Free Printable CDF 8

1.

A polynomial having one term is called a ----------.

a)

trinomial

b)

binomial

c)

MONOMIAL

d)

multinomial

2.

A polynomial having two terms is called a --------.

a)

trinomial

b)

monomial

c)

binomial

3.

A polynomial having two or more than two terms is called .

a)

multinomial

b)

trinomial

c)

binomial

4.

The highest exponent of the term in the polynomial is called its ....

a)

power

b)

degree

c)

equation

d)

none

5.

A polynomial with degree 1 is called a .................... polynomial.

a)

linear

b)

quadratic

c)

cubic

d)

none

6.

A polynomial with degree 2 is called a .................... polynomial.

a)

linear

b)

quadratic

c)

cubic

d)

none

7.

A polynomial with degree 3 is called a .................... polynomial.

a)

linear

b)

quadratic

c)

cubic

d)

none

8.

The value of a polynomial p(x) at x=a is ............. obtaining by replacing x by a.

a)

1

b)

p(x)

c)

p(a)

d)

a

9.

Number of zeroes of polynomial is equal to the ............... of a polynomial.

a)

exponent

b)

power

c)

1

d)

degree

10.

Algebraic fraction is said to be in its simplest form or in lowest terms if the numerator and denominator have no common factor except .............

a)

1

b)

o

c)

2

d)

3

11.

If p(x) and q(x) are two polynomials then their H.C.F and L.C.M are related as

H.C.F x L.C.M=

a)

p(x) / q(x)

b)

p(x) + q(x)

c)

p(x) x q(x)

d)

p(x) - q(x)

12.

The product of first 'n' natural numbers is denoted by........

a)

n!

b)

1

c)

0

d)

n

13.

What is the formula of Permutation?

a)

$P_r^n=\frac{n!}{\left(n-r\right)!}$

b)

$P_r^n=\frac{n!}{\left(n+r\right)!}$

c)

$P_r^n=\frac{n!}{r!}$

d)

$P_r^n=\frac{n!}{r!\left(n-r\right)!}$

14.

What is the formula of Combination?

a)

$C\ _r^n=\frac{n!}{\left(n-r\right)!}$

b)

$C\ _r^n=\frac{n!}{\left(n+r\right)!}$

c)

$C\ _r^n=\frac{n!}{r!}$

d)

$C\ _r^n=\frac{n!}{r!\left(n-r\right)!}$

15.

Let p(x) be any polynomial of degree greater than or equal to one and 'a' be any real number. When p(x) is divided by (x-a), then the remainder is .....

a)

a

b)

0

c)

p(a).

d)

p(x).

16.

Constant polynomial is an algebraic expression is of the form....................... for some number ‘c’.

a)

1

b)

p(x)=a

c)

p(x)=c

d)

x

17.

Let p(x) be the polynomial of degree n≥1 and 'a' be a real number. If p(a)=0

then......... is a factor of p(x) conversely ............ if (x-a) is factor of p(x).

a)

(x-a), p(a)=0

b)

(x-a), p(x)=0

c)

(x-b), p(a)=0

d)

(y-a), p(a)=0

18.

If f(x), g(x) are two non zero polynomials, then there exist a pair of polynomials q(x) and r(x) uniquely such that ................. where r(x)=0 as degree of r(x) < degree of g(x), q(x) is quotient and r(x) is re- mainder]

a)

f(x) = q(x).r(x)+g(x)

b)

f(x) = r(x)g(x)+q(x),

c)

f(x) = q(x).g(x)+r(x)

d)

f(x) = q(x).g(x)+(x)

19.

$n_{c_x}=n_{c_y}$ then

a)

x=y or x+y=1

b)

x=y or x + y=n

c)

x=y or x+ y=o

d)

none

20.

The general form of the binomial expression is (a + b)ⁿand the expression of

(a + b)ⁿ = ........... n ε N is called the binomial theorem

a)

$\sum_{r=0}^nn_{c_n}a^{n-r}\ b^r$

b)

$\sum_{r=0}^nn_{c_r}a^{n-r}\ b^a$

c)

$\sum_{r=0}^nn_{c_r}a^{n-r}\ b^r$

d)

$\sum_{r=1}^nn_{c_r}a^{n-r}\ b^r$

21.

General term in (a + b)ⁿ is $T_{r+1}=$

a)

$n_{c_n}a^{n-r}\ b^r$

b)

$n_{c_r}a^{n-r}\ b^a$

c)

$n_{c_r}a^{n-r}\ b^r$

d)

$n_{c_r}a^{n-n}\ b^r$

22.

Total number of terms in the expansion of (a + b)ⁿ is ...........

a)

n+3

b)

n+1

c)

n

d)

n+2

23.

