Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

If the order pairs (a, -1) and (5, b) blongs to {(x, y) | y = 2x + 3}, then a and b are __________

(a)

-13, 2

(b)

2, 13

(c)

2, -13

(d)

-2,13

The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

(a)

37

(b)

39

(c)

35

(d)

36

If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

(a)

3

(b)

-3

(c)

\(\frac { 1 }{ 3 } \)

(d)

13

If f(x) = 2 - 3x, then f o f(1 - x) = ?

(a)

5x+9

(b)

9x-5

(c)

5-9x

(d)

5x-9

If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

(a)

5

(b)

-1

(c)

-9

(d)

1

If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

(a)

Constant function

(b)

Quadratic function

(c)

Cubic function

(d)

Identify function

If a and b are the two positive intergs when a > b and b is a factor of a then HCF (a, b) is ____________

(a)

b

(b)

a

(c)

ab

(d)

\(\frac { a }{ b } \)

If 3 is the least prime factor of number and 7 is least prime factor of b, then the least prime factor a + b is ____________

(a)

a + b

(b)

2

(c)

5

(d)

10

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

(a)

2

(b)

1

(c)

0

(d)

3

44 ≡ 8 (mod12), 113 ≡ 85 (mod 12), thus 44 x 113 ≡______(mod 12):

(a)

4

(b)

3

(c)

2

(d)

1

The first term of an A.P. whose 8^th and 12^th terms are 39 and 59 respectively is ____________

(a)

5

(b)

6

(c)

4

(d)

3

How many terms are there in the G.P : 5, 20, 80, 320,..., 20480

(a)

5

(b)

6

(c)

7

(d)

9

If p^th, q^th and r^th terms of an A.P. are a, bc respestively, then (a(q - r) + b(r - p) + c(p - q) is____________

(a)

0

(b)

a + b + c

(c)

p + q + r

(d)

pqr

In an A.P if the p^th term is q and the q^th term is p, then its n^th term is ____________

(a)

p+q-n

(b)

p+q+n

(c)

p-q+n

(d)

p-q-n

Which of the following are linear equation in three variables ___________

(a)

2x = z

(b)

2sin x + y cos y + z tan z = 2

(c)

x + 2y² + z = 3

(d)

x - y - z = 7

Consider the following statements:
(i) The HCF of x+y and x⁸-y⁸ is x+y
(ii) The HCF of x+y and x⁸+y⁸ is x+y
(iii) The HCF of x-y nd x⁸+y⁸ is x-y
(iv) The HCF of x-y and x⁸-y⁸ is x-y

(a)

(i) and (ii)

(b)

(ii) and (iii)

(c)

(i) and (iv)

(d)

(ii) and (iv)

The square root of 4m² - 24m + 36 is ___________

(a)

4(m-3)

(b)

2(m-3)

(c)

(2m-3)²

(d)

(m-3)

Axis of symmetry in the term of vertical line seperates parabola into ___________

(a)

3 equal halves

(b)

5 equal halves

(c)

2 equal halves

(d)

4 equal halves

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(a)

(i) and (iii) only

(b)

(iii) only

(c)

(iv) only

(d)

(ii) and (iv) only

If \(A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right] \) and \(I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \) then A² = 16 I for ___________

(a)

y = 4

(b)

y = 5

(c)

y = -4

(d)

y = 16

If \(A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }\) \(B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }\) then which of the following products can be made from these matrices 
(i) A²
(ii) B²
(iii) AB
(iv) BA

(a)

(i) only

(b)

(ii) and (iii) only

(c)

(iii) and (iv) only

(d)

all the above

If triangle PQR is similar to triangle LMN such that 4PQ = LM and QR = 6 cm then MN is equal to ____________

(a)

12 cm

(b)

24 cm

(c)

10 cm

(d)

36 cm

I the given figure DE||AC which of the following is true.

