maths question papers for revision for tenth class ap board

8/3/2019 maths question papers for revision for tenth class ap board

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TENTH CLASS A.P . S.S.C BOARD SYLLUBUS:

NO OF REVISION TESTS : 18

NO OF GRAND TEST AS PARTS: 4

NO OF PRE FINALS :2

EXAM CHAPTER NO:

M1X STATEMENTS

M2X FUNCTIONS

M3X POLYNOMIALS OVER INTEGERS 1 TO 4EXERSICES

M4X POLYNOMIALS OVER INTEGERS 5 TO 8EXERSICES

M5X COMPLETE : POLYNOMIALS OVER INTEGERS

GT1X 1 TO 3 CHAPTERS

M6X LINEAR PROGRAMING

M7X REAL NUMBERS

M8X PROGRESSIONS 1TO 4 EXERSICES

M9X PROGRESSIONS 1TO 4 EXERSICES

GT2X 4 TO 6 CHAPTERS

M10X ANALYTICAL GEOMETRY 1 TO 2EX

M11X ANALYTICAL GEOMETRY 3 TO 4EX

M12X Trignometry 1 TO 3 EXERSICES

M13X Trignometry 4 TO 7 EXERSICES

M14X COMPUTING

GT3X 8 ,9, 12 CHAPTERS

M15X GEOMTERY

M16X MATRICES 1 TO 2EX

M17X MATRICES 3 TO 4EXM18X STASTICS

GT4X 7, 10 11 CHAPTERS

PRE FINAL I

PRE-FINAL II

PREPARED BY:

T. JAGADEESHWAR 9642321222


2/31

AVANTHI HIGH SCHOOLHUNTER ROAD HNK

REVSION TEST M1

DATE : 23 .10 .2011 (MOR.)

SUB: MATHEMATICS MAX.MARKS:30

1.ANSWER THE FOLLOWING : 5X1=51.write the inverse and contra positive of the following statement- If two triangles are congruent , then

they are similar .

2.Write in set- builder form, A= { -3,-2,-1,0,1,2,3 }

3.If n(AUB) =51, n(A)= 20 , n(B) =44; Find the value of n(A B)4.Show that (A

)= A

5.Write the symbols for universal quantifier and existential quantifier.

II.ANSWER THE FOLLOWING : 4X2 =8

6.Show that ( ~p ) v (p q) (pq)7.write the truth table for p

(

~q)

p

8.Define Direct proof . prove that: If x is even then x2

is even

9.Using element wise proof , show that A B = A B

III.ANSWER THE FOLLOWING : 3X4 =12

10.At a social sports club with 290 member s ,it was found that 120 played tennis,110 played tennikoit,

130 played badminton; 70 played both tennis and tennikoit; 55 played tennikoit and badminton ; 60 played

tennis and badminton . it was also discovered that 75 members had joined only for the social side of the

club and did not play any of the three games . how many played all the three games.

11.Show that A ( B U C ) = ( A B ) ( A C)12.Prove A

(B U C ) = (A

B) U (A

C)

IV. CHOOSE THE CORRECT ANSWER : 5X = 2

1.p v p = p , this is ______ law

A) commutative B) Idompotent C) associtative D) Identity

2.The complement ofA) B) C) A D) A3.If A B then A U B =A) A B) C) B D) 4.p v(q r) = (pvq) (pvr) isA) commutative B) distributive C) de-morgans D) Identity

5. (AUB) = ?A) A

UB

B) A

B C) A- B D)A- B

V.FILL IN THE BLANKS: 5X = 2

6.If two sets A and B are disjoint , then n(AU B) = __________

7.If A B and B A then _____________8. ( AU B) ( B U A) = _______

9.Denial of the statement is called as ___________

10.The truth value of If 3+2 =5 then 1x0 =0 is ___________

*******


3/31


REVSION TEST M2

DATE : 27 .10 .2011 (MOR.)


1.ANSWER THE FOLLOWING : 5X1=5

1.f={(1,2),(3,4),(5,2),(7,4)} , g = { (2,11),(6,11),(4,13),(8,13} find gof.

2.Express the meaning of composite function (gof)

3.If f(x) = ,find f(0), f(1),

4.Define onto function.

5.f: R R ; f(x) = ax+b ; a,b R .Find f-1 .


6. If f: R R is defined by f(x) = show that f(

)= x for x=1

7. If f(x) =x+2 ; g(x) = x2

x-2 ;find

8. f(x)= ; show that f(x) +f(

) = 0

9. If y = f(x) = , then prove that f(y) = x


10.Let f,g,h be functions defined by f(x) = x+2, g(x) =x , h(x) = x2

find (hog)of = ho(gof)..

11. f: R R. defined by f(x) =2x+3 ; then find i)f-1 (4) ii){f-1(x) : 2 x 3} iii) f-1(x) : x 512.Let f,g,h be functions defined by f(x) = x, g(x) =1- x , h(x) = x +1 find i) (hog)of ii) ho(gof).

iii)what do you conclude


1.f(x) =x2+2x-k and if f(2)=8 ; then k=

A)1 B) 2 C) 0 D)3

2. Let f(x)=x2; g(x)=3x+2 then fog(2)=

A)64 B) 12 C) 14 D)16

3.If f is a function from A to B , then f is a subset of =

A) f(a) B) BX A C) AXB D) AXA

4.f(x) = 2x-3 , then zero of the function is

A) 3/2 B) 0 C) -3/2 D) 2/35. If f:R R , f(x) = 2x-3 , then f(x+1) =A) 2x-1 B) x-3 C) 2x-3 D)x-1


6. f: A B to be a function ad if f(x1)=f(x2) x1=x2 then f is _____________7. The range of constant function is ________

8. If f(x) =x+1 then 3.f(2)-2.f(3)=________

9. f={(1,2),(2,2)(3,2)} then range of f= ___________

10. f={(1,4),(3,2), (4,3) then f-1

(4) = _________

*******


4/31


REVSION TEST M3

DATE : 30 .10 .2011 (MOR.)SUB: MATHEMATICS MAX.MARKS:30

I.ANSWER THE FOLLOWING : 5X1=5

1. Write the conditions if x-1 and x+1 are the factors of f(x).

2. Find the sum and the product of the roots of the equation 2x2

-6x +9 =0.