In (a+b)ⁿif n is odd, there are two middle terms given by

a)

$T_{\frac{n+1}{2}}and\ T_{\frac{n+3}{2}}$

b)

$T_{\frac{n+2}{2}}and\ T_{\frac{n+1}{2}}$

c)

$T_{\frac{n+1}{2}}$

d)

none

24.

In the quadratic formula, the expression
b²-4ac is called

a)

discrim

b)

determinant

c)

discriminant

d)

none of these

25.

$\sin\ \left(90\degree-A\right)\ =$

a)

sin A

b)

cos A

c)

tan A

26.

$COS\ \left(180\degree-A\right)=$

a)

-cos A

b)

sin A

c)

tan A

27.

Sin ( 90⁰ + A) =

a)

Sin A

b)

Cos A

c)

- Sin A

d)

- cos A

28.

Cos ( 90⁰+ A) =

a)

- cos A

b)

Cos A

c)

SinA

d)

- sin A

29.

If tanθ = Cotθ then the θ =

a)

30

b)

90

c)

45

d)

0

30.

Value of Cosec90° is ?

a)

0

b)

1

c)

Not defined

d)

2

31.

Value of Sec90° is ?

a)

1

b)

0

c)

2

d)

Not defined

32.

cos(90°-A) =.....

a)

cosA

b)

sinA

c)

cosecA

d)

secA

33.

If sin θ = cos θ, then θ is equal to ____

a)

30°

b)

45°

c)

60°

d)

90°

34.

sin 60 =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

35.

tan 60 =

a)

0

b)

1

c)

√3

d)

^√3/₃

36.

If a²+b^{2 =} c², What type of triangle do you have?

a)

Acute

b)

Right

c)

Obtuse

d)

None

37.

$\sec^2x-\tan^2x\ =\ ...$

a)

1

b)

2

c)

-1

38.

$\cot^2x+1=...$

a)

$\sec^2x$

b)

$\operatorname{cosec}^2x$

c)

$\sin^2x$

39.

$\frac{1}{\cot\ x}=\ ...$

a)

cosec x

b)

sec x

c)

tan x

40.

$1-\sin^2x=...$

a)

$\cos^2x$

b)

$\tan^2x$

c)

$\operatorname{cosec}^2x$

41.

$\frac{\sin\ x}{\cos\ x}=...$

a)

tan x

b)

cot x

c)

sec x

42.

$\frac{1}{\cos\ x}=...$

a)

tan x

b)

cot x

c)

sec x

43.

cos (90⁰ - A ) = sec A

a)

TRUE

b)

FALSE

44.

sin B =

a)

1/ cosB

b)

1/cosec B

c)

cosec B

d)

None of the above

45.

$1+\tan^2\theta\ is\$

a)

$\operatorname{cosec}^2\theta$

b)

$\sec^2\theta$

c)

$\cos^2\theta$

d)

$None$

46.

$\cot^2\theta\ \ is\$

a)

$\operatorname{cosec}^2\theta\ -1$

b)

$1+\operatorname{cosec}^2\theta$

c)

$\frac{\cos\theta}{\sin\theta}$

d)

None

47.

$\sin\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{opposite}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

48.

$\cos\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

49.

$\tan\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{opposite}$

d)

$\frac{opposite}{adjacent}$

50.

Q 1The value of Sin30

a)

1/2

b)

1

c)

2

d)

None of these

51.

Q.2 The value of cos60 is

a)

1

b)

1/2

c)

1/√3

d)

None of these

52.

The value of tan 30

a)

1/√3

b)

1/²

c)

1/√2

d)

None of these

53.

The value of Cot 45 is

a)

1/3

b)

1

c)

1/√2

d)

None

54.

Sin 90°=

a)

0

b)

1

c)

1/2

d)

None

55.

$1-Sin^2\theta=?$

a)

$Cos^2\theta$

b)

$Cos\theta$

c)

$Tan\theta$

d)

$Co\sec\theta$

56.

$1+Tan^2\theta=?$

a)

$Cos^2\theta$

b)

$Sin^2\theta$

c)

$Sec^2\theta$

d)

$Sin\theta$

57.

$\frac{\sin\theta}{Cos\theta}$ = ?

a)

$Tan\theta$

b)

$Cot\theta$

c)

$Sec\theta$

d)

$Co\sec\theta$

58.

$Sec\ 45\degree$ $=?$

a)

1

b)

2

c)

4

d)

$\sqrt{2}$

59.

$Tan\ 45\degree=?$

a)

1

b)

2

c)

$\sqrt{2}$

d)

$\frac{1}{2}$

60.

In the quadratic formula, the expression
b²-4ac is called

a)

discrim

b)

determinant

c)

discriminant

d)

none of these

61.

