Free Printable RUBI THERESA - 10th SAMACHEER MATHEMATICS

1.

If the ordered pairs (a + 2, 4) and (5, 2a +b) are equal then (a,b) is

a)

(2,-2)

b)

(3,-2)

c)

(5,1)

d)

(2,3)

2.

If A = { 1,2} , B= {1,2,3,4}, C= {5,6} and D={5,6,7,8} then state which of the following statement is true

a)

$\left(B\times D\right)\subset\left(A\times C\right)$

b)

$\left(A\ \times B\right)\subset\left(A\times D\right)$

c)

$\left(D\ \times A\right)\subset\left(B\times A\right)$

d)

$\left(A\times C\right)\subset\left(B\times D\right)$

3.

A = { a,b,p}, B = {2,3}, C = {p,q,r,s} then n[(A U C) x B] is

a)

20

b)

12

c)

8

d)

16

4.

If there are 1024 relations from a set A ={1,2,3,4,5} to a set B, then the number of elements in B is

a)

2

b)

3

c)

4

d)

8

5.

Let n(A) =m and n(B) =n, then the total number of non - empty relations that can be defined from A to B is

a)

$2^{mn}$

b)

$m^n$

c)

$n^m$

d)

$2^{mn}\ -\ 1$

6.

If n(A x B) = 6 and A = {1,3} then n(B) is

a)

2

b)

1

c)

3

d)

6

7.

The range of the relation R = {( $x,\ x^2$ ) | x is a prime number less than 13} is

a)

{2,3,5,7}

b)

{2,3,5,7,11}

c)

{4,9,25,49,121}

d)

{1,4,9,25,49,121}

8.

Let A = {1,2,3,4} and B = {4,8,9,10}. A function $f\ :\ A\ \rightarrow B$ given by f={(1,4),(2,8),(3,9),(4,10)} is a

a)

Many - one function

b)

One to One function

c)

Identity function

d)

Into function

9.

If { (a,8), (6,b) } represents an identity function, then the value of a and b are respectively

a)

(8,8)

b)

(6,8)

c)

(6,6)

d)

(8,6)

10.

Let f and g be two functions given by

f= {(0,1), (2,0), (3,-4), (4,2), (5,7)}

g={(0,2), (1,0), (2,4), (-4,2), (7,0)}

then the range of $f\circ g$ is

a)

{0,1,2}

b)

{1,2,3,4,5}

c)

{-4,1,0,2,7}

d)

{0,2,3,4,5}

11.

If $f:\ A\ \rightarrow\ B\$ is a bijective function and if n(B) =7 , then n(A) is equal to

a)

14

b)

49

c)

1

d)

7

12.

If $f\left(x\right)\ =\ 2x^2\$ and $g\left(x\right)\ =\ \frac{1}{3x},\$ then $f\circ\ g$ is

a)

$\frac{3}{2x^2}$

b)

$\frac{2}{9x^2}$

c)

$\frac{2}{3x^2}$

d)

$\frac{1}{6x^2}$

13.

Let $f\left(x\right)\ =\ \sqrt[]{1\ +\ x^2}$ then

a)

$f\left(xy\right)\ =\ f\left(x\right).f\left(y\right)$

b)

$f\left(xy\right)\le f\left(x\right).f\left(y\right)$

c)

$f\left(xy\right)\ge f\left(x\right).f\left(y\right)$

d)

None of these

14.

$f\left(x\right)=\ \left(x+1\right)^3\ -\left(x-1\right)^3\$ represents a function which is

a)

quadratic

b)

reciprocal

c)

cubic

d)

linear

15.

If g= {(1,1), (2,3), (3,5), (4,7)} is a function given by $g\left(x\right)\ =\ \alpha x\ +\beta$ then the values of $\alpha$ and $\beta$ are

a)

(-1,2)

b)

(-1,-2)

c)

(2,-1)

d)

(1,2)

16.

If the HCF of 65 and 117 is expressible in the form of $65m\ -\ 117$ , then the value of $m$ is

a)

1

b)

3

c)

4

d)

2

17.

Euclid's division lemma states that for positive integers $a$ and $b$ , there exist unique integers $q$ and $r$ such that $a=bq+r$ , where $r$ must satisfy

a)

$0\le r<b$

b)

$0<r\le b$

c)

$1<r<b$

d)

$0<r<b$

18.

