Assignment

1. CHAPTER -1
Q1. 3 / 8 in decimal form is :
(A) 0.125 (B) 0.0125 (C) 0.0375 (D) 0.375
Q2. Decimal expansion of will be :
(A) terminating (B) non-terminating
(C) non-terminating and repeating (D) non-terminating and non-repeating
Q3. The prime factors of 98 are :
(A) 22
X 7 (B) 23
X 7 (C) 2 X 72
(D) 22
X 72
Q4. Which of the following rational numbers has terminating decimal expansion ?
(A)7/3 (B)3/7 (C)3/5 (D)5/3
Q5. A number N when divided by 14 gives the remainder 5. The remainder when the same number is divided by 7
is
(A) 7 (B) 0 (C) 5 (D) 4
Q6. Which of the following is a rational number ?
(A) √10 (B) √12 (C) √14 (D) √16
Q7. The product of three consecutive positive integers is always divisible by :
(A) 5 (B) 6 (C) 7 (D) 8
Q8. n2
- 1 is divisible by 8 if n is :
(A) an integer (B) natural number (C) an odd number (D) an even interger
Q9. Two positive integers p and q can be expressed as p =ab2
and q = a2
b, a and b being prime numbers. LCM of p
and q is :
(A) ab (B) a2
b2
(C) a2
b3
(D) a3
b3
Q10. (√5 +√2 - √7 ) is
(A) a natural number (B) an integer (C) a rational number (D) an irrational number
Q11. The number
√
√
is
(A) a rational number (B) an irrational number (C) an integer (D) a natural number
Q12. The product of two irrational numbers is :
(A) always a rational number (B) always an irrational number
(C) sometimes a rational number, sometimes irrational (D) not a real number
Q13. The reciprocal of an irrational number is :
(A) an integer (B) rational (C) a natural number (D) irrational
Q14. If „a‟ and „b‟ are two consecutive natural numbers, then H.C.F (a, b) is :
(A) ab (B) a + b (C) 1 (D) 2
Q15. √ 3 + √12 equals
(A) √15 (B) √36 (C)3√ 3 (D)2√ 6
Q16. = is :
(a) a rational number (b) an irrational number (c) a prime number (d) an even number
Q17. A rational number can be expressed as a terminating decimal if the denominator has factors
(A) 2, 3 (or) 5 only (B) 2 (or) 3 only (C) 3 (or) 5 only (D) 2 (or) 5 only
Q18. The least number that is divisible by all the numbers from 1 to 10 is :
(A) 10 (B) 100 (C) 504 (D) 2520
Q19. For q to be an integer, then any integer can be expressed as a = :
(A) 3q+1 (B) 3q, 3q+1, 3q+2 (C) 3q (D) 3q+1, 3q+2, 3q+3
Q20. If q is some integer, then any positive odd integer is of the form :
(A) 6q (B) 6q+1 (C) 6q+2 (D) 6q+4
Q21. The decimal expansion of the rational number will terminate after :
(A) 4 places of decimal (B) 3 place of decimal (C) 2 places of decimal (D) one place of decimal
Q22. Which of the following numbers is a prime number ?

2. (A) 105 (B) 109 (C) 117 (D) 119
Q23. The decimal expansion of 189/125 will terminate after :
(A) 1 place of decimal (B) 2 places of decimal (C) 3 places of decimal (D) 4 places of decimal
Q24. For any positive integer a and 3, there exist unique integers q and r such that a = 3q + r,where r must satisfy.
(a) 0 ≤ r < 3 (b) 1 < r < 3 (c) 0 < r < 3 (d) 0 < r ≤ 3
Q25. The values of x and y in the given figure are :
(A) x= 10 ; y = 14 (B) x = 21 ; y = 84 (C) x = 21 ; y =25 (D) x =10 ; y =40
Q26. The HCF of the smallest composite number and the smallest prime number is :
(A) 1 (B) 3 (C) 2 (D) 4
Q27. L.C.M. of 23
x 32
and 22
x 33
is
(A) 23
(B) 33
(C) 23
x 33
(D) 22
x 32
Q28. A rational number which has non terminating decimal representation is :
(A) (B) (C) (D)
Q29. The least positive integer divisible by 20 and 24 is :
(A) 240 (B) 480 (C) 120 (D) 960
Q30. If HCF (a, b) = 12 and a X b = 1800, then LCM (a, b) is :
(A) 1800 (B) 900 (C) 150 (D) 90
Q31. Find the HCF of 255 and 867 by Euclid division algorithm.
Q32. Complete the following factor tree and find the composite number x.
Q33. Prove that √5 is irrational and hence show that 3 + √5 is also irrational.
Q34. If = , find the values of m and n where m and n are non-negative integers.
Hence write its decimal expansion without actual division.
Q35. Find HCF of 105 and 1515 by prime factorisation method. Hence find their LCM also.
Q36. Show that any positive odd integer is of the form 8q+1 or 8q+3 or 8q+5 or 8q+7 where q is some integer.
Q37. Prove that 2√3 + √5 is an irrational number. Also check whether (2√3 + √5). ( 2√3 - √5) is rational or
irrational.
Q38. Show that any positive even integer is of the form 4q or 4q + 2 and any positive odd integer is of the form 4q
+ 1 or 4q + 3 where q is any integer.
Q39. The LCM of 2 numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find
the other number.
Q40. Find the largest number that divides 2623 and 2011 and leaves remainders 5 and 9 respectively.
Q41. Use Euclid’s Division Algorithm to find the largest number which divides 957 and 1280 leaving remainder 5 in
each case.

3. Q42. Find the LCM and HCF of 12, 72 and 120 using prime factorisation. Also show that
HCF X LCM ≠ Product of three given numbers.
Q43. Express 1547 as the product of its prime factors.
Q44. Find the HCF and LCM of 404 and 96 and verify HCF X LCM = Product of two given numbers.
Q45. By Euclid division algorithm, show that square of any positive integer is of the form 3n or 3n+1.
Q46. Prove that n2
- n is divisible by 2 for every positive integer n.
Q47. Show that the number 4n
, when n is a natural number cannot end with the digit zero for any natural number,
n.
Q48. Using Euclids division algorithm, find whether the pair of numbers 847, 2160 are coprimes or not.
Q49. Find the value of x, y, and z in the following factor tree. Can the value of 'x' be found without finding the value
of y and z , if yes, explain :
Q50. Prove that 4- 3 √2 is an irrational number.
Q51. Express the number 0.3178""""" the form of rational number a/b .
Q52. The HCF of 65 and 117 is expressible in the form 65 m - 117. Find the value of m. Also find the LCM of 65 and
117 using prime factorization method.
Q53. Use Euclid division algorithm to find HCF of 210 and 55. If HCF is expressible in the form of 210 x + 55y ,find x
and y.
Q54. Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer.
Q. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will
they next toll together.
Q55. Prove that one of every three consecutive positive integers is divisible by 3.
Q56. Explain why 7X13X11+11 and 7X6X5X4X3X2X1+3 are composite numbers.
Q57. 144 cartons of coke cans and 90 cartons of pepsi cans are to be stacked in a canteen. If each stack is of the
same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack
would have ?