In the quadratic formula, if b²-4ac>0, then the quadratic equation has

a)

two imaginary solutions

b)

two different real solutions

c)

two equal real solutions

d)

none of these

62.

The quadratic equation has degree

a)

0

b)

1

c)

2

d)

3

63.

For a quadratic equation ax²+bx+c=0 if Discriminant is equal to zero, then the roots are

a)

Real and Unequal

b)

Unreal and Unequal

c)

Real and Equal

d)

Real and Distinct

64.

Formula to find the roots of the quadratic equation $ax^2+bx+c=0$ is

a)

$x=\frac{b\pm\sqrt{b^2-4ac}}{2a}$

b)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

c)

$x=\frac{-b\pm\sqrt{b^2+4ac}}{2a}$

d)

$x=\frac{-b\pm\sqrt{b^22a}}{4ac}$

65.

Discriminant of the quadratic equation $ax^2+bx+c=0\ \left(a\ne0\right)$ is

a)

$a^2-4bc$

b)

$b^2+4ac$

c)

$b^2-4ac$

d)

$a^2+4bc$

66.

A quadratic equation $ax^2+bx+c=0$ has non real complex number roots if

a)

$b^2-4ac>0$

b)

$b^2-4ac<0$

c)

$b^2-4ac=0$

d)

$b^2-4ac=1$

67.

If discriminant of a quadratic equation is negative, then roots of the equation are __________.

a)

Distinct Roots

b)

Equal roots

c)

Unequal roots

d)

Non Real , complex and conjugate

68.

what is standard of quadratic equations

a)

A ) ax = b for all a not equal to zero , where a , b are real numbers

b)

B ) ax+ by + c = 0 for all a not equal to zero, a b c are real numbers

c)

C ) a $x^2$ + bx + c = 0 for all a not equal to zero and a, b, c are real numbers

d)

D ) ax + by + c = 0 for all a , b, c not equal to zero

69.

Condition for the

$Equation\ ax^2+bx+c=\ 0\ has\ equal\ roots\$ is......

a)

$b^2-4ac>0$

b)

$b^2-4ac=0$

c)

$b^2-4ac<0$

d)

$None$

70.

If b² - 4ac >0, and perfect square, then roots of ax² + bx + c = 0 are

a)

irrational

b)

imaginary

c)

Rational and Distinct

d)

Equal

71.

What is the formula in finding the SUM of the roots of quadratic equation α+β=

a)

$-\frac{b}{a}$

b)

$\frac{c}{a}$

72.

What is the formula in finding the PRODUCT of the roots of quadratic equation αβ=

a)

$-\frac{b}{a}$

b)

$\frac{c}{a}$

73.

If the value of the discriminant is zero, the nature of the roots is ________

a)

Real and distinct

b)

Real and imaginary

c)

Real and complex

d)

Real and equal

74.

. A quadratic equation whose roots are negative of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(x)=0

b)

f(-x)=0

c)

f(x/2)=0

d)

$None$

75.

A quadratic equation whose roots are the reciprocal of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(1/x)=0

b)

f(-x)=0

c)

f(x/2)=0

d)

$None$

76.

A quadratic equation whose roots are p more than the roots of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(1/x)=0

b)

f(x+p)=0

c)

f(x-p)=0

d)

$None$

77.

A quadratic equation whose roots are p less than the roots of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(1/x)=0

b)

f(x+p)=0

c)

f(x-p)=0

d)

$None$

78.

A quadratic equation whose roots are p' times the roots of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(x/p)=0

b)

f(x+p)=0

c)

f(xp)=0

d)

$None$

79.

A quadratic equation whose roots are square of the roots of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(x/p)=0

b)

f(√x)=0

c)

f(xp)=0

d)

$None$

80.

A quadratic equation whose roots are 1/p times the roots of the equation

$\ ax^2+bx+c=\ 0\$ is

a)

f(x/p)=0

b)

f(x+p)=0

c)

f(xp)=0

d)

$None$

81.

If b=0; then the quadratic equation

$\ ax^2+bx+c=\ 0\$ is is called

a)

Zero quadratic equation

b)

pure quadratic equation

c)

Monic quadratic equation

d)

$None$

82.

If a=1; then the quadratic equation

$\ ax^2+bx+c=\ 0\$ is called

a)

Zero quadratic equation

b)

pure quadratic equation

c)

Monic quadratic equation

d)

$None$

83.

If 'a' is first term and 'd' is common difference of an A.P, then the nth term is given

by a_n=

a)

a+(n)d

b)

a+(n+1)d

c)

a+(n-1)d

d)

a-(n-1)d

84.

What is the formula for finding the value of the $n^{th}$ term of an AP?

a)

$T_n=a-\left(n+1\right)d$

b)

$T_n=d+\left(n-1\right)a$

c)

$T_n=a+\left(n+1\right)d$

d)

$T_n=a+\left(n-1\right)d$

85.