Using Euclid's division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

a)

0,1,3

b)

1,3,5

c)

0,1,8

d)

1,4,8

19.

The sum of the exponents of the prime factors in the prime factorization of 1729 is

a)

3

b)

2

c)

1

d)

4

20.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

a)

5025

b)

2520

c)

2025

d)

5220

21.

$7^{4k}\ \equiv$ ______ (mod 100)

a)

3

b)

2

c)

1

d)

4

22.

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

a)

7881

b)

10091

c)

4551

d)

13531

23.

Given F₁ = 1, F₂= 3 and F_n= F_n-1 + F_n-2 then F₅ is

a)

3

b)

11

c)

5

d)

8

24.

An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

a)

16 m

b)

31 m

c)

62 m

d)

$\frac{31}{2}$ m

25.

If the sequence $t_1,\ t_2,\ t_3,\ \ldots$ are in A.P. then the sequence $t_6,\ t_{12},\ t_{18},\ldots$ is

a)

a Geometric Progression

b)

neither an Arithmetic Progression nor a Geometric Progression

c)

a constant sequence

d)

an Arithmetic Progression

26.

If 6 times of 6^th term of an A.P. is equal to 7 times the 7^th term, then the 13^th term of the A.P. is

a)

6

b)

7

c)

13

d)

0

27.

The value of $\left(1^3+2^3+3^3+\ldots+15^3\right)-\left(1+2+3+\ldots+15\right)\$ is

a)

14400

b)

14280

c)

14200

d)

14520

28.

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

a)

8

b)

6

c)

7

d)

9

29.

If $A\ =\ 2^{65}\$ and $B\ =\ 2^{64}+2^{63}+2^{62}+\ldots+2^0$ which of the following is true?

a)

B is 2⁶⁴ more than A

b)

A and B are equal

c)

A is larger than B by 1

d)

B is larger than A by 1

30.

The next term of the sequence $\frac{3}{16},\ \frac{1}{8},\ \frac{1}{12},\frac{1}{18},\ldots$ is

a)

$\frac{1}{24}$

b)

$\frac{2}{3}$

c)

$\frac{1}{27}$

d)

$\frac{1}{81}$

31.

The solution of the system $x+y-3z=-6,\ -7y+7z=7,\ 3z=9$ is

a)

$x=-1,\ y=2,\ z=3$

b)

$x=1,\ y=2,\ z=3$

c)

$x=-1,\ y=-2,\ z=3$

d)

$x=1,\ y=-2,\ z=3$

32.

If $\left(x-6\right)$ is the HCF of $x^2-2x-24$ and $x^2-kx-6$ then the value $k$ of is

a)

5

b)

3

c)

6

d)

8

33.

A system of three linear equations in three variables is inconsistent if their planes

a)

intersect only at a point

b)

intersect in a line

c)

do not intersect

d)

coincides with each other

34.

$y^2+\frac{1}{y^2}$ is not equal to

a)

$\frac{y^4+1}{y^2}$

b)

$\left(y-\frac{1}{y^{ }}\right)^2$

c)

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

d)

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

35.

If the roots of the equation $q^2x^2+p^2x+r^2=0$ are the squares of the roots of the equation $qx^2+px+r=0$ ,then p,q,r are in _______

a)

None of these

b)

G.P

c)

A.P

d)

Both A.P and G.P.

36.

$\frac{3y-3}{y}\div\frac{7y-7}{3y^2}$ is

a)

$\frac{9y^3}{21y-21}$

b)

$\frac{9y}{7}$

c)

$\frac{7\left(y^2-2y+1\right)}{y^2}$

d)

$\frac{21y^2-42y+21}{3y^3}$

37.

Which of the following should be added to make $x^4+64$ a perfect square

a)

$4x^2$

b)

$-8x^2$

c)

$8x^2$

d)

$16x^2$

38.

The square root of $\frac{256x^8y^4z^{10}}{25x^6y^6z^6}$ is equal to

a)

$\frac{16}{5}\left|\frac{x^2z^4}{y^2}\right|$

b)

$\frac{16}{5}\left|\frac{xz^2}{y^{ }}\right|$

c)

$16\left|\frac{y^2}{x^2z^4}\right|$

d)

$\frac{16}{5}\left|\frac{y}{xz^2}\right|$

39.

