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CBSE Sample Paper-02SUMMATIVE ASSESSMENT –II

MATHEMATICS Class – X

Time allowed: 3 hours Maximum Marks: 90

General Instruct !ns"

a) All questions are compulsory.b) The question paper consists o 3! questions di"ided into our sections # A$ %$ & and '.c) (ection A contains questions o ! mark each which are multiple choice questions$ (ection %

contains * questions o + marks each$ (ection & contains !0 questions o 3 marks each and(ection ' contains !! questions o marks each.

d) ,se o calculator is not permitted.

Sect !n A

!. The probability that two di erent riend ha"e di erent birthdays -i norin a leap year) is:

-a)364

365 -b)

1

365 -c)

1

73 -d)

3

73

+. The centroid o the trian le whose "ertices are ( ) ( )1 1 2 2, , , x y x y and ( )3 3, x y is:

-a) 1 2 3 1 2 3,3 3

x x x y y y+ + + +

-b) ( )1 2 3 1 2 3, x x x y y y+ + + +

-c) 1 2 3 1 2 3,6 6

x x x y y y+ + + +

-d) 1 2 3 1 2 3,4 4

x x x y y y+ + + +

3. /n an A $ i 5, 2.5, 10,na d a= = = then the "alue o n is:

-a) ! -b) + -c) 3 -d) . / in a ∆ A%&$∠ & 1 90 and ∠ % 1 45 , then state which o the ollowin is true:

-a) %ase 1 erpendicular -b) %ase 1 2ypotenuse-c) erpendicular 1 2ypotenuse -d) %ase erpendicular 1 2ypotenuse

Sect !n B

4. /n the i ure$ 5 is the centre o the circle. The area o sector 5A % is5

18 o the area o the circle.

6ind . x

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*. 2ow many shots each ha"in radius 3 cm can be made rom a cubical lead solid o dimensions9 cm x 3* cm x ++ cm7

8. Three cubes o a metal whose ed es are in the ratio 3 : : 4 are melted and con"erted into a

sin le cube o dia onal 24 3 cm. 6ind the ed es o the three cubes.. / ! is a ero o the polynomial ( ) ( )2 3 1 1, p x ax a x= − − − then ind the "alue o .a

9. / the irst term o an A is 4− and the common di erence is +$ then ind the sum o irst !0

terms.

!0. / ,a b and c are the sides o a ri ht an led trian le where c is the hypotenuse$ then pro"e that

the radius r o the circle which touches the sides o the trian le is i"en by .2

a b cr

+ −=

Sect !n C

!!. 6ind the ratio in which the point ( )3, k − di"ides the line se ment ;oinin the points ( )5, 4− −

and ( )2, 3 .− 2ence$ ind the "alue o .k

!+. (how that the points A -!$ +)$ % -4$ )$ & -3$ ) and ' ( )1, 6− are the "ertices o a square.!3. Three horses are tethered at 3 corners o a trian ular plot ha"in sides +0 m$ 30 m$ 0 m with

ropes o 8 m len th each. 6ind the area o the plot which can be ra ed by the horses.22

Use =7

π

! . A rectan le cm x * cm is inscribed in a circle as shown in i ure. 6ind the area o the shadedre ion. ( )Use = 3.14π

!4. A solid iron rectan ular block od dimensions . m x +.* m x ! m is cast into a hollowcylindrical pipe o internal radius 30 cm and thickness 4 cm. 6ind the len th o the pipe.

!*. (ol"e the quadratic equation: 23 2 2 2 3 0 x x− − = !8. The sum o n terms o an A is 23 5 .n n+ 6ind the A and hence ind its !* th term.

8/16/2019 2016 10 Mathematics Sample Paper Sa2 02

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! . A point is !3 cm rom the centre o the circle. The len th o the tan ent drawn rom to thecircle is !+ cm. 6ind the radius o the circle.

!9. The an les o depression o the top and the bottom o a buildin 40 meters hi h as obser"edrom the top o a tower are 30 and 60 respecti"ely. 6ind the hei ht o the tower and the

hori ontal distance between the buildin and the tower. ( )Take 3 1.73= +0. &ards marked with the numbers + to !0! are placed in a box and mixed thorou hly. 5ne card is

drawn rom this box. 6ind the probability that the number on the card is:-i) an e"en number.-ii) a number less than ! .-iii) a number which is a per ect square.

Sect !n #

+!. 'raw a circle o radius 3 cm. 6rom a point 4 cm away rom the centre o the circle$ draw two

tan ents to the circle. 6ind the len ths o the tan ents.++. The an le o ele"ation o the top o a tower as obser"ed rom a point on the round is ' 'α and

mo"in ' 'a meters towards the tower$ the an le o ele"ation is ' '. β ro"e that the hei ht o the

tower istan tan

.tan tan

a α β β α −

+3. A card is drawn at random rom a wells.+0 per litre. ( )Use = 3.14π

+8. (ol"e or : x ( )2 2 0abx b ac x bc+ − − = + . (um o the areas o two squares is * m +. / the di erence o their perimeters is + m$ then

ind the sides o two squares.

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+9. >am asks the labour to di a well up to a depth o !0 m. ?abour char es ` !40 or irst meter and`

40 or each subsequent meters. As labour was uneducated$ he claims`

440 or the whole work.

>ead the abo"e passa e and answer the ollowin questions:

-i)

@hat should be the actual amount to be paid to the labour7-ii) @hat "alue o >am is depicted in the question$ i he pays ` *00 to the labour7

30. The incircle o ∆ A%& touches the sides %&$ &A and A% at '$ = and 6 respecti"ely. (how that:

A6 %' &' 1 A= %6 &= 11

2- erimeter o ∆ A%&)

3!. ro"e that the tan ent at any point o a circle is perpendicular to the radius throu h the pointo contact.,sin the abo"e result$ pro"e the ollowin :A tan ent at a point o a circle o radius 4 cm meets a line throu h the centre o a point so that 5 1 !3 cm. 6ind the len th o .