3. Expand a2 (b2 c2 ).4. Write the quadratic equation whose roots are 3+5 ; 3- 5 .5. Find the remainder when 3x

3-2x

2+x+2 is divided by (x-1) .

II.ANSWER THE FOLLOWING : 4X2 =86. The product of two consecutive odd numbers is 143 . find them.

7. Find the value of m in order that x4

2x3

+3x2

mx +5 may be exactly divisible by (x-1)

8. State and prove remainder theorem.

9. The product of two consecutive numbers is 72 . find them.


10. The expression ax2

+ bx +c equals -2 when x =0 . leaves the remainder 3 when divided by (x-1)

and a remainder -3 when divided by (x+1) .Find a, b and c .

11. Factorise : x4+ 5x

3+ 5x

2-5x-6

12. A play field is 100 m by 60 m , has a foot path all around it on the outside .What should be the width ofthe path , if its area be 3/5 of the area of the play field .


1. One of the roots of the equation X2-2x-1 =0

A) -1 B) 3-1 C) 2-1 D)2+12. The quadratic equation whose roots are 2+3 , 2- 3A) x

2+4x+1 B) x

2- 4x+1 C) x

2- 4x+1 D) x

2+4x-1

3.If x-2 isa factor of x-2 then f(2) = ____

A) 0 B) -2 C) 2 D)

2

4.if x +1 is a factor of ax2 +bx +c, then

A) a+b+c =0 B) a+b =c C) a+c =b D) b+c=a

5. If x2- 4x+3 =0 ; x

2- 5x+k =0 have a common root then k=

A) 3,6 B) 4,6 C) 1,4 D)1,3


6. The product of the roots of 4x2

= 1 is______

7. The roots of px2+qx+r=0 are equal then ________

8. If (x-y) is a factor of xn-y

n,then n is _____

9. If f(b/a) =0 ,then the factor of f(x)= _____

10. If the sum of the coefficients of a polynomial is zero ,then ________ is a factor

*******


5/31


REVSION TEST M4

DATE : 02 .11 .2011 (MOR.)



1. Find the middle terms of the expansion ! # $%

2. Find the 4th

term of the expansion + # $'

3. Expand (2x +3)5


4. Find the independent term of (! )

$

5. using principle of mathematical induction , show that 1 +2 + 3+ . = **


6. Draw the graph ofx2

-5x +6 =0 and find the roots .

7.Using the graph ofy = x2

; solve the equation x2

x -6 =0


1. If (2,k) lies on the parabola y=2x -3 then k=

A) -1 B) 1 C) 2 D) 12.

6

C2 +

6

C4 =A) 25 B) 35 C) 30 D) 20

3.The curve x=my2

lies in ____ quadrant

A) 1 and 2 B) 2 and 3 C) 3 and 4 D) 1 and 4

4.the in equation with solution 1< x< 3 is

A) x2

+4x +3>0 B) x2

-4x +3 0

5. 0 =A) 1 B) 2 C) 3 D)4


6. If x2-x-6


6/31


REVSION TEST M5

DATE : 04 .11 .2011 (eve.)SUB: MATHEMATICS MAX.MARKS:30


1. Find the points where the parabola y= 2x2

+x -1 cuts the x-axis

2. Find the sum and the product of the roots of the equation 3 x2 +9x +63.3. Finds the value of k so that x

3 3x

2+4x +k is exactly divisible by (x-2).


4. Find the number which is less than its square by 132..

5. If a and b are unequal and x2 +ax+b and x2+bx+a have a common factor, show that a+b+1=06. State and prove remainder theorem.


7. Find the middle terms of the expansion ! + $'

8. Factorise : 4x4- 12x

3+ 7x

2+3x-2

9. If f(x) = x2+5x +p ; and Q(x) = x

2+ 3x+q have a common factor , then

i) find the common factor

ii) show that (p-q)2

= 2(3p-5q) .

IV.ANSWER THE FOLLOWING : 1X5=510. Using y=x2

; solve x2

-4x+3 =0

V. CHOOSE THE CORRECT ANSWER : 4X = 2

1. - + 1 =3 , x =A) 8 B) 6 C) 9 D10

2. sum of the binomial coefficients of the expansion of (x+y)4

A) 6 B) 16 C) 4 D) 32

3.If (2x-1) exactly divides ax2+bx+c, then

A) a+2b+4c=0 B) a-b-c=0 C) a+b D) a+b-2c=0

4.the third term in the expansion of (3x-5)

4

isA) 81x4

B) 9x3

.25 C) 54 .25x2

D) 27. 5x3

VI.FILL IN THE BLANKS: 4X = 2

5. If f(4/5)=0 then ______ is a factor of f(x)

6. If xn

yn

is divisible by x+y , then n is _________

7. The quadratic equation whose roots are 2 and -5 is ______ _____

8. If there is no common point for the graphs y=x and y=4x-5 ; then the equation _____ does not

have real roots

*******


7/31


GRAND TEST -1

MATHEMATICS

H.T NO & NAME INVIGILATOR SIGN

CLASS: X

DATE : 08 .11 .2011 (MOR.) PART-A( MAX. MARKS :35) TIME 2 HRS.

SECTION-I 5X2 =10

Note: 1.Answer ANY FIVE questions choosing at least TWO from each group

2.Each question caries 2 marks.

GROUP-A

1.Show that [ p (~q ) ] [ (~p) v q] is a contradiction.2.IfA,B are any two sets , then prove A

B

= B - A.