$\frac{x}{x^2-25}-\frac{8}{x^2+6x+5}$ gives

a)

$\frac{x^2-7x+40}{\left(x-5\right)\left(x+5\right)}$

b)

$\frac{x^2+7x+40}{\left(x-5\right)\left(x+5\right)\left(x+1\right)}$

c)

$\frac{x^2+10}{\left(x^2-25\right)\left(x+1\right)}$

d)

$\frac{x^2-7x+40}{\left(x^2-25\right)\left(x+1\right)}$

40.

The solution of $\left(2x-1\right)^2=9$ is equal to

a)

-1

b)

2

c)

-1,2

d)

none of these

41.

Graph of a linear equation is a __________

a)

hyperbola

b)

circle

c)

straight line

d)

parabola

42.

The values of a and b if $4x^4-24x^3+76x^2+ax+b$ is a perfect square are

a)

-120,100

b)

100,120

c)

12,10

d)

10,12

43.

If in triangles ABC and EDF, $\frac{AB}{BE}=\frac{BC}{FD}$ ,then they will be similar,

a)

$\angle B\ =\angle D$

b)

$\angle B\ =\angle E$

c)

$\angle A\ =\angle D$

d)

$\angle A=\angle F$

44.

If $\Delta ABC$ is an isosceles triangle with $\angle C=90\degree$ and $AC=5cm$ , then $AB$ is

a)

$10cm$

b)

$5\sqrt[]{2}cm$

c)

$5cm$

d)

$2.5cm$

45.

In $\Delta LMN,\ \angle L=60\degree,\ \angle M=50\degree.\$ If $\Delta LMN\ \sim\Delta PQR$ then the value of $\angle R$ is

a)

$40\degree$

b)

$110\degree$

c)

$30\degree$

d)

$70\degree$

46.

If in $\Delta ABC,\ DE\parallel BC,\ AB=3.6\ cm,\ AC=2.4\ cm\ and\ AD=2.1\ cm\$ then the length of $AE$ is

a)

1.8 cm

b)

1.2 cm

c)

1.05 cm

d)

1.4 cm

47.

The perimeters of two similar triangles $\Delta ABC\$ and $\Delta PQR$ are 36 cm and 24 cm respectively. If PQ =10 cm, then the length of AB is

a)

$6\frac{2}{3}$ cm

b)

$\frac{10\sqrt[]{6}}{3}$ cm

c)

$15$ cm

d)

$66\frac{2}{3}$ cm

48.

In a given figure $ST\parallel QR$ , $PS\ =2cm$ and $SQ=3cm$ . Then the ratio of the area of $\Delta PQR$ to the area of $\Delta PST$ is

a)

25:13

b)

25:4

c)

25:7

d)

25:11

49.

In a $\Delta ABC,\ AD$ is the bisector of $\angle BAC.\$ If $AB\ =8\ cm,\ BD\ =6\ cm\ and\ DC\ =3\ cm.$ The length of the side $AC$ is

a)

4 cm

b)

6 cm

c)

3 cm

d)

8 cm

50.

The area of triangle formed by the points (-5,0), (0,-5) and (5,0) is

a)

0 sq.units

b)

5 sq.units

c)

25 sq. units

d)

none of these

51.

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

a)

y=0

b)

x=0

c)

x=10

d)

y=10

52.

The straight line given by the equation $x=11$ is

a)

parallel to Y axis

b)

parallel to X axis

c)

Passing through the origin

d)

Passing through the point (0,11)

53.

If (5,7), (3,p) and (6,6) are collinear, then the value of 'p' is

a)

3

b)

9

c)

6

d)

12

54.

The point of intersection of $3x\ -y=4$ and $x+y=8$ is

a)

(3,5)

b)

(4,4)

c)

(2,4)

d)

(5,3)

55.

The slope of the line joining (12,3), (4,a) is $\frac{1}{8}$ . The value of 'a' is

a)

1

b)

4

c)

-5

d)

2

56.

The slope of the line which is perpendicular to a line joining the points (0,0) and (-8,8) is

a)

-1

b)

-8

c)

$\frac{1}{3}$

d)

1

57.

If slope of the line PQ is $\frac{1}{\sqrt[]{3}}$ then slope of the perpendicular bisector of PQ is

a)

$\sqrt[]{3}$

b)

$\frac{1}{\sqrt[]{3}}$

c)

$-\sqrt[]{3}$

d)

0

58.