4. CHAPTER -2
Q1. The zeroes of the polynomial p(x) = 4x2
– 12x +9 are
(A) 3/2 , 3/2 (B) -3/2, -3/2 (C) 3, 4 (D) -3, -4
Q2. The maximum number of zeroes that a polynomial of degree 3 can have is :
(A) One (B) Two (C) Three (D) None
Q3. If - 1 is a zero of the polynomial f (x) = x2
- 7x - 8, then the other zero is :
(A) 6 (B) 8 (C) - 8 (D) 1
Q4. The product and sum of the zeroes of the quadratic polynomial ax2
+ bx + c respectively are :
(A) –b/a , c/a (B)c/b , 1 (C)c/a, b/a (D)c/a, -b/a
Q5. The polynomial whose zeroes are - 5 and 4 is :
A) x2
- 9x – 20 (B) x2
+ x -20 (C) x2
- 5x +4 (D) x2
+ 5x – 4
Q6. The number of zeroes that the polynomial f(x) = (x - 2)2
+ 4 can have is :
(A) 1 (B) 2 (C) 0 (D) 3
Q7. If ∝ $%& ' are the zeroes of the polynomial 2x2
+ 5x + 1, then the value of ∝ '+ ∝ + ' is :
(A) -2 (B) -1 (C) 1 (D) 3
Q8. If the sum of the zeroes of the quadratic polynomial 3x2
- kx + 6 is 3, then the value of k is :
(a) 9 (b) 3 (c) - 3 (d) 6
Q9. The number of zeroes of a cubic polynomial is :
(A) more than 3 (B) atmost 3 (C) only 3 (D) None
Q10. If the zeroes of a quadratic polynomial are equal in magnitude but opposite in sign then :
(A) sum of its zeroes is 0 (B) product of its zero is 0
(C) one of the zero is 0 (D) there are no zeroes of the polynomial
Q11. If y = p(x) is represented by the given graph, then the number of zeroes are :
(A) 4 (B) 3 (C) 2 (D) 1
Q12. The number of zeroes lying between -2 and 2 of the polynomial f (x) whose graph is given below is :
(A) 2 (B) 3 (C) 4 (D) 1
Q13. If p, q are zeroes of polynomial f(x)= 2x2
-7x + 3, find the value of p2
+q2
.
Q14. Find the quadratic polynomial whose zeroes are √2 and 2√2 .
Q15. Find the polynomial whose zeroes are 5 +√19 and 5 -√19
Q16. Write the quadratic polynomial whose zeroes are -4/5 and 1/3 .
Q17. If ∝ $%& ' are zeroes of the polynomial x2
- 6x + a , find a if ' =- 2.
Q18. Find the perimeter of a square whose diagonal is 3√2 cm.
Q19. If p(x)= 8x2
- 9x + 9, find the difference between the sum of its zeroes and the product of its zeroes.
Q20. Find the zeroes of the polynomial 4t2
- 5.
Q21. For what value of h is the polynomial f (x) =2 x3
- hx2
+ 5x + 9 exactly divisible by (x +2).
Q22. If one zero of the polynomial p(x) = (a2
+ 9) x2
+ 45x + 6a is reciprocal of the other, find the value of a.
Q23. If one zero of the polynomial ax2
+bx+c is double of the other, then show that 2b2
=9ac.
Q24. Find the value of „p‟ for which the polynomial p(x) = 2x3
+ 9x2
– x - p is exactly divisible by g(x)=2x+3.
Q25. If the sum of the zeroes of the polynomial p(x) = (a + 1)x2
+ (2a + 3)x + (3a + 4) is - 1, then find the product of
its zeroes.

5. Q26. Form a quadratic polynomial whose one zero is 8 and the product of the zeroes is - 56.
Q27. Find the values of a and b so that 8x4
+ 14x3
- 2x2
+ ax + b is exactly divisible by 4x2
+3x- 2.
Q28. If ∝ $%& ' are the zeroes of the polynomial p(x) = x2
- 5x + 6, find a quadratic polynomial whose zeroes are
∝
(
$%&
(
)
Q29. If the sum and product of the zeroes of the polynomial ax2
- 5x + c is equal to 10 each, find the value of „a‟
and „c‟.
Q30. If ∝ $%& ' are the two zeros of the polynomial 21x2
- x - 2. Find a quadratic polynomial whose zeros are
2∝ $%& 2 ' .
Q31. For what value of k, the number - 4 is a zero of the polynomial x2
– x - (2k + 2). Also find the other zero.
Q32. Show that ½ and -3/2 are the zeroes of the polynomial 4x2
+ 4x -3 and verify the relationship between zeroes
and co-efficients of polynomial.
Q33. Show that 3 is a zero of the polynomial 2x3
– x2
- 13x - 6. Hence find all the zeroes of this polynomial.
Q34. Check by division whether x2
- 2 is a factor of x4
+ x3
+ x2
- 2x - 3.
Q35. Find the zeroes of the quadratic polynomial f(x) = abx2
+ (b2
- ac)x - bc.
Q36. Find the value of b for which (2x+3) is a factor of 2x3
+9x2
-x-b.
Q37. If m and n are the zeroes of the polynomial 3x2
+ 11x - 4, find the value of
*
+
+
+
*
Q38. What must be subtracted or added to p(x)=8x4
+14x3
-2x2
+8x-12 so that 4x2
+3x-2 is a factor of p(x)?
Q39. If the polynomial x4
- 6x3
+ 16x2
- 25x + 10 is divided by (x2
- 2x + k) the remainder comes out to be x + a, find k
and a.
Q40. Find the other zeroes of the polynomial x4
- 5x3
+ 2x2
+ 10x - 8 if it is given that two of its zeroes are - √2 and
√2 .
Q41. If one zero of a polynomial 3x2
- 8x + 2k + 1 is seven times the other, find the value of k.
Q42. If ∝ $%& ' are the zeroes of a quadratic polynomial such that ∝ + ' =24 and ∝ − ' =8. Find the quadratic
polynomial having ∝ $%& ' as its zeroes. Verify the relationship between the zeroes and coefficients of the
polynomial.
Q43. On dividing the polynomial 2x3
+ 4x2
+ 5x +7 by a polynomial g(x), the quotient and the remainder were 2x and
7 - 5x respectively. Find g(x).
Q44. If the zeroes of the polynomial x2
+ px + q are double in value to the zeroes of 2x2
- 5x - 3, find the value of p
and q.
Q45. Show that one zero of 8x2
- 30x + 27 is the square of the other.
Q46. If ∝ $%& ' are the zeros of the polynomial 6y2
- 7y - 2, find a quadratic polynomial whose zeros are
1/∝ $%& 1/' .
Q47. Given that x - √5 is a factor of the polynomial x3
– 3√5 x2
– 5x + 15√5, find all the zeroes of the polynomial.
Q48. If ∝ $%& ' are the two zeroes of f(x)= 2x2
- 4x + 6, find a quadratic polynomial whose zeroes are
)
(
$%&
(
∝
Q49. If (x - 2) is a factor of x2
+ ax+ b and a – b = 2 find the values of a and b.
Q50. If ∝ $%& ' are the zeroes of the quadratic polynomial f(x)= 3x2
- 5x - 2, then evaluate
(i) ∝ + ' (ii) ∝ + '
Q51. If ∝ $%& ' are zeroes of the quadratic polynomial x2
- 7x + a, find the value of a when 3 ∝ +4 ' = 24 .