$\sec\left(270\degree-\theta\right)\ =$

a)

$\sec\theta$

b)

$\operatorname{cosec}\theta$

c)

$-\sec\theta$

d)

$-\operatorname{cosec}\theta$

86.

*

a)

sin x

b)

cos x

c)

tan x

d)

csc x

87.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

88.

*

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

89.

tanθ=

a)

1/tanθ

b)

1/sinθ=

c)

1/cscθ=

d)

1/cotθ=

90.

cosec²x-Cot²x =

a)

1

b)

2

c)

-1

d)

0

91.

If a, b, c are in an AP, then 'b' is called arithmetic mean between a and c.

i.e. b=

a)

1

b)

a + c/2

c)

a - c/2

d)

a c/2

92.

If A₁ A₂.............A_n, are 'n' arithmetic means between a and b then the common

difference is d=

a)

$\frac{b-a}{n-1}$

b)

$\frac{b-a}{n+1}$

c)

$\frac{b+a}{n+1}$

d)

1

93.

Formula to find sum of n terms in an AP is ________

a)

sn = a+ (n - 1)d

b)

$s_n$ = $\frac{n}{2}$ (a +(n-1)d)

c)

$s_n$ = $\frac{n}{2}$ (2a +(n-1)d)

d)

$s_n$ = $\frac{n}{2}$ (2a +(n+1)d)

94.

$1+2+3+4+5+.......+n\ =?$

a)

$n\left(n+1\right)$

b)

$\frac{n\left(n+1\right)}{2}$

c)

$\frac{n\left(n+2\right)}{2}$

d)

$\frac{n\left(n+1\right)}{4}$

95.

If the terms of an Arithmetic progression are denoted by T₁, T₂,........T_n then the common difference is

a)

$T_1-T_2=T_3-T_2$

b)

$T_2-T_1=T_2-T_3$

c)

$T_2-T_1=T_3-T_1$

d)

$T_2-T_1=T_3-T_2$

96.

$1^2+2^2+3^2+4^2+5^2+......+n^2=?$

a)

$\left(\frac{n\left(n+1\right)}{2}\right)^2$

b)

$\frac{n\left(n+1\right)\left(2n+3\right)}{6}$

c)

$\frac{n\left(n+1\right)\left(2n+1\right)}{6}$

d)

$\frac{n\left(n+1\right)\left(2n+1\right)}{4}$

97.

If 'a' is first term and is common ratio of G.P then n^th term is given by

a)

$a_n=a.r^{n-1}$

b)

$a_n=r^{n-1}$

c)

$a_n=a.r^{n+1}$

d)

$a_n=a.r^n$

98.

In a G.P, the first term is 'a' and common ratio 'r', then the sum of first 'n' terms

of G.P is S_n = ............; if r> 1

a)

$a\left(\frac{r^n+1}{r-1}\right)$

b)

$a\left(\frac{r^n-1}{r-1}\right)$

c)

$a\left(\frac{1-r^n}{1-r}\right)$

d)

$a\left(\frac{r^n+1}{r+1}\right)$

99.

If a,b,c are in G.P, then b is called geometric mean between a and c. i.e.

b=.........

a)

1

b)

$\sqrt[]{ac}$

c)

$\sqrt[]{ab}$

d)

$\sqrt[]{ar}$

100.

Σ1 = 1+1+1+1+ ...... +n(times) =

a)

n+1

b)

n-1

c)

n

d)

1

101.

In an A.P k^th term from last is equal to (n-k+1)^th term from beginning.

i.e, a_(n-k+1) =

a)

a + (n-k)

b)

a - (n-k)d

c)

a + (n+k)d

d)

a + (n-k)d

102.

. If G, G., G............ are 'n' G.M's between a and b Then the common ratio of G.P is r=

a)

1

b)

$\left(\frac{-b}{a}\right)^{\frac{1}{n+1}}$

c)

$\left(\frac{b}{a}\right)^{\frac{1}{n+1}}$

d)

$\left(\frac{b}{a}\right)^{\frac{1}{n-1}}$

103.

If the first term of an infinite G.P is 'a' and its common ratio is 'r', then the sum to

its infinite terms is S_∞.= ............. where |r|<1

a)

a/1r

b)

a/1+r

c)

a/1-r

d)

1

104.

Formula to find sum of n terms in an AP is ________

a)

$s_n$ = $\frac{n}{2}$ (a -l)

b)

$s_n$ = $\frac{n}{2}$ (a +l)

c)

$s_n$ = $\frac{n}{2}$ (a l)

d)

$s_n$ = $\frac{n}{2}$ (2a +(n+1)d)

CDF 8

Total questions: 104

Worksheet time: 3hrs 36mins

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