3. If f: R R is defined by f(x) = .. show that f(.. )= x for x 1..

4. f:RR is defined as f(x) =3x-4 then show that f-1 exists and find the formula for f-1(x)GROUP-B

5. let f(x) =x2+2x+3 ; find

00

6. write the truth table p (~q) p.7. Expand ( 2x + 3y )

5.

8.. Find the value of k so that x -3x +4x+k is exactly divisible by (x-2)

SECTION-II 4X1=4

NOTE: Answer ANY FOUR of the following

Each question carries 1 Mark.

9. Write the Inverse and Converse of the In a triangle ABC If AC > AB then B = C10. A ={ 1.8,27,64,125,216} write the set builder form.

11. If f= { (1,3),(2,5),(3,7)} g= {(3,7),(5,9),(7,10)} find g0f

12.Find the nature of the roots of x2

- 4x +5 =0

13. Expand a2

(b2

- c2)

14. Define on to function


8/31

SECTION-III 4X4=16

NOTE: Answer any FOUR of the following choosing at least TWO from each group.

Each question caries 4 Marks.

GROUP-A

15. Prove A (B C) = ( A-B ) ( A- C).

16. Prove A (B C) = ( A B) (A C)

17. If f(x) =x ; g(x)= 1-x ; h(x)=x+1 find i) (h0g)0f ii)h0(g0f) what do you conclude

18. Factorise x4+ 5x

3+ 5x

2-5x-6

GROUP-B

19.At a social sports club with 290 member s ,it was found that 120 played tennis,110 played tennikoit,130 played badminton; 70 played both tennis and tennikoit; 55 played tennikoit and badminton ; 60 played

tennis and badminton . it was also discovered that 75 members had joined only for the social side of the

club and did not play any of the three games . how many played all the three games.

20. Find the roots of

4 +x =

4 +b.

21. Find the independent term of x . (6x-)

)12

22. f: R R. defined by f(x) =2x+3 ; then find i)f-1

(4) ii){f-1

(x) : 2 x 3} iii) f-1

(x) : x 5.SECTION-IV 1X5=5

NOTE: Answer any ONE of the following

Question carries 5 Marks

23. Using the graph y = x2

solve x2-3x+2 =0; and find the roots.

24. Draw the graph ofy=x2

and x=y2on a graph paper. Find the the intersecting points.

*******


9/31


GRAND TEST -1

MATHEMATICS


CLASS: X PART-B( MAX. MARKS :15) TIME 2 HRS

Note : 1. Each Question carries mark.2. Answers are to be written in the question paper only.3.All questions are to be answered.4.Marks will not be given for over-written , re-written or erased answers.

I . write the CAPITAL LETTER of the correct answer in the brackets provided .

1.~[p (~q)] = [ ]A) ~ p ~q B) ~ p v ~q C) ~ p q D) ~p v q2 A B = [ ]

A)A - B B) C) B A D) 3. .~(p q) = [ ]A)p (~q) B)p q C)~p ~q D)p~q

4. Let f(x)=x2; g(x)=3x+2 then fog(2)= [ ]

A)64 B) 12 C) 14 D)16

5 f(x) = then778 [ ]

A) -1 B) 1 C) 0 D) -2

6. The zero value of the function of f(x)=2x-3 is [ ]

A)3/2 B) 2/3 C) 0 D)14

7. one of the roots of the equation X2-2x-1 =0 [ ]

A) -1 B) 3-1 C) 2-1 D)2+18. If

nC8 =

nC7 then n= [ ]

A)15 B) 56 C) 1 D)0

9. the discriminate of2x2-7x+3=0 [ ]

A)20 B) 24 C) 25 D)26

10. p q is F only when [ ]A)p is F, q is T B) p is F q is F C) p is T q is F D)p is T q is T

II. Fill in the blanks with suitable answers.

11. (p q) = ______________12. The converse of a conditional is equivalent to its __________________

13. ussing appropriate symbols ,the statement either p or not p is rewritten as____________________14. If n(A) =7 n(B) = 5 ; then the maximum number of elements in A B _______

15. f: A A ,f(x) =x this is a ________function

16. y=f(x)=5x ; thenf-1

(x) = ____________________

17. The range of the function f(x)=3 is _____18. The solution set which satisfies the quadratic equation x

2-4x +3= 0 is _____

19. In a pascal triangle each row of coefficients is bounded on both sides by __________________

20. If (x+1) is a factor of ax2+bx+c then __________

15


10/31

III Match the following

(i) Group A Group B

21.f: A B to be a function

And if f(x1)=f(x2) x1=x2 then f is [ ] A) {2}22.f:A B to be a function and if f(x)=f; the f is [ ] B) 13

23.f(x)=x2-3 the f(4)= [ ] C)identity

24.f={(1,2),(2,2)(3,2)} then range of f= [ ] D)one-one

25.n(A)=2 ;n(B)=2 then [ ] E))4

n(AXB)= F)constant

(ii) Group A Group B

26.sum of the roots of6x2-5 [ ] A) III & IV

27.If (x-2)is a factor ofx2-3x+l then k= [ ] B)b-4ac

28.the discriminate ofax2+bx+c=0 [ ] C)r/p

29.The curve y=2x

2

goes through the quadrants [ ] D)0

30.the product of the roots ofpx2+qx+r=o [ ] E)-q/p

F)2

G) I & II

********


11/31


REVSION TEST M6

DATE : 15 .11 .2011 (MOR.)


I.ANSWER THE FOLLOWING : 3X1=31. Maximise the objective function p = O +

P.8 at ( 90 , 105 ) and (150 , 0)

2 .what is meant by linear programming problem

3. What is an Objective function


4. Draw the graphs of the In-equalities x ;y ; x ; x 6 ;y 3 ; y 65. Minimise f=3x+2y, when the vertices of polygon are (0,0),(6,0), (4,21 2V ),(0,5).