6. CHAPTER-3
Q1. If x=a cos>, y=b sin>, then b2
x2
+ a2
y2
– a2
b2
is equal to
(A) 1 (B) -1 (C) 0 (D) 2ab
Q2. The value of sin2
600
- sin2
300
is
(A) (B) (C) (D) -
Q3. The maximum value of sin > is :
(A) 1/2 (B)
√
(C) 1 (D) 1/ √2
Q4. The value of ?@AB C
− @AD C
E is
(A) 11 (B) 0 (C) 1/ 11 (D) - 11
Q5. If A, B and C are interior angles of a ∆ ABC, then tan?
G H
E equals :
(A) sin
I
(B) cos
I
(C) cot
I
(D) tan
I
Q6. tan > is not defined when > is equal to :
(A) 0 (B) 30 (C) 60 (D) 90
Q7. If ∆ PQR is right angled at Q, then cosec(P + R) is :
(A) 1 (B) 0 (C) ½ (D) √3/2
Q8. If tan > = cot > , then the value of sec > is :
(A) 2 (B) 1 (C)2/ √3 (D) √2
Q9. If tan(A + B)= √3 and tan(A - B)= 1/√3 where A and B are acute angles, then :
(A) A = 2B (B) 2A = B (C) A = 3B (D) 3A = B
Q10. If x = 2sin2
> and y = 2cos2
> + 1 then x + y is :
(A) 2 (B) 3 (C) 1 (D)1/2
Q11. 3sin2
20 - 2tan2
45 + 3sin2
70 is equal to :
(A) 0 (B) 1 (C) 2 (D) -1
Q12. sin(45 + > ) - cos(45 - > ) is equal to :
(A) 2 cos > (B) 0 (C) 2 sin> (D) 1
Q13. If A + B = 90 ; sin A = 3/4, then sec B is :
(A)3/4 (B)4/3 (C)1/4 (D)1/3
Q14. If AB=BC=a units and AC= √2 a units be the sides of a triangle ABC, then the measure of angle B is :
(A) 45 (B) 30 (C) 60 (D) 90
Q15. In the given figure, if AB =14 cm, then the value of tan B is :
(A)4/3 (B)14/3 (C) 5/3 (D)13/3
Q16. Given that sin > = $/J, then tan > is equal to :
(A)
L
√M L
(B)
M
√M L
(C)
L
√L M
(D)
M
√L M
Q17. Maximum value of
NOP C
, 00
< > < 900
is :
(A) 1 (B) 2 (C) ½ (D)1/ √2
Q18. If tanx = sin45 cos45 + sin30 then x equals :
(A) 45 (B) 90 (C) 30 (D)1/2

7. Q19.
NQRS
PTNS
is :
(A)
PTNS
NQRS
(B)
PTNS
NQRS
(C)
NQRS
PTNS
(D)
PTNS
PTNS
Q20.
DU@ G
@ADU@ G
equals :
(A) -sec2
A (B) tan4
A (C) -tan4
A (D) 1
Q21. The value of
2 tan30
1+ V$%230
(A) sin60 (B) cos60 (C) tan60 (D) sin30
Q22. If tan > + cot > = 5, then the value of tan2
> + cot2
> is :
(a) 23 (b) 25 (c) 27 (d) 15
Q23. If 5 tan > = 4, then the value of
NQR C PTNS
NQR C PTNS
is
(A) 0 (B) 1 (C)1/7 (D)2/7
Q24. If cosec > – cot > = ¼ , then the value of cosec > + cot > is :
(A) 4 (B)1/4 (C) 1 (D) – 1
Q25. If 2 cos2
?
G
E = 1, then A is :
(A) 90 (B) 45 (C) 30 (D) 60
Q26. If sec 2A = cosec(A - 27) where 2A is an acute angle, then the measure of A is :
(a) 35 (b) 37 (c) 39 (d) 21
Q27. (1+ tan2
> )cos2
> is equal to :
(A) sin2
> - cos2
> (B) sec2
> (C) 1 (D) sin2
>
Q28. If 5 tan2
> - 5 tan > – 1 = 0, then the value of 5 tan > - cot > is :
(A) 5 (B) -5 (C) 0 (D) 1
Q29. If A is an acute angle of a ABC, right angled at B, then the value of sinA + cosA is :
(A) equal to one (B) greater than one (C) less than one (D) equal to two
Q30. If 3x = sec > and 3/x = tan > then 9 ?W − X
Eis equal to :
(A) 9 (B) 3 (C)1/9 (D) 1
Q31. If sinA= √3/2, find the value of 2cot2
A-1.
Q32. If > be an acute angle and 5 cosec > =7, then evaluate sin > + cos2
> −1
Q33. Express sinA and secA in terms of cotA.
Q34. If sinx + cosy = 1 ; x = 30 and y is acute angle, find the value of y.
Q35. Express cot 85+ cos 75 in terms of trigonometric ratio of angles between 0 and 45.
Q36. Find the value of the following without using trigonometric tables :
PTN
NQR
+
(YTNOP – [R )
[R
− tan12 tan78 . sin90
Q37. Evaluate :
a)
^OP .NQR PTN .PTNOP
√
([R .[R .[R )
(D_+ D_+ )
b) 2cosec2
30 + 3sin2
60 – ¾ tan2
30
c)
PTN
D_+
−
@AD . @ADU@ . @AD
(BM+ . BM+ . BM+ . BM+ . BM+ )
d)
PTN NOP [R
NQR PTN
E) sec41 . sin49 + cos49 . cosec41 - √
tan20 tan60 tan70 - 3(cos2
45 - sin2
90)
F)
PT[( S )NQR( S)
NQRS
+
PT[
[R
- ( cos2
20 + cos2
70)
G)
NOP PT[
PTNOP [R
+ 2 sin2
38 . sec2
52 - sin2
45