(a)

\(x=\frac { ay }{ b+a } \)

(b)

\(x=\frac { a+b }{ ay } \)

(c)

\(x=\frac { ay }{ b-a } \)

(d)

\(\frac { x }{ y } =\frac { a }{ b } \)

S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

(a)

4 ST

(b)

5 ST

(c)

3 ST

(d)

3 QR

The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the traiangle is ____________

(a)

108 cm²

(b)

54 cm²

(c)

27 cm²

(d)

216 cm²

A line which intersects a circle at two distinct points ic called ____________

(a)

Point of contact

(b)

sccant

(c)

diameter

(d)

tangent

In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

(a)

23 cm

(b)

24 cm

(c)

27 cm

(d)

30 cm

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

(a)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(b)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(c)

\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

(d)

\(2\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

(a)

7:2

(b)

3:4

(c)

2:7

(d)

5:3

The area of triangle formed by the points (a, b+c), (b, c+a) and (c, a+b) is ____________

(a)

a+b+c

(b)

abc

(c)

(a+b+c)²

(d)

0

Find the slope of the line 2y = x + 8 ____________

(a)

\(\frac { 1 }{ 2 } \)

(b)

1

(c)

8

(d)

2

Find the value of P, given that the line  \(\frac { y }{ 2 } =x-p\) passes through the point (-4, 4) is ____________

(a)

-4

(b)

-6

(c)

0

(d)

8

Find the slope and the y-intercept of the line \(3y-\sqrt { 3x } +1=0\) is ____________

(a)

\(\frac { 1 }{ \sqrt { 3 } } ,\frac { -1 }{ 3 } \)

(b)

\(-\frac { 1 }{ \sqrt { 3 } } ,\frac { -1 }{ 3 } \)

(c)

\(\sqrt { 3 } ,1\)

(d)

\(-\sqrt { 3 } ,3\)

A line passing through the point (2, 2) and the axes enclose an aream ∝. The intercept on the axes made by the line are given by the roots of ____________

(a)

x²-2-∝x+∝ = 0

(b)

x²+2∝x+∝ = 0

(c)

x²-∝x+2∝ = 0

(d)

none of these

Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

(a)

3x+5y+15 = 0

(b)

3x+5y-20 = 0

(c)

2x+7y-20 = 0

(d)

4x+3y-15 = 0

The value of the expression [cosec (75^o + θ) - sec (15^o - θ) - tan (55^o + θ) + cot(35^o - θ] is ___________

(a)

-1

(b)

0

(c)

1

(d)

\(\frac{3}{2}\)

Given that sinθ = \(\frac{a}{b}\), then cosθ is equal to ___________

(a)

\(\frac { b }{ \sqrt { { b }^{ 2 }-{ a }^{ 2 } } } \)

(b)

\(\frac { b }{ a } \)

(c)

\(\frac { \sqrt { { b }^{ 2 }-{ a }^{ 2 } } }{ b } \)

(d)

\(\frac { b }{ \sqrt { { b }^{ 2 }-{ a }^{ 2 } } } \)

If cos9∝ = sin∝ and 9∝ < 90^o, then the value of tan t∝ is

(a)

\(\frac{1}{\sqrt{3}}\)

(b)

\({\sqrt{3}}\)

(c)

1

(d)

0

Given that sin ∝ = \(\frac{1}{2}\) and cos β = \(\frac{1}{2}\), then the value of (∝ + β) is ___________

(a)

0^o

(b)

30^o

(c)

60^o

(d)

90^o

A pole 6 m high a shadow 2\(\sqrt{3}\) m long on the ground, then the sun's elevation is ___________

(a)

60^o

(b)

45^o

(c)

30^o

(d)

90^o

If A is an assets angle of Δ ABC, right angle at 3, then the value of sin A T cos A is ___________

(a)

=1

(b)

>1

(c)

<1

(d)

=2

From the figure, the value of cosec θ + cot θ is ___________

(a)

\(\frac { a+b }{ c } \)