6. A Shopkeeper sells not more than 30 shirts of each colour .At least twice as many White ones aresold as green ones .If the profit on the White be Rs.20 and that on green be Rs 25 .How many of

each kind should be sold to give him maximum profit.

7. Maximise f=3x+y subject to constraints x 0 ; y 0 ; 8x +5 y 40 ; 4x+3y 12.


7. Maximise f=2x+3y subject to constraints x 0 ; y 0 ; x + y 5 ; 3x+y 9.8. A sweet shop makes gift packet of sweets combines two special types of sweets A and B which

weigh 7kg. At least 3kg of A and no more than 5kg of B should be used. The shop makes a profit

of Rs15 on A and Rs 20 on B per kg. Determine the product mix so as to obtain maximum profit.


1. the value of an objective function F=x+2y at(0,9) is _______________

A) 0 B) 18 C) 19 D 92. .( -2,3) is in ____________ quadrant

A) 1 B) 2 C) 3 D) 4

3.The point which does not lie in the region 2x -3y > 5 is

A) (1,1) B) (3,-3) C) (-3,1) D) (-3.-1)

4.Find the point minimizing C if C= 20x +25y

A) (100,0) B) (0,100) C) (10,20) D) (50,60)

5. If x>0,y0,y


12/31


REVSION TEST M7

DATE : 18 .11 .2011 (MOR.)


1.ANSWER THE FOLLOWING : 5X1=5

1. Solve x- = -X where x>02. -YZ$

[= x

2; then find p

3. Evaluate : lim. Y\8

. 4. Solve : |2 - 5| = 75. Solve : ^O` ^ < 4


6.Show that -Ycdcd . -cdYcd . -cdcdY = x3 if a+b+c=0.7.Evaluate : lim8

Y

8. If ax=b; b

y=c ; c

z=a ; then show that xyz=1

9. If (64)x

=

.f =22 ; then show that 3x+4y =0III.ANSWER THE FOLLOWING : 3X4 =12

10. If x =0.1 find [ 1-(1-(1- x3

)-1

)-1

]1/3

.

11. If y = 3Z + Z show that 3y3

9y =10

12. If dZ + jdZ + kdZ = 0 ;Then show that (a+b+c)3 =27abc.


1. .lim = ___________A) 0 B) x C) D) 12. . x+

=4 then x-

= ____________

A) 2 B) 1 C) 4 D) 63. If 2

x+3=4

x+1;then value of x=___________

A) 1 B)2 C) 3 D) 4

4.(16)1.25

=

A) 32 B) 64 C) 16 D) 5/45 . If 2 = 16 then x =A) 8 B) 4 C) 2 D)10


6. .If a2

= 0.004 ,then a3=_______________

7. lim . Y`

. = ___________

8. 3 = 81 ; then x = _____________9. |- + 1| 6 _______________10. lim

= ______________

*******


13/31


REVSION TEST M8

DATE : 22.11 .2011 (MOR.)



1.Find the values of x so that -2/7 .x. -7/2 are three consecutive terms of an G.P.2.If the sum of the first three terms of an A.P is 36, find the first term3. Find the sum of First 100 natural numbers.


4. Determine K so that k+2 ,4k-6 and 3k-2 are the three consecutive terms of an A.P.5. The 5th , 8th , and 11th terms of an G.P are p,q,and s respectively .show that q2 =ps6. Which term of the A.P is 10,8,6, is -28.

7. Insert 5 arithmetic means between 4 and 22.8. Find the sum of all the natural numbers between 1 and 100 which are multiples of 3.


9. If the sum of the first n natural numbers is S 1 and that of the squares is S2 and cubes S3 ,show that 9S22 = S3 (1+8S1)

11. Find the sum of n terms of the series 1.3 +3.5 +5.7 + ..12. If 17 times the 7th term of an A.P is equal to 11 times the 11th term .prove that the 18th of the

A.P is zero.

IV. CHOOSE THE CORRECT ANSWER : 5X = 2 1. .if n = x , then n3 =A) x B) x2 C) - D) 2x2. tn = n(n+1) then t3 =A) 9 B) 4 C) 1 D) 123. in the A.P 21,25, 29 ., d= ____A) 2 B)4 C) 3 D) 64.the A.M of a-2 ,a , a+2 is ..A) a B) a-2 C) 4a-3 D) a-15 If a,b,c are in G.P then b/a= ___A) b/c B) a/c C) a/b D)none


6. If 2, 8,4,........ are in G.P then common ratio is ___________7. 7th term in the series 1,-1/2,1/4,....is __8. Ifn=10 then n3= ______9. If there are n arithmetic mean between a and b then common difference =________10. a,a+d,a+2d,....then tn =____________

*******


14/31


REVSION TEST M9

DATE : 24.11 .2011 (Eve.)



1.Find the sum of first 8 terms of 3,6,12.2. Find the sum to infinity of the G.P 5 ,20/7 .80/49 3. Find the sum to 10 terms 1,2/3,4/9 .


4. Insert 4 Harmonic means between 1/12 and 1/42.

5. If g1 ,g2 ,g3, are three geometric means between m and n show that g1 . g3 =g22 =mn6. (2 + 3 @ ) 1 where j =1,2,3,.67. prove A.M , G,M and H.M of a and b are in G.P.8. Determine the 12th term of G.P whose 8th term is 192 and common ratio is 2.