8. H)
@AD ( C) @AD ( C)
BM+( C)BM+( C)
+ `abc`(75 + >) − sec (15 − >)
I) 3?
[R
PT[
E - 2 ?
NQR
PTN
E + 2 cot21 cot13 cot77 cot69
J)
[R PTN NOP PTN
PTNOP NOP PT[
K) (cos2
25+ cos2
65) + cosec > . sec(90- > ) - cot > . tan(90 - > )
L)
DU@ ( C) @AB C
(D_+ D_+ )
−
@AD BM+ BM+
(DU@ @AB )
M)
[RS PT[( S)NOPS PTNOP( S ) NQR NQR
[R [R [R [R [R
N)
PTN PTN
NOP PT[
+
PTNOP PT[ .[R
[R .[R .[R
Q38. If sin3 > =cos(> - 60
), where 3 > and > - 60
are both acute angles, find the value of >.
Q39. If √3 tan > =3 sin > , then find the value of sin2
> - cos2
> .
Q40. If sin > = 1/3 , find the value of 2 cot2
> + 2
Q41. Find the value of cos2 > if 2 sin2> = √3.
Q42. If sin > + cos > = m and sec > + cosec > =n, then prove that n(m2
- 1) = 2m
Q43. If tan > = 4/3, show that d
D_+C
D_+C
=
Q44. If √3 sin > − cos > = 0 and 0 < > < 90, find the value of >.
Q45. If √3 cot2
> - 4cot > +√3 = 0, then find the value of cot2
> +tan2
>
Q46. If x = r sinA cosC ; y = r sinA sinC and z = r cosA, prove that r2
= x2
+ y2
+ z2
Q47. Prove that (sinA +secA)2
+ (cosA + cosecA)2
= (1 + secA cosecA)2
Q48. If cosec > = 13 / 12 , then evaluate
D_+C @ADC
D_+C @ADC
Q49. Prove that :
a)
[R C NQR C
[R C NQR C
=
NOP C
NOP C
b)
( BM+ G)@ABG
@ADU@ G
= tanA
c)
DU@C BM+C
BM+C DU@C
=
@ADC
D_+C
d)
@ABC
@ADU@C
+
@ADU@C
@ABC
= 2 bc`>
e)
[Re
NOPe
+
[Re
NOPe
= 2cosecA f)
@ADC
BM+C
+
D_+C
@ABC
= (`ab> + bg%>)
g)
NOPe
NOPe
=
D_+ G
@ADG
h)
@AD C D_+ C
@ADC D_+C
+
@AD C D_+ C
@ADC D_+C
= 2
i)
NQRS PTNS
NQRS PTNS
+
NQRS PTNS
NQRS PTNS
=
D_+ C
=
@AD C
j) d
DU@C
DU@C
+ d
DU@C
DU@C
= 2`abc`>
k) ?V$%> +
@ADC
E + ?V$%> −
@ADC
E = 2 ?
D_+ C
D_+ C
E l) (secA-tanA)2
(1+sinA) = 1-sinA
m) sec2
> - cos2
> = sin2
> (sec2
> + 1) n)
BM+ C
@AB C
= ?
BM+C
@ABC
E
o) sin6
> + cos6
> = 1 - 3 sin2
> cos2
> p) (cosec > - cot > )2
=
PTNS
PTNS
q) (1 + cotA - cosecA)(1 + tanA + secA) = 2. R)
PTN( S ). PTNS
BM+C
+ `ab (90 − >) = 1
s)
D_+C
@ABC @ADU@C
= 2 +
D_+C
@ABC @ADU@C
t) -1 +
D_+G D_+( G)
PT[ ( G)
= - sin2
A
u) (1 –sin > + cos >)2
= 2(1 + cos >)(1 – sin >)
v) 2 sec2
> – sec4
> - 2 cosec2
> + cosec4
> = cot4
> - tan4
>
w) sin2
> . tan > + cos2
> . cot > + 2 sin > cos > = tan > + cot >
x) sin8
> –cos8
> = (sin2
> – cos2
>)(1 -2 sin2
> cos2
>)