(b)

\(\frac { c }{ a+b } \)

(c)

\(\frac { b+c }{ a } \)

(d)

\(\frac { b }{ a+c } \)

The value of \(\cfrac { 3 }{ cot^{ 2 }\theta } -\cfrac { 3 }{ { cos }^{ 2 }\theta } \) is equal to ___________

(a)

\(\frac { 1 }{ 3 } \)

(b)

3

(c)

0

(d)

-3

If sin(α + β) = 1 then cos(α - β) can be reduced to ___________

(a)

sin α

(b)

cos β

(c)

sin 2β

(d)

cos 2β

The top of two poles of height 18.5m and 7m are connected by a wire. If the wire makes an angle of measures 360^o with horizontal, then the length of the wire is ____________

(a)

23m

(b)

18m

(c)

28m

(d)

25.5m

If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

(a)

64

(b)

216

(c)

512

(d)

16

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is ___________

(a)

15 cm

(b)

12 cm

(c)

10 cm

(d)

17 cm

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

(a)

10 cm

(b)

15 cm

(c)

18 cm

(d)

24 cm

When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as \(\frac { 1 }{ 3 } \). What is the radius of the sphere?

(a)

24 cm

(b)

9cm

(c)

54cm

(d)

4.5cm

A semicircular thin sheet of a metal of diameter 28 cm is bentt and an open conical cup is mader. What is the capacity of the cup?

(a)

\(\left[ \frac { 1000 }{ 3 } \right] \sqrt { 3 } { cm }^{ 3 }\)

(b)

\(300\sqrt { 3 } { cm }^{ 3 }\)

(c)

\(\left[ \frac { 700 }{ 3 } \right] \sqrt { 3 } { cm }^{ 2 }\)

(d)

\(\left[ \frac { 1078 }{ 3 } \right] \sqrt { 3 } { cm }^{ 3 }\)

If a letter is chosen at random from the English alphabets {a, b....,z}, then the probability that the letter chosen precedes x ____________

(a)

\(\frac { 12 }{ 13 } \)

(b)

\(\frac { 1 }{ 13 } \)

(c)

\(\frac { 23 }{ 26 } \)

(d)

\(\frac { 3 }{ 26 } \)

IF the probability of the non-happening of a event is q, then the probability of happening of that event is 

(a)

1-q

(b)

q

(c)

q/2

(d)

∝q

The mean of a observation x₁, x₂, x₃, ......... x_n is \(\bar { x } \). If each observation is multiplied by p, there the mean of the new observations is ___________

(a)

\(\frac { \bar { x } }{ p } \)

(b)

p\(\bar { x } \)

(c)

\(\bar { x } \)

(d)

P+\(\bar { x } \)

A letter is selected at randam from the the word 'PROBABILITY'. The probability that its is nota vowel is ___________

(a)

\( \frac { 4 }{ 11 } \)

(b)

\(\frac { 7 }{ 11 } \)

(c)

\(\frac { 3 }{ 11 } \)

(d)

\(\frac { 6 }{ 11 } \)

A nuber x is chosen at random drom -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

(a)

\(\frac { 3 }{ 9 } \)

(b)

\(\frac { 4 }{ 9 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

\(\frac { 7 }{ 9 } \)

If the probability of non-happening of an event is, then probability of happening of the event is ___________

(a)

1-q

(b)

q

(c)

\(\frac { q }{ 2 } \)

(d)

2q

In one thousand lottery tickets, there are 50 prizes to be given. The probability of happenning of the event is ___________

(a)

1-q

(b)

q

(c)

\(\frac { q }{ 2 } \)

(d)

2q

When three coins are tossed, the probability of getting the same face on all the three coins is ___________

(a)

\(\frac { 1 }{ 8 } \)

(b)

\(\frac { 1 }{ 4 } \)

(c)

\(\frac { 3 }{ 8 } \)

(d)

\(\frac { 1 }{ 3 } \)