9. Find the sum to n terms of the series 0.5+0.55+0.555+.. n terms11. If (b+c) , (c+a) and (a+b) are in H.P . Show that 1a2 ,

1

b2 ,12 will also be in H.P

12. The A.M , G,M and H.M of two numbers is A,G, H respectively show that A> G> H .

IV. CHOOSE THE CORRECT ANSWER : 5X = 2 1. . geometric mean of 5 and 125 ________A) 125 B) 5 C) 625 D) 25

2 H.M of 2 and 6A) 3 B)4 C) 5 D) 12

3. if n = x , then n3 =A) x B) x2 C) - D) 2x

4. the n th term of a G.P is 2(0.5)n-1 , then the common ratio is ____________A) 1 B) 0 C) 1/2 D) 55 In a G.P. a=2 , s =6 , then r=

A) 4/9 B) 2/3 C) 4/3 D)3/4V.FILL IN THE BLANKS: 5X = 2

6. If tn =

+1 then t2011 =__________7. First term of an A.P is a ; common difference is d then 15th term of H.P is _____________8. The H.M=2, A.M=8 then G.M= ________9. If 1/a,1/b, 1/c are in H.P then b=______10. the common ratio of the G.P , -1/4 ,1/8 ,-1/16 ,........is _____________

*******


15/31


GRAND TEST -2

MATHEMATICS


CLASS: X


SECTION-I 5X2 =10

Note: 1.Answer ANY FIVE questions choosing at least TWO from each group2.Each question caries 2 marks.

GROUP-A

1.If the 8th term of an A.P is 17 and 19th term is 39 Find 25th term.

2.Insert 3 geometric means between 4 and 64.

3. Evaluate lim- -+ 2

-

4. shade the region represented by the in-equation 4x+3y 12

GROUP-B

5 show that lim- 2 [1

-2 1

-(-1)(-2)]

6. .Evaluate : lim-0Q1+-+-2 1

-

7. The 4th term of H.P is 1/9 and the 11th term is 1/23. Find the series.

8. Draw the graphs of the in equalities x 1 , y 1 , x 3 ,y 3SECTION-II 4X1=4



9.Find S of the G.P -3/4 ,3/16 ,-3/64,..

10. Find the values of x so that -2/7 .x. -7/2 are three consecutive terms of an G.P..

11. If 3|-|+5 = 9|-| Show that x = -5 or +5

12. Evaluate lim- 2x+33-+5

13. Define Iso profit line

14. What is meant by open convex polygon.


16/31

SECTION-III 4X4=16



GROUP-A

15. Find the sum of the series 1.2 +2.3 +3.4 +.

16. If ax = by = cz andj =

kj show that

- =

2-

17. A sweet shop makes gift packet of sweets combines two special types of sweets A and B whichweigh 7kg. At least 3kg of A and no more than 5kg of B should be used. The shop makes a profitof Rs15 on A and Rs 20 on B per kg. Determine the product mix so as to obtain maximum profit

18. Insert 5 geometric means between 1/3 and 243.

GROUP-B

19.Find the sum of n terms of the progression 7,77,777,..20. If the sum of the first n natural numbers is S1 and that of the squares is S2 and cubes S3 ,

show that 9S22 = S3 (1+8S1)

21. . If l m n =1 show that1

1++v1 +1

1+v+1 +1

1++1

22. If y = 33 +

1

33 show that 3y3 9y =10

SECTION-IV 1X5=5



23. Maxmise f = 5x+7y subject to the conditions 2x+3y 12 ,3x +y 12 and x 0 and y 0.

24A Shopkeeper sells not more than 30 shirts of each colour .At least twice as many White ones aresold as green ones .If the profit on the White be Rs.20 and that on green be Rs 25 .How many ofeach kind should be sold to give him maximum profit.

*******


17/31


GRAND TEST -2MATHEMATICS





1.Find the point minimizing of C . if C= 20x+25 y [ ]A) (100,0) B) ( 0,100) C) (10,20) D) (50,60)2 The point lies in the half plane x+y


18/31


(i) Group A Group B21.The value of f=2x+y At theintersection Point of x=2 and x=3 [ ] A) -3

22.if x+1 =2 ; then x= [ ] B) 3

23.log-1

- [ ] C)4

24.If the first and 4th terms of as G.Pare 1 and 27 Respectively ,then the [ ] D)7common ratio r=

25.In an A.P ,if 4times of4th term is equal to 5times [ ] E)05th term ___term is zero F) 9th

G)10th


26.The arithmetic mean of 5 and 85 [ ] A) chord

27.The limiting position of a secant of a circle is [ ] B)II & IV

28.If x= -8 ;then | 2| = [ ] C)I & IV

29.The curve x=2y2 goes through the quadrants [ ] D)11

30. n = 66 then n= [ ] E) tangentF)5 or -2G) 45

********


19/31


REVSION TEST M10

DATE : 01.12 .2011 (Morn.)



1.Find the co-ordinates of the centriod of the triangle whose vertices are (-4,4) ,(-2,2)and (6,12).2. Find the x-intercept of the equation 2x+3y-5=03. Find the slope of the line making an angle 150o in the positive direction of x-axis.4. Find the co-ordinates of the center of the circle having the points (9,3) and (1,-1) as the end

points of the diameter.5. Find the slope of the line perpendicular to the line 2x+3y+5=0.


6. In what ratio does P (4,6) divide the joining of A(-2,3) and B(6,7) 7. Find the point on X-axis which is equidistant from(2,3) and (4,-2)..8. Find the co-ordinates of a point P which divides A(2,0) ;B(0,3) internally in the ratio 2:3 .9. In what ratio is the segment joining the points (-3,2) and (6,1) divided by Y-axis.


10. Find the coordinates of the point of trisection of a segment joining A(-3,2) and B(9,5).11. if the triangle formed with A(8,-10) B(7,-3) and C(0,p) is aright angled triangle with

right angled at B .Find p.12. Show that A(-3,-2) B(3,2) and C(-23 ,33 ) form an equilateral triangle. .

IV.FILL IN THE BLANKS: 5X = 2

1.The slope of a line y=5x+3 is __________________2. The line y=mx+c Cuts Y-axis at _____________3.The line y=5 is parallel to _____________4. The slope of X-axis is ______________5.The line y=mx passes through ________________6.The slope of line joining (4,6) and (2,-5) is _________________7.Two lines are parallel , if their slopes are ___________

8. Two lines are perpendicular , then their _____________9. Equation of x-axis is __________________10. Mid point of the line joining A(8,4) , B(6, -2) is ______________

*******


20/31


REVSION TEST M11

DATE : 05.12 .2011 (Morn.)