9. y)
@ADU@G @ABG
−
D_+G
=
D_+G
−
@ADU@G @ABG
z)
D_+C
D_+C
= (bc`> − V$%>)
i) d
DU@C BM+C
DU@C BM+C
=
NQRS
PTNS
ii)
@ABC
BM+C
+
BM+C
@ABC
= (1 + `aV> + V$%>)
iii)
D_+C @ADC
D_+C @ADC
=
DU@C BM+C
iv)
( D_+C) ( D_+C)
@AD C
= 2 i
D_+ C
D_+ C
j
Q50. If sec A = 17 / 8 , verify that :
D_+ G
@AD G
=
BM+ G
BM+ G
Q51. If 15 tan2
> + 4 sec2
> = 23, then find the value of (sec > + cosec > )2
- sin2
>
Q52. In a ABC, angle C = 90, AB = 26 units. AC = 10 units and angle ABC = >.
(i) Verify the identity 1 + cot2
> = cosec2
>
(ii) Evaluate sec > - tan >
Q53. If 2(cos2
45 + tan2
60) - x(sin2
45 – tan2
30) = 6, find the value of x.
Q54. If cosec > + cot > = p, then prove that cos > =
k
k
Q55. Find the value of tan 30 geometrically.
Q56. If cos (A + B) = 0 and sin ( A - B) = 1/ 2, then find the value of A and B where A and B are acute angles.
Q57. An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
Q58. In an acute angled triangle ABC, if sin (A + B - C )= 1/2 and cos (B + C - A ) = 1/√2, find A, B and C.
Q59. In a rectangle ABCD, AB=20 cm and angle BAC=60. Find the measure the side BC and diagonals AC and BD.
Q60. If 4 sin > = 3, find the value of x if d
@ADU@ C @AB C
DU@ C
+ 2`aV> =
√
X
+ `ab>
Q61. Find the value of x if 4 ?
DU@ @AB
E − sin 90 + 3V$% 56 . V$% 34 =
X
Q62. If A + B= 90, prove that d
BM+G BM+H BM+G @ABH
D_+G DU@H
−
D_+ H
@AD G
= V$%m
Q63. If cosec ∝ =5 /4, verify that
[R∝
BM+ ∝
=
D_+∝
DU@∝
Q64. If
@AD)
@AD(
= n and
@AD)
D_+(
= %, show that (m2
+ n2
) cos2
' = n2
.
Q65. If x sin3
> + y cos3
> = sin> cos > and x sin > = y cos > prove that x2
+ y2
= 1
Q66. ABC is a right triangle, right angled at C. If A= 300
and AB=40 units, find the remaining two sides and angle B of
triangle ABC.
Q67. If sec(4 > + 40) = cosec >, where > and (4 > + 40) are acute angles, find > .
Hence show that sin2
(2 > + 10)+ cos2
(5 > - 20)= 1
Q68. If A, B and C are interior angles of a triangle, prove that
(i) cosec2 I
– tan2 G H
= 1 (ii)tan
H I
= cot
G
Q69. Using the formula sin(A - B) = sinA cosB - cosA sinB, find the value of sin15.
Q70. In ∆ABC right angled at A, if AB=24 cm and AC=7 cm, find all trigonometric ratios of angle B and verify the result
sec2
B - tan2
B = 1.
Q71. If sin > = 3/5 , evaluate o
@ADC
p
qr s
@ABC
t
Q72. In the given figure, BD=CD. Calculate (i)
[R ∠euv
[R ∠eYv
(ii)
[R ∠uev
[R ∠Yev

10. CHAPTER-4
Q1. In the given figure if ∆ ABC ~ ∆PQR
The value of x is :
(A) 2.5 cm (B) 3.5 cm (C) 2.75 cm (D) 3 cm
Q2. ∆DEF ~ ∆ABC ; If DE : AB = 2 : 3 and ar(∆DEF) is equal to 44 square units, then area (∆ABC) in square units is :
(A) 99 (B) 120 (C)176 / 9 (D) 66
Q3. If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm, then EF is equal to :
(A) 12 cm (B) 4 cm (C) 16 cm (D) 8 cm
Q4. If in ∆ABC, AB = 6 cm and DEIIBC such that AE = 1/4 AC, then the length of AD is :
(A) 2 cm (B) 1.2 cm (C) 1.5 cm (D) 4 cm
Q5. The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ=9 cm, then AB
equals :
(A) 6 cm (B) 10 cm (C) 15 cm (D) 24 cm
Q6. ABC is an isosceles triangle right angled at C, then :
(A) AB2
=2 AC2
(B) AC2
=2 AB2
(C) BC2
=AB2
(D) AC2
=AB2
Q7. If in the given figure AB ||ED, then ∆ABC and ∆DEC are :
(A) similar (B) congruent (C) both isosceles (D) neither similar nor congruent
Q8. ABC and BDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ABC
and BDE is :
(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4
Q9. If ∆ABC ~ ∆PQR, then y + z equals : Q10. In the given figure, DE II AC. Which of the following is
true ?
(A) 2 + √3 (B) 4+ 3√3 (A) x =
M L
Mx
(B) y =
MX
M L
(C) 4 + √3 (D) 3 + 4√3 (C) x =
Mx
M L
(D)
X
x
=
M
L
Q11. In the figure given below, length of AD is :
(A) 10 cm (B) 26 cm (C) 24 cm (D) 25 cm
Q12. Altitude of an equilateral triangle of side ‘a’ is :
(A) a/2 (B) (√3/4)a2
(C) (√3/2) a (D) a

11. Q13. If the given figure ∆AEC and ∆CBD are equilateral triangles. ∆ABC is right angled at B. If AB= 3cm, BC=4cm
then ar (∆AEC) : ar (∆BDC) is.
(A) 3 :4 (B) 4 :5 (C) 16 : 25 (D) 25 : 16
Q14. In the given figures, find the measure of ∠X.
Q15. AD is an altitude of an equilateral triangle ABC. On AD as base another equilateral triangle ADE is constructed.
Prove that ar(ADE) : ar(ABC) = 3 : 4.
Q16. In the given figure, OA X OB = OC X OD. Q17. In the given figure, ABCD is a rectangle in which
Show that ∠A = ∠C and∠ B =∠ D segment AP and AQ are drawn such that
∠ APB= ∠ AQD = 300
. Find the length of (AP + AQ).
Q18. In the given triangle PQR, ∠QPR= 900
, Q19. In the given figure, if ABIIDC, find the value of x.
PQ=24 cm and QR=26 cm and in ∆ PKR,
∠PKR=900
and KR= 8 cm find PK.
Q20. In the given figure, ∠ADC= 90. Q21. In the given figure, DEIIBC. If DE : BC = 3 : 5, find
Prove that AC2
=AB2
+BC2
+2.BC.BD.
y(∆euz)
y([y{.vYzu)

