        Pp6f l;SsfnfO{ b'O{k6s ;Dd pkmfbf{ aGg] ;DefJotfnfO{ j[Iflrqdf k|:t't ug{'xf];\ .

A coin is tossed two times and represents the probabilities in a tree diagram.

5.         a.      lqe'h ABC  df  AB=8 ;]=ld= BC= 12 ;]=ld= / ÐABC=60° eP  ;f] lqe'hsf] If]qkmn kQf nufpg'xf];\ .

In ∆ABC, AB=8cm, BC= 12 cm and  ÐABC=60°.

Find the area of the triangle.

b.         lbOPsf] lrq lqe'hfsf/ cfwf/ ePsf] Pp6f 7f]; lk|Hd xf] . olb AB= 3;]=ld= BC=5;]=ld= / CF= 12;]=ld= eP pQm lk|Hdsf] cfotg kQf nufpg'xf];\ .

The adjoining diagram is a triangular based solid prism. If AB= 3cm, BC=5cm and CF= 12cm find the volume of the prism.

6. a .                Pp6f a]ngfsf] cw{Jof; / prfOsf] of]ukmn 12 ;]=ld / cfwf/sf] kl/lw 416 ;]=ld= eP pQm

a]ngfsf] k"/f ;txsf] If]qkmn lgsfNg'xf];\ .

 If the sum of radius and height of cylinder is 12 cm and circumference of base is    416 cm find the total surface area of that cylinder.

b.       ;Fu} lbOPsf] lrq Pp6f 7f]; uf]nfsf] xf] . olb cfwf/sf] Jof;  -  AB)= 28 ;]=ld= eP pQm uf]nfsf] cfotg lgsfNg'xf];\ .

The diagram given alongside is of a solid sphere. If AB= 28 cm, Find the volume of the sphere.

7.      a.            Pp6f j:t'sf] jf:tljs d"Nodf15%  a9fO{ clª\st d"No ?= 2760 sfod ul/of] . ;f] j:t'sf] jf:tljs d"No kQf nufpg'xf];\ .

The marked price of an article was fixed to Rs. 2760 by increasing 15% in its actual price. Find its actual price.

b.        ?= 5000 sf] k|ltjif{ 10%  jflif{s rqmLo Aofhb/n] 2 jif{df x'g] rlqmo ld>wg kQf nufpg'xf];\ .

Find the compound amount on Rs. 5000 in 2 years at 10% per annum.

8.           a.      lbOPsf] lrqdf, WXYZ Pp6f ;dfgfGt/ rt'e{'h 5 . olb WX nfO laGb'   V ;Dd

a9fpFbf ag]sf] ∆ZYV sf] If]qkmn 15cm² eP ∆WXT sf] If]qkmn kQf nufpg'xf];\ .

If the given figure, WXYZ is a parallelogram . WX is extended       up to U and ∆ZYU is formed. If Area of ∆ZYU is 15cm², find             the area of ∆WXT.

b.     lbOPsf] lrqdf PR^QS 5 . olb ÐPQS=46° eP ÐQSR kQf         nufpg'xf];\ . In the given figure, PR^QS. If  ÐPQS=46°, find ÐQSR.

9.         a.     lbOPsf] lrqdf laGb'x? A, D, C /  B cw{j[Qdf 5g\ . olb ÐDAC=30° /  ÐABC= 70° eP ÐACD kQf nufpg'xf];\ .      

In the given figure, points A, D, C and B are on semi-circle. If     ÐDAC=30° and ÐABC= 70°, find ÐACD.

b. lbOPsf] lrqdf PT n] laGb'  A df j[QnfO{ :kz{ u/]sf] 5 . olbÐBAT=60°  / ÐBAC=50° eP ÐABC kQf nufpg'xf];\ .

In the given figure, PT touches a circle at a point A. If ÐBAT=60° and ÐBAC=50°, find ÐABC.

;d'x …vÚ (Group ‘B’)                      [16×4=36]

10        Pp6f ljBfyL{x¿sf] ;d"xdf ul/Psf] ;j{]If0fdf 70%  ljBfyL{x¿n] j}1flgsx¿sf ;DaGwdf , 65%  n] v]nf8Lx?sf ;DaGwdf / 430 hgfn] b'j}sf af/]df cWoog u/]sf] kfOof] . olb 8%  n] s'g} sf] af/]df klg cWoog u/]sf] kfOPg eg] M

In a survey of the group of students, it was found that 70% of students studied   about scientists, 65% about players and 430 studied about both scientists and players. If 8% did not study about scientists and players, then,

i)           dflysf] tYofªsnfO{ e]glrqdf k|:t't ug{'xf];\ .

     Represent the above information in a Venn-diagram.

ii)         ;j{]If0fdf efu lnPs]f hDdf ljBfyL{;ª\Vof kQf nufpg'xf];\ . 

     Find the total number of students who took part in the survey.

11.       dxQd ;dfkjt{s lgsfNg'xf];\ . (Find the H.C.F of):

 and 

12.       xn ug{'xf];\ . (Solve) : 5^x-1 + 5^-x = 1

13.     ;/n ug{'xf];\ . (Simplify):-         

14.   b'O{ cÍsf] s'g} Pp6f ;ª\Vof, Tof] ;ª\Vofsf] cª\sx¿sf] of]usf] rf/ u'0ff 5 . olb Tof] ;ª\Vofsf] cª\sx¿sf] :yfg abn]/ aGg] ;ª\Vof / 9 sf] of]ukmn] pQm ;ª\Vofsf] b'O{ u'0ff x'G5 eg], ;f] ;ª\Vof kQf nufpg'xf];\ .