1.Find the slope of the line parallel to 3x-2y+1=02. Find the line perpendicular to the line 2x-3y=123. Find the slope of the line making an angle 150o in the positive direction of x-axis.4. Find the area of the triangle whose vertices are (3,0); (0,4) and (0,0).5. Find the slope of the line x/a + y/b =1.


6.Find the equation of the line passing through the point (3,5) with slope is 7/3.

7. Find the equation of the line passing through the point (3,4) and is parallel to 2x-3y =11.8. Find the area of the triangle so formed by the axes and line passing through the points

(8,-3) and (-4,12) .9. show that the points are collinear A(1,2) ,B(-3,4) and C(7,-1).


10. Find the equation of the line that cuts off intercepts a and b on x and y-axis such thata+b=3 and ab=2.

11Find the equation of the line perpendicular to the line joining (3,-5) ;(5,7) and passing through(2,-3)

12. Show that A(-3,-2) B(3,2) and C(-23 ,33 ) form an equilateral triangle. .


1.The area of the triangle whose vertices are (0,0) ;(1,0) ;(0,1) is _____________2. The slope of the line y=5 is ________________3.Find the sum of the intercepts made by 3x+4y=12 on the axis ______________.4. ______________________ a French mathematician introduced analytical geometry .5.The equation of the line passing through two points A(x1 ,y1) B (x2 ,y2) is _________________6.The slope of line y= 2x-3 _________________7.The slope of the line joining the points (3,2) and (4,k) is 2 then k= ___________8. The equation of y-axis is ______________________

9. slope intercept form of the equation is __________________10. Intercept form of a line is ______________

*******


21/31


REVSION TEST M12

DATE : 08.12 .2011 (MOR.)



1.Find the value of sin2 30 +cos2 60.2.Express in radian measure: 1353Express the circular measure in sexagesimal measure :

34


4.From the adjoining figure write down the value of secA; tanC ;SecC ;Sec2 C-tan2 C5. Given that 5sinA =3 Find Sec2 A tan2 A6. If tan(A+B) = and tan A =1 .What is the measure of B.

7. Show that cos 60 =1@ @ @ 2 30

1+@ @ @ 2 30.

8. A ladder makes an angle 60 with the floor .Its lower end is at a distance of 3mts from the wall .Find the length of the ladder.


9. Find the value of 32 cot2x4

- 8 sec2x3

+8 cot3x6

11. prove that 4(sin4 300 +cos4 600 )- 3(cos2 450 sin2 900 )= 2

12. Given that 4 cotA =3 ; FindsinA+cosA

sinAcosA .


1. cos xtan = _______________A) cos B) sin C) tan D) 12 cos

z = ___________

A) 2 /3 B) 3 /2 C) 1/2 D) 23. 2700 =___________radians

A)x6

B)2x6

C)3x2

D)2x3

4. .one radian = _____________ degreesA) 45 B) 60 C) 90 D) 1805. 450 = ______________ radiansA)

x4

B)x6

C)x2

D)x3


6. Tan2 500 sec2 500 =_____________7. sin =1/2 then cot =___________8. sin30 + cos 60 = ____________9 . sin90 x cos0 x tan45 =_____________-10 If tan=3/4 then sin= ____________

*******


22/31

AVANTHI HIGH SCHOOL

HUNTER ROAD HNK

REVSION TEST M13

DATE : 10.12 .2011 (Eve.)



1.Show that sec2 +cosec2 = sec2 cosec2 2. Show that

cos1+sin =

1sincos

3. Ifa= xcos + ysin and b= x sin ycos obtain the relation in x and y by eliminating .

II.ANSWER THE FOLLOWING : 3X4 =124. Show that Cos6 +sin6 = 1-3 sin2 cos2 5. prove :

tan+se1tanse+1 =

1+sinos

6. If sec +tan =p ,show that sin = [Y[Y

III.ANSWER THE FOLLOWING : 2X5 =107. An aero plane at an altitude of 2500 mts . observes the angles of depression of opposite points on the two banks

of the river to be 41020 and 52

010 . find the width of the river. (Tan 41

020=0.8795 . tan 52

010 = 1.2877)

8. There are two temples , one on each bank of a river , just opposite to each other, one of the

temples A is 40 mts high. As observed from the top of this temple A , the angles of the depressionof the top and foot of the other temple B are 12.30 and 21.48 respectively .Find the width of theriver and the height of the temple B.


1. cos(A+B) =________________2. sin4200 = _________3. If sin2 = cos3 then cot5 =_________4 x= asec ,y=a tan then x2 -y 2=________

*******


23/31

AVANTHI HIGH SCHOOL

HUNTER ROAD HNKREVSION TEST M14

DATE : 14 .12 .2011 (MOR.)



1.Define Algorithm.

2.What is a Flow Chart.

3. Expand C.P.U.4. What is meant by hard ware.

5. State any four Langauges you have known that are used in computers.


6. Draw the structure of the computer and write in detail.

7. What are the different boxes used in a flow chart? Write their functions in detail.

8. What are the types of operations a computer performs.

9. What is meant by step- wise refinement.


10. Draw a flow chart for solving an equation ax2

+ bx +c = 0 considering all possible cases.

11. Gopal purchased a radio set for Rs.500 and sold it for Rs 600 Execute a flow chart using this data to

determine loss or gain.

12.If P = Rs 1000 ; r=12% then draw the flow cart to calculate the amount for 6 years .


1. Vaccum tubes are used in _________ generation of computers

A) fourth B) First C) Second D) Third

2. Small transistors are used in this generation of computers.

A) fourth B) First C) Second D) Third

3.The language the computer understands is called

A) low level language B) Higher language C) computer language D) understand language

4. a unit that performs arithmetical operations in C.P.U is

A) M.U B) C.U C) A.U D) A.L.U

5. The Unit that gains result from C.P.U is

A) control unit B) Input C) Output D)lowput


6. father of the computer is __________

7. all parts of the computer are controlled by ____________

8 all information is stored in_________ unit of the computer.