12. Q22. In the given figure, in ABC, D and E are the Q23. In the given figure, XYIIAC in triangle ABC
two points on side AB such that AD=BE. and it divides the triangle into two parts of equal area.
If DP||BC and EQ||AC, prove that PQ||AB Find
G
GH
Q24. In the given figure, AD I BC and BD = 1/3 CD. Q25. In the given figure, in a triangle PQR,
Prove that 2AC2
= 2AB2
+ BC2
ST||QR and
|}
}~
= and PR=28 cm, find PT.
Q26. In the given figure, AD is an altitude of ∆ABC Q27. In the given figure, DE is parallel to OB
in which ∠A is obtuse and AD =10cm. and DF is parallel to OC.
If BD =10cm and CD =10√3cm , Show that EF is parallel to BC.
Determine ∠ A, AB and AC.
Q28. O is any point inside a rectangle ABCD. Prove that OB2
+ OD2
= OA2
+ OC2
Q29. Prove that the sum of squares on the sides of a rhombus is equal to sum of squares on its diagonals.
Q30. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of
one of its altitudes.
Q31. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their medians.
Q32. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ABE ~
∆CFB.
Q33. In a triangle ABC, P is the mid point of BC and Q is the mid point of AP. If BQ is produced to meet AC at R,
prove that RA= 1/3 AC.
Q34. ABCD is a rectangle, points M and N are on BD such that AM I BD and CN I BD prove that BM2
+ BN2
= DM2
+
DN2
Q35. CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC~ ∆PQR prove that
(i) ∆AMC~ ∆PNR (ii)
I•
ۥ
=
GH
|~
Q36. In the given figure, O’ is a point in the interior Q37. In the given figure, G is the midpoint of the side
of the triangle ABC. OD, OE, OF are the perpendiculars PQ of ∆PQR and GHIIQR. Prove that H is the mid
drawn to sides BC, CA and AB respectively. point of the side PR of the triangle PQR.
Show that AF2
+ BD2
+ CE2
= AE2
+ CD2
+ BF2

13. Q38. Sides AB and BC and median AD of a ∆ABC are respectively proportional to sides PQ, QR and median PM of
another ∆PQR. Show that ∆ABC ~ ∆PQR.
Q39. E is a point on side CB produced of an isosceles triangle ABC with AB =AC. If AD I BC and EF I AC, prove that
GH
zY
=
G‚
ƒ„
Q40. The sides AB and AC and the perimeter P1 of ∆ABC are respectively three times the corresponding sides DE and
DF and the perimeter P2 of ∆DEF. Are the two triangles similar ? If yes, find
y(∆evY)
y(∆DEF )
Q41. In the given figure, PA, QB and RC are Q42. In the given figure, D, E, F are points on OA, OB,
perpendiculars to AC. Prove that 1/x = 1/y + 1/z OC respectively such that DE is parallel to AB
and DF is parallel to AC. Show EF is parallel to BC.
Q43. D, E, F are respectively the mid-point of the sides AB, BC and CA of ∆ ABC. Find the ratios of the area of ∆DEF
and ∆ABC.
Q44. In a quadrilateral ABCD, ∠ B = 90. If AD2
= AB2
+ BC2
+ CD2
, prove that ∠ACD = 90.
Q45. If the areas of two similar triangles are equal, then prove that they are congruent.
Q46. Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 : 25. Find the ratio of their
corresponding heights.
Q47. If the altitudes of two similar triangles are in the ratio of 2 : 3 then find the ratio of their areas and also the
ratio of their corresponding medians.
Q48. If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium.
Q49. In the given figure, P and Q are points on the sides Q50. In the given figure, PQR is a triangle right angled at
AB and AC respectively of ∆ABC, such that AP = 3.5 cm Q and XYIIQR. If PQ=6 cm, PY=4 cm and
PB = 7 cm ; AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC. PX : XQ= 1 : 2.Calculate the lengths of PR and QR.
Q51. In the given figure
|G
G~
=
|H
H€
. Q52. In the given figure, ABC is a triangle
If the area of ∆PQR is 32 cm2
, in which∠A=∠B and AD = BE. Prove that DEIIAB.
then find the area of the quadrilateral AQRB.

14. Q53. In the given figure, if ABCD is a trapezium Q54. In the given figure, ABC is a triangle, right angled at B
in which ABIICDIIEF, then prove that
ez
ƒ‚
=
H„
„I
and BD I AC. If AD = 4 cm and CD = 5 cm, find BD and AB.
Q55. In the given figure, two triangles ABC and DBC Q56. In the given figure, if AD I BC, prove that
lie on same side of BC such that PQIIBA AB2
+CD2
=BD2
+AC2
and PRIIBD. Prove that QRIIAD.
Q57. In the given figure, CDIILA and DEIIAC. Q58. In the given figure, ABC and DBC are two triangles
Find the length of CL if BE = 4 cm and EC = 2 cm. on the same base BC. If AD intersects BC at O,
Show that
y(evY)
y(uvY)
=
eˆ
‚‰
Q59. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of
one its altitudes.
Q60.Through the midpoint M of the side CD of a Q61. In the given figure,
~€
~}
=
~Š
|€
and∠ 1= ∠ 2,
parallelogram ABCD, a line BM is drawn intersecting show that ∆PQS ~ ∆TQR
AC in L and AD produced in E. Prove that EL = 2BL
Q62. In the given figure, BL and CM are medians of Q63. In the given figure, DB I BC ; DE I AB and AC I BC.
a triangle ABC right angled at A. Prove that Prove that
vz
‚ƒ
=
eY
HI
4(BL2
+ CM2
) = 5BC2

15. Q64. In ∆ABC, P and Q are the points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that
median AD drawn from A to BC bisects PQ also.
Q65. The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the
side BC. Prove that DF X EF = FB X FA
Q66. In ∆ABC, if BD I AC and BC2
= 2AC.CD, then prove that AB = AC.
Q67. In a ∆ABC, if BD I AC and AC2
- AB2
= BC2
, prove that BD2
= AD X DC.
Q68. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove AE2
+ BD2
=
AB2
+ DE2
Q69. Prove that the area of the equilateral triangle described on one side of a square is half the area of the
equilateral triangle described on its diagonal.
Q70. In the given figure PQ II BA ; PR II CA. Q71. In the given figure,
‹^
}~
=
|Š
Š€
and ∠PST = ∠PRQ
If PD = 12 cm. Find BD X CD. Prove that PQR is an isosceles triangle.
Q72. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their
corresponding sides.
Q73. If a line segment intersects sides AB and AC of a ∆ABC at D and E respectively and is parallel to BC, prove that
eu
GH
=
Gƒ
GI
Q74. The diagonals of a trapezium ABCD, in which ABIIDC intersect at O. If AB= 2CD, then find the ratio of areas of
triangles AOB and COD.
Q75. ∆ABC is right angled at B and D is the mid-point of BC. Prove that : AC2
= 4AD2
- 3AB2
and AC2
= AD2
+ 3CD2
Q76. In an equilateral ∆ABC, AD I BC. Prove that 3AB2
= 4AD2
Q77. In the given figure, AB = AC. E is a point on CB Q78. In the given figure, PQR is a right triangle
produced. If AD is perpendicular to BC and EF right angled at Q and QS I PR. If PQ=10 cm,
perpendicular to AC. Prove that ∆ABD ~ ∆CEF. PS=8 cm, find the measure of QS, RS and QR.
Q79. In a right triangle ABC with∠C = 90. If p is the length of a perpendicular drawn from C on AB and BC = a, AC =
b and AB = c then show that :
(i) pc = ab (ii)1/p2
= 1/a2
+ 1/b2