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5, then the equation of the line AB is

a)

$8x+5y=40$

b)

$x=8$

c)

$8x-5y=40$

d)

$y=5$

59.

The equation of a line passing through the origin and perpendicular to the line $7x-3y+4=0$ is

a)

$7x-3y+4=0$

b)

$3x+7y=0$

c)

$3x-7y+4=0$

d)

$7x-3y=0$

60.

Consider four straight lines

(i) $l_1;\ 3y=4x+5$ (ii) $l_2;\ 4y=3x-1$ (iii) $l_3;\ 4y+3x=7$ (iv) $l_4;\ 4x+3y=2$

Which of the following statement is true?

a)

$l_2\ and\ l_3$ are parallel

b)

$l_1\ and\ l_4$ are parallel

c)

$l_1\ and\ l_2$ are perpendicular

d)

$l_2\ and\ l_4$ are perpendicular

61.

A straight line has equation $8y=4x+21$ . Which of the following is true?

a)

The slope is 0.5 and the y intercept is 2.6

b)

The slope is 5 and the y intercept is 1.6

c)

The slope is 0.5 and the y intercept is 1.6

d)

The slope is 5 and the y intercept is 2.6

62.

When proving that a quadrilateral is a trapezium, it is necessary to show

a)

Two sides are parallel

b)

Two parallel and two non parallel sides

c)

Opposite sides are parallel

d)

All sides are of equal length

63.

When proving that a quadrilateral is a parallelogram by using slopes you must find

a)

The slopes of two sides

b)

The lengths of all sides

c)

The slopes of two pair of opposite sides

d)

Both the lengths and slopes of two sides

64.

(2,1) is the point of intersection of two lines

a)

$3x+y=3\ ;\ x+y=7$

b)

$x+y=3\ ;\ 3x+y=7$

c)

$x+3y-3=0\ ;\ x-y-7=0$

d)

$x-y-3=0\ ;\ 3x-y-7=0$

65.

The value of $\sin^2\theta+\frac{1}{1+\tan^2\theta}$ is equal to

a)

$\tan^2\theta$

b)

1

c)

$\cot^2\theta$

d)

0

66.

$\tan\theta\ \operatorname{cosec}^2\theta-\tan\theta$ is equal to

a)

$\sec\theta$

b)

$\cot\theta$

c)

$\cot^2\theta$

d)

$\sin\theta$

67.

If $\left(\sin\propto+\operatorname{cosec}\propto\right)^2+\left(\cos\propto+\sec\propto\right)^2=k\ +\tan^2\propto+\cot^2\propto$ then the value of 'k' is equal to

a)

9

b)

5

c)

3

d)

7

68.

If $\sin\theta+\cos\theta=a\$ and $\sec\theta+\operatorname{cosec}\theta=b$ , then the value of $b\left(a^2-1\right)$ is equal to

a)

2a

b)

3a

c)

0

d)

2ab

69.

If $5x=\sec\theta$ and $\frac{5}{x}=\tan\theta$ , then $x^2-\frac{1}{x^2}$ is equal to

a)

25

b)

5

c)

1

d)

$\frac{1}{25}$

70.

If $\sin\theta=\cos\theta,$ then $2\tan^2\theta+\sin^2\theta-1$ is equal to

a)

$-\frac{2}{3}$

b)

$\frac{2}{3}$

c)

$-\frac{3}{2}$

d)

$\frac{3}{2}$

71.

If $x=a\tan\theta$ and $y=b\sec\theta$ then

a)

$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$

b)

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

c)

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

d)

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=0$

72.

$\left(1+\tan\theta+\sec\theta\right)\left(1+\cot\theta-\operatorname{cosec}\theta\right)$ is equal to

a)

0

b)

1

c)

2

d)

-1

73.

$a\cot\theta+b\operatorname{cosec}\theta=p$ and $b\cot\theta+a\operatorname{cosec}\theta=q$ then $p^2-q^2$ is equal to

a)

$b^2-a^2$

b)

$b^{ }-a^{ }$

c)

$a^2-b^2$

d)

$a^2+b^2$

RUBI THERESA - 10th SAMACHEER MATHEMATICS - QUARTERLY 1 MARKS

Total questions: 73

Worksheet time: 37mins

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