9. _____________ were used in fourth generation of computers.10. method of a solving a problem is called _____________

******


24/31


GRAND TEST -3

MATHEMATICS


CLASS: X


SECTION-I 5X2 =10

Note: 1.Answer ANY FIVE questions choosing at least TWO from each group2.Each question caries 2 marks.

GROUP-A

1.Find the value of p , if three points A(p,2); B(-3,4);and C(7,-1) are collinear..2.Find the equation of the line passing through the point (1,-1) and is parallel to 2x-3y=11..3. Find the value of sin55 40 from the table.

Deg/min o 6 12 18 24 30 36 42 48 54 1 2 3 4 555 0.8192 8251 8261 8271 8281 2 3 5 7 8

4. What are the different types of the boxes that are used in Flowchart. Describe their function in

detail.

GROUP-B

5. Prove that sec2 + cosec2 = sec2. cosec26. Find the value of 32 cot2

x4

- 8 sec2x3

+8 cot3x6

7. In what ratio P(4,6) divide the joining of A(-2,3) and B(6,7) .8. What should be kept in mind while writing an Algorithm.

SECTION-II 4X1=4



9.Find the slope of the line perpendicular to 5x-2y+4=010. Find the co-ordinates of the center of the circle having the points (9,3) and (1,-1) as the endpoints of the diameter.

11. x= a sin ; y=cos , Eliminate 12. Convert 2700 into circular measure.13.Define Flow chart.14. What are the essential components of the computer.


25/31

SECTION-III 4X4=16



GROUP-A

15. Find the equation of the line whose slope is 4/5 and which bisects the line joining the pointsp(1,2) and Q(4,-3)

16. If sec +tan =p ,show that sin = 212+1

17. prove :

tan+sec1

tansec+1 =

1+sin

cos 18. Draw a flow chart to find the value of the product of the first n natural numbers..

GROUP-B

19. If the area of triangle formed with the vertices (t,2t);(-2,6); (3,1). Is 5 sq units , then find t.

20. Given sin = 1517

; Evaluate :15ot+1sintan+16sec .

21.Find the equation of the line passing through (4,3) and making intercepts on the co-ordinateaxes whose sum is -1.

22. Write an algorithm and draw a flowchart to pick the largest of the three given numbers.SECTION-IV 1X5=5



23. Two boys are on opposite sides of a tower of 100mts height .They measure the angle of elevationof the top of ther tower as 30 and 45 respectively. Find the distance through which the boys areseparated.

24. The upper part of a tree , broken by wind into two parts, makes an angle of 30 with the ground.The top of the tree touches the ground at a distance of 20mts from the foot of the tree. Find theheight of the tree before it was broken.

*******


26/31


GRAND TEST -3

MATHEMATICSH.T NO & NAME INVIGILATOR SIGN




1.The line 3x+4y=0 intersects y-axis at [ ]A) (0,3) B) ( 0,4) C) (0,0) D) (3,4)2 The point of intersection of the line y=2x+1 and y=3x-2 is [ ]A)(3,7) B) (5,13) C) (4,10) D) (2,5)3. Find the sum of the intercepts made by 3x+4y=12 [ ]A) 4 B) 7 C) 3 D) 24. The slope of the points (-a,a) and (0 ,a+a 3 ) [ ]A) 3 B)1/3 C) 2a D) 05 . If sin(90- )=1 then = [ ]A) 0 B) 45 C) 60 D)906. if sec

+tan

=4 then sec

-tan

[ ]

A) 4 B) 3 C) 1/4 D) 167. sin2 9 +sin2 81 = ________ [ ]A)1 B) 0 C) 1/2 D) 3/28.A type of box used in flow chart is [ ]A)Sector B) Rectangle C) pentagon D)Decagon9. All parts of the computer are controlled by [ ]A) input B) Output C) Memory unit D) C.U

10. vaccum tubes are used in [ ]A) Fourth B)First C) Second D) Third

II. Fill in the blanks with suitable answers .

11. tan X _____________ = sin 12. Cos 360 =______________13. If Cos = 3/2 then sin =________________14. Tan(A+B)= 3 tanA=1 thenB=__________15. The equation of the line passing through (1,1) and (0,0) is _______________16. The line y=mx+c intersects the y-axis at ___17. The slope of the line x/a+y/b=1 is ________18 ._____________- were used in fourth generation of computers19._____________ is a design or plan of obtaining a solution to the problem

20. input,output,cpu are __________ of computer.

15


27/31


(i) Group A Group B21. sec + tan = then sec tan = [ ] A) 1

22. If cos =sin then [ ] B) 223. sec

260 tan

260= [ ] C) 1/2

24.cos 0 sin 90 = [ ] D) x2

25.tan 45 + cot 45 = [ ] E)x

F) 0

G)90

H)45


26 . The equation of the line passing through [ ] A) -3/2A (x1 ,y1 ) B(x2 ,y2 ) is

27. The slope of x/2+y/3=1 [ ] B) (y-y1) =P P (x-x1)

28. The point- slope of equation [ ] C) 1/2

29. The slope of x =2y . [ ] D) 0

30.The slope of x- axis [ ] E) y= mx+c

F) (y-y1) = m(x-x1)

G) (y1-y) = m(x1-x)********


28/31


REVSION TEST M15

DATE : 20 .12 .2011 (MOR.)


I.ANSWER THE FOLLOWING : 2X1=21.Mention the properties of similar triangles.

2.State the alternate segment theorem.


3.In Rhombus ABCD , prove that AB2

+BC2

+CD2

+DA2

= AC2

+BD2

=4 AB2

4.Prove that tangents at the ends of the diameter are parallel.