16. CHAPTER-5
Q1. If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4, then the respective values of a and b are :
(A) 3, 5 (B) 5, 3 (C) 3, 1 (D) -1, -3
Q2. The point of intersection of the lines represented by 3x-2y=6 and the y-axis is :
(A) (2, 0) (B) (0, -3) (C) (-2, 0) (D) (0, 3)
Q3. x = 2, y = 3 is a solution of the linear equation :
(A) 2x + 3y – 13 = 0 (B) 3x + 2y – 31 = 0 (C) 2x - 3y + 13 = 0 (D) 2x + 3y+ 13= 0
Q4. If a pair of linear equations is consistent, then the lines represented by these equations will be :
(A) parallel (b) coincident always (C) intersecting (or) coincident (D) intersecting always
Q5. Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14. The equation of the second
line can be :
(a) 3x + 4y = 14 (b) 8x + 6y = 28 (c) 12x + 9y = 42 (d) - 12x = 9y
Q6. The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have a solution if :
(A) k =5 (B) k =10 (C) k ≠10 (D) k ≠ 5
Q7. If the pair of linear equations 2x + ky = 7 and 3x - 9y = 12 is consistent and independent, then the value(s) of k are :
(A) 6 (B) all real numbers except 6 (C) - 6 (D) all real numbers except -6
Q8. The graph of the polynomial f(x) = 2x - 5 is a straight line which intersects the x-axis at exactly one point namely :
(A)? , 0E (B)?0, E (C) ? , 0E (D) ? , E
Q9. If ad ≠ bc, then the pair of linear equaWons ax + by = p and cx + dy = q has :
(A) no solution (B) infinitely many solutions (C) unique solution (D) exactly 2 solutions
Q10. The lines represented by the equations a1x+b1y+c1=0 ; a2x+b2y+c2=0 are parallel if :
(A)
M
M
=
L
L
=
@
@
(B)
M
M
≠
L
L
(C)
M
M
≠
L
L
≠
@
@
(D)
M
M
=
L
L
≠
@
@
Q11. The pair of equations x = 4 and y = 3 graphically represents lines which are :
(A) parallel (B) intersecting at (3, 4) (C) coincident (D) intersecting at (4, 3)
Q12. The value of k for which the pair of equations 4x - 5y = 5 and kx + 3y = 3 is inconsistent, is :
(A)12/5 (B) -12/5 (C) -3 (D) 1
Q13. Using graph, find whether the pair of linear equations 3x-5y=20, 6x-10y+40=0 is consistence or inconsistent.
Write its solution.
Q14. Solve for x and y :
X
−
x
= 1
X
+
x
= 2 , where x≠ 1, y ≠ 2
2(3x - y) = 5xy ; 2(x + 3y) = 5xy
3x + 2y = 9xy ; 9x+ 4y = 21xy ; x, y ≠ 0.
X
M
+
x
L
= 2 , ax – by = a2
– b2
Q15. Solve the following pair of equations graphically :
2x + 3y + 4 = 0 ; 2x - 3y – 8 = 0
Also shade the region formed by the lines with the x- axis.
Q16. For what values of p and q will the following pair of linear equations has infinitely many solutions ?
4x + 5y= 2 ; (2p + 7q)x +(p + 8q)y = 2q – p + 1
Q17. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and the breadth is
increased by 3 units. The area is increased by 67 square units if length is increased by 3 units and breadth is
increased by 2 units. Find the perimeter of the rectangle.
Q18. The sum of digits of a two-digit numbers is 7. If the digits are reversed, the new number decreased by 2
equals twice the original number. Find the number.
Q19. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km
downstream in 9 hours. Find the speed of the boat in still water and that of the stream.
Q20. The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the
sum of the ages of his children. Find the age of the father.
Q21. A two digit number is obtained by either multiplying the sum of digits by 8 or then subtracting 5 or by
multiplying the difference of digits by 16 and adding 3. Find the number.

17. Q22. When a two digit number is divided by the sum of the digits, the quotient is 8, and remainder is zero. If the
tens digit is diminished by 3 times the units digit, we get 1. Find the number.
Q23. The ratio of incomes of two persons is 11 : 7 and the ratio of their expenditures is 9 : 5. If each of them
manages to save Rs. 400 per month, find their monthly incomes.
Q24. A woman has 60 notes in all of Rs. 10 and Rs. 20 denominations. If the total worth of the notes is Rs. 850, find
out how many notes of each kind does she have ?
Q25. A and B are two points 150 km apart on a highway. Two cars start with different speeds from A and B at the
same time. If they move in the same direction, they meet in 15 hours but if they move in the opposite directions
they meet in one hour. Find their speeds.
Q26. A fraction becomes 9/11 , if 2 is added to both its numerator and the denominator. If 3 is added to both its
numerator and the denominator, it becomes 5/6. Find the fraction.
Q27. 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys.
How long would it take for one man alone and one boy alone to do it ?
Q28. There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in
each room becomes same. If 20 candidates are sent from room B to A, the number of students in room A becomes
doubles the number of students in room B. Find the number of students in each room.
Q29. A bird flying in the same direction as that of the wind, covers a distance of 45 km in 2 hours 30 minutes. But it
takes 4 hours 30 minutes to cover the same distance when it flies against the direction of the wind. Ignoring
conditions other than the wind conditions, find (i) the speed of the bird in still air (ii) the speed of the wind.
Q30. Draw the graphs of the following pair of linear equations :
4x - 3y – 6 = 0 ; x + 3y – 9 = 0
Determine the co-ordinates of the vertices of the triangle formed by the lines represented by these equations and
the y-axis.
Q31. For what value of k will the pair of equations have no solution ?
3x+y=1 and (2k-1)x+(k-1)y=2k+1
Q32. Find the value of • $%& ' for which the following pair of linear equations has infinite number of solutions :
2x + 3y = 7 2 • x + (• + ')y = 28
Q33. Solve the following pair of equations for x and y
M
X
−
L
x
= 0
M L
X
+
L M
x
= $ + J
ax + by = 3ab ; a2
x + b2
y = a + b
133x + 87y= 353 and 87x+ 133y= 307
ax + by =
M L
3x+ 5y = 4
X
+
x
= Ž − 2
X
+
x
= x – 1
Q34. Find whether the following pair of linear equations has a unique solution. If yes, find the solution.
7x - 4y = 49 ; 5x - 6y = 57
Q35. Solve the following pair of equations for x and y, also find the value of ‘m’ such that y = mx + 2.
x +
x
= 5 2x -
x
= 6
Q36. On selling a tea set at 10% loss and a lemon set at 20% gain a shop keeper gains Rs. 60. If he sells tea set at 5%
gain and lemon set at 5% loss he gains Rs. 10. Find the cost price of the Tea set and the lemon set.