A two digit number is four times the sum of its digits. If the sum of the number formed by reversing its digits and 9 is two times the original number, find the original number.

15.       olb tn lbOPs]f cfFs8fsf] dWos 68 eP x sf] dfg kQf  nufpg'xf];\ .

If the mean of the following data is 68, find the value of x.

Marks obtained -k|fKtfÍ_	40-50	50-60	60-70	70-80	80-90	90-100
No.of students  -ljBfyL{sf] ;+Vof_	17	22	28	26	x	12

16.       Pp6f gbLsf] lsgf/df ePsf] 40 ld6/ cUnf] ¿vsf] 6'Kkf]df pQm gbLsf] csf{] lsgf/af6 cjnf]sg ubf{ pGgtf+z sf]0f 30° kfOof] eg] ;f] gbLsf] rf}8fO kQf nufpg'xf];\ .

The angle of elevation of the top of a tree, 40m high situated at the bank of a river when observed from the opposite bank of the river is found to be 30°, find the breadth of the river.

17.       lbOPsf] 7f]; a:t' j]ngf / cw{uf]nf ldn]/ ag]sf] 5 . h;sf] cfwf/sf] Jof; 14;]=ld= / k"/f nDafO 21;]=ld= 5 eg] ;f] 7f]; a:t'sf] k"/f ;txsf] If]qkmn kQf nufpg'xf];\ .

The given solid object is made up of a cylinder and a hemisphere whose diameter of the base is 14cm and total length is 21 cm. Find the total surface area of the solid object.

 

18.       tn lbOPsf ju{ cfwf/ ePsf] lk/fld8sf] k"/f ;txsf]   

If]qkmn lgsfNg'xf];\ .

Find the total surface area of the following

square based pyramid.

19.       A / B n] Pp6f sfd s|dz M 12 / 16 lbgdf ug{ ;S5g\ . A / B b'j}hgf ldn]/ 4 lbg sfd u/]kl5 B n] ;f] sfd 5f]8\5 eg] afFsL sfd ug{ A nfO{ slt lbg nfUnf < kQf nufpg'xf];\ .

A and B can do a piece of work in 12 and 16 days respectively. A and B work together for 4 days and B leaves the work, find how long will A take to complete the remaining work.

20.       Pp6f Sofd/f 25% 5'6 lbP/ 10% d"No clej[l4 s/ nufO{ a]lrof] . olb 5'6 /sd ?= 750 eP pQm Sofd/fsf] d"Nodf d"No clej[l4 s/ /sd slt lyof] kQf nufpg'xf];\ .

A camera was sold after allowing 25% discount on the marked price and then levying 10% value added tax (VAT). If the discounted amount was Rs.750, how much value added tax (VAT) was levied on the price of the camera?

21.       Pp6f ufpFsf] hg;ª\Vof k|To]s jif{ 5 k|ltztn] a9\b} hfG5 . olb b'O{ jif{sf] cGTodf 1025 hgf a;fOF ;/]/ cGoq hfFbf ;f] ufpFsf] hg;ª\Vof 10,000 eof] eg] ;'?df ;f] ufpFsf] hg;ª\Vof slt lyof] <

The population of a village increases every year by 5%. If 1025 people leave the village at the end of two years and the population of the village is 10,000, find the population of the village in the beginning.

22.       Pp6} cfwf/ QR / pxL ;dfgfGt/ /]vfx? QR / PS sf] jLrdf ag]sf lqe'hx¿ PQR / SQR sf] If]qkmn a/fa/ x'G5g egL k|dfl0ft ug'{xf];\ .

Prove that the triangles PQR and SQR standing on same base QR and between same parallel lines QR and PS are equal in area.

23.       ;Fu}sf] lrqdf PT j[Qsf] Jof; xf] / O s]Gb|laGb' xf] olb  rfk SR= rfk RT eP PS//OR.x'G5 egL l;4 ug'{xf];\ .

In alongside diagram, PT is the diameter and O is centre of circle. If  arc SR=arc RT, prove that PS//OR.

24.       Pp6f j[Qsf] pxL rfkdf cfwfl/t kl/lwsf]0fx¿ a/fa/ x'G5g\ egL k|of]u4f/f l;4 ug'{xf];\ . -slDtdf 3;]=ld= cw{Jof; ePsf b'O{ cf]6f j[Qx¿ cfjZos 5g\._ Verify experimentally that the angles at the circumference standing on the same arc of  a circle are equal.(Two circles of radii at least 3 cm are necessary.)

25.       rt'e'{h ABCD sf] /rgf ug'{xf];\ h;df AB=5.8 ;]=ld, BC=6.2;]=ld , CD=5.1;]=ld , DA=4.8;]=ld /  ÐBAD=60° 5g\ .;fy} pQm rt'e'{h;Fu If]qkmn a/fa/ x'g] lqe'hsf] /rgf ug'{xf];\ .

Construct a quadrilateral ABCD in which AB=5.8cm, BC=6.2cm , CD=5.1cm , DA=4.8cm and ÐBAD=60°.also construct a triangle equal in area to the quadrilateral ABCD.