5. State and prove converse of Pythagorean Theorem.

6.State and Prove basic proportionality Theorem.

7. State and prove Pythagorean Theorem.

IV.ANSWER THE FOLLOWING : 2X5 =10

8. Construct a triangle ABC in which BC=5cm , A =700 and the Median AD=3.5cm9.Construct a cyclic quadrilateral ABCD where AB =3cm ; BC=6cm ; AC=4cm and AD=2cm


1. In ABC, BC2+ AB

2=AC

2,then__________is a right angle

2. If two circles touch internally ,then the number of their common tangents________

3.

ABC PQR; AB=3.6cm,PQ=2.4cm, AC=8.1 ,then PR=____________

4. ABC DEF A=500, B=600 then R=______________

*******


29/31


REVSION TEST M16

DATE : 23.12 .2011 (Morn.)


I.ANSWER THE FOLLOWING : 5X1=51. For a given data mean=39 ,median=38 .find mode.2. Find the arithmetic mean of 2/5 ,5/3, 1/3, 5/6 and 1/6.3. Find the median of the observations. -3,-5,-8,0,3,2,-104. The sum of 15 observations is 420 .find the mean.5. Find the range of first natural numbers.


6 .The median of the data

),

,

,

, x (x > 0 ) Is 8 Find the value of x

7. The mean of 10 observations is 16.3 by an error .One observation is registered as 32 instead of 23 .find correct mean.

8. Write merits of Arithmetic mean9. The mean of 20 observations is 12.5 By an error one observation is registered as -15 instead of 15

Find the correct mean.

III.ANSWER THE FOLLOWING : 3X4 =1210. Find the mean

11. Find medianmarks 0-5 5-10 10-15 15-20 20-25

students 10 18 42 23 7

12. find modemarks 15-24 25-34 35-44 45-54 55-64 65-74

Student 8 20 28 30 10 4


1. The A.M of 10 observations is 7 .The A.M of 15 observations is 12 .Then the mean of allobservations is ____________

2. .If the A.M of 3,5,9,x,11 is 7 then x = _________________3. In a histogram ,the breadths of the rectangles represent the ______________-4. The A.M of first n natural numbers is _____5. The range of the scores 10,18,15,12,13,15 and 16 is ____________6 Father of statistics is ___________7 For the construction of frequency polygon ______________ and frequencies are taken8.The median of 5,10,3,7,2,9,6,2,119. The mid point of the class 40-50 is ______________10. The median of ,1/2,2/3,1/6,7/12 is ___________

*******

c.I 0-9 10-19 20-29 30-39 40-49

frequency 8 15 20 45 12


30/31


REVSION TEST M17

DATE : 27.12 .2011 (Morn.)



1. If 2 56 3 has no multiplicative inverse , find a .2. If the value ofIf 2 5 2 =0 find d3. If A= 1 2 3 then show that A= A-1 4. Define non-singular matrix.

5. If A = 1 1 then find A-1


6. If A = 1 22 3 B= 2 5 3 Find the matrix B + A

-1

7. If B= 1 22 3 Show that B + B-1 =4I


8. A = 1 12 1 ; B = 2 5 3 then show that ( AB)-1 = B-1 A-1

9. Solve by Matrix Inversion method : 7x-2y +5 =0 ; 11x-6y+25 =0

10. Solve by Cramers Method : 2x -3y +6 =0 and 6x +y+8 =011. Solve using matrix inversion method a1 x+b1 y+c1=0 ; a2 x+b2 y+c2=0


1. If j k is a singular matrix then ac=____2. A . A-1 = __________

3. - 63 2- is asingular matrix then x= ______4. If p = 5 k is to be scalar matrix then c = ___________5. ( A-1 )-1 = _________

6.

k k

=__________

7. Matrices is introduced by ____________8. If A y = B then y is called __________9. In solving matrix 3x-2y =1 ; 4x +3y=7 the constant matrix is _____________10. For ___________ matrices Inverse does not exist.

*******


31/31


REVSION TEST M18

DATE : 23.12 .2011 (Morn.)SUB: MATHEMATICS MAX.MARKS:30


1. For a given data mean=39 ,median=38 .find mode.2. Find the arithmetic mean of 2/5 ,5/3, 1/3, 5/6 and 1/6.3. Find the median of the observations. -3,-5,-8,0,3,2,-104. The sum of 15 observations is 420 .find the mean.5. Find the range of first natural numbers.II.ANSWER THE FOLLOWING : 4X2 =8

6 .The median of the data),

,

,

, x (x > 0 ) Is 8 Find the value of x

7. The mean of 10 observations is 16.3 by an error .One observation is registered as 32 instead of 23 .find correct mean.8. Write merits of Arithmetic mean9. The mean of 20 observations is 12.5 By an error one observation is registered as -15 instead of 15Find the correct mean.III.ANSWER THE FOLLOWING : 3X4 =12

10. Find the mean

11. Find medianmarks 0-5 5-10 10-

15

15-

20

20-

25

students 10 18 42 23 7

12. find modemarks 15-

24

25-

34

35-

44

45-

54

55-

64

65-

74

Student 8 20 28 30 10 4


1. The A.M of 10 observations is 7 .The A.M of 15 observations is 12 .Then the mean of all

observations is ____________2. .If the A.M of 3,5,9,x,11 is 7 then x = _________________3. In a histogram ,the breadths of the rectangles represent the ______________-4. The A.M of first n natural numbers is _____5. The range of the scores 10,18,15,12,13,15 and 16 is ____________6 Father of statistics is ___________7 For the construction of frequency polygon ______________ and frequencies are taken8. The median of 5,10,3,7,2,9,6,2,119. The mid point of the class 40-50 is ______________10. The median of ,1/2,2/3,1/6,7/12 is ___________

*******

c.I 0-9 10-

19

20-

29

30-

39

40-

49

frequency 8 15 20 45 12

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maths question papers for revision for tenth class ap board

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