18. CHAPTER-6
Q1. The class mark of the class 10 – 25 is :
(A) 17 (B) 18 (C) 17.5 (D) 15
Q2. If the „less than‟ type ogive and „more than‟ type ogive intersect each other at (20.5, 15.5),then the median of
the given data is :
(A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5
Q3. Relationship among mean, median and mode is :
(A) 3 Median = Mode + 2 Mean (B) 3 Mean = Median + 2 Mode
(C) 3 Mode = Mean + 2 Median (D) Mode = 3 Mean - 2 Median
Q4. The mean and median of a data are respectively 20 and 22. The value of mode is :
(A) 20 (B) 26 (C) 22 (D) 21
Q5. Mode is the value of the variable which has :
(a) maximum frequency (b) minimum frequency
(c) mean frequency (d) middle most frequency
Q6. In a statistical data, the difference between mode and mean is k times the difference between median and
mean then the value of k is :
(A) 3 (B) 4 (C) 5 (D) 6
Q7. The abscissa of the point of intersection of the “less than type” and of the “more than type” cumulative
frequency curve of a grouped data is :
(A) mean (B) median (C) mode (d) half of the total frequency
Q8. A data has 13 observations arranged in descending order. Which observation represents the median of data ?
(A) 7th
(B) 6th (C) 13th
(D) 8th
Q9. The time (in seconds) taken by 50 athletes to run a 110 m hurdle race are tabulated below:
Time (in seconds) 13.8 – 14 14 – 14.2 14.2 – 14.4 14.4 – 14.6
Number of athletes 2 14 16 18
The number of athletes who completed the race in less than 14.4 seconds is :
(A) 2 (B) 16 (C) 32 (D) 50
Q10. Consider the following frequency distribution :
Monthly Income (Rs) Number of families
More than or equal to 10000 100
More than or equal to 13000 85
More than or equal to 16000 69
More than or equal to 19000 50
More than or equal to 22000 33
More than or equal to 25000 15
The number of families having income range form Rs 16000 to Rs 19000 is
(A) 15 (B) 16 (C) 17 (D) 19
Q11. In an arranged series of an even number of 2n terms the median is :
(A) nth
term (B) (n + 1)th
term (C) Mean of (n)th
term and (n+1)th
term (D) ?
+
E
B•
term
Q12. The median class for the following data is :
Class 20 – 40 40 – 60 60 – 80 80 – 100
Frequency 10 12 20 22
(A) 20 - 40 (B) 40 – 60 (C) 60 – 80 (D) 80 – 100
Q13. Median of a data is 52.5 and its mean is 54, use empirical relationship between three measures of central
tendency to find its mode.
Q14. In the following data, find the values of p and q. Also find the median class and modal class.
Class 100 – 200 200 – 300 300 – 400 400 – 500 500 – 600 600 – 700
Frequency 11 12 10 q 20 14
Cumulative 11 p 33 46 66 80
frequency
Q15. Find the sum of lower limit of median class and the upper limit of modal class :
Classes : 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
Frequency : 1 3 5 9 7 3

19. Q16. Find the unknown entries a, b ,c, d in the following distribution of heights of students in a class :
Height to in cm 150 – 155 155 – 160 160 – 165 165 – 170 170 – 175 175 - 180
Frequency 12 a 10 c 5 2
Cumulative 12 25 b 43 48 d
frequency
Q17. Form the cumulative frequency table from the following data :
Marks less than 10 less than 20 less than 30 less than 40 less than 50
Number of students 2 12 37 57 60
Write the frequencies of the classes (20 – 30) and (30 – 40)
Q18. Convert the following data into more than type distribution :
Class : 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80
Frequency : 2 8 12 24 38 16
Q19. Find the mean and mode of the following frequency distribution :
Class : 0 – 6 6 – 12 12 – 18 18 – 24 24 – 30
Frequency : 7 5 10 12 6
Q20. If the mean of the following distribution is 27, find the value of p :
Class : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Frequency : 8 p 12 13 10
Q21. Draw ‘less than’ and ‘more than’ ogives for the following distribution :
Scores : 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
Frequency : 8 10 14 12 4 2
Hence find they median. Verify the result through calculations.
Q22. Find the value of f1 from the following data if its mode is 65 :
Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120
Frequency 6 8 f1 12 6 5
where frequency 6, 8, f1 and 12 are in ascending order.
Q23. Find the unknown entries a, b, c, d, e and f in the following distribution and hence find their mode.
Height : 150–155 155–160 160–165 165–170 170–175 175–180 Total
(in cm)
Frequency : 12 b 10 d e 2 50
Cumulative : a 25 c 43 48 f
frequency
Q24. The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Find the
values of „p‟ and „q‟ :
Classes : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
Frequency : 5 p 20 15 q 5
Q25. Calculate the median for the following distribution :
Marks obtained Below 10 Below 20 Below 30 Below 40 Below 50 Below 60
Number of students 6 15 29 41 60 70
Q26. Find the mean of the following data.
Class less than 20 less than 40 less than 60 less than 80 less than 100
Frequency 15 37 74 99 120
Q27. Construct a frequency distribution table for the data given below :
Daily wages : Below 200 Below 400 Below 600 Below 800 Below 1000 Below 1200
No. of workers : 10 50 130 270 440 500
Q28. Compute the median for the following data :
Marks Number of students
more than or equal to 70 0
more than or equal to 60 11
more than or equal to 50 23
more than or equal to 40 43
more than or equal to 30 58
more than or equal to 20 72
more than or equal to 10 82