Solve the system of equations
 

a) (2, 4)

b) (4, 2)

c) (4, 16)

d) (16, 4)

Solve the simultaneous equations
 

a)  

b)  

c)  

d)  

Solve the system of equations
log_x log₃ log_x y = 0
log_y 27 = 1

a) (3, 3)

b) (3, 27)

c) (27, 3)

d) (27, 27)

Solve the system of equations
 
 

a) (2, 6)

b) (6, 2)

c) (2, 2)

d) (6, 6)

Solve the system of equations
 

a) (9, 25)

b) (25, 9)

c) Both of the above

d) None of the above

Solve the inequality
 

a) Φ

b) (0, 2)

c)

d)

Solve the inequality
 

a)

b)

c)

d)

Solve the inequality
 

a) (- 2, 1)

b) (3, 6)

c) (1, 3)

d) (- 2, 1) ∪ (3, 6)

Solve the inequality
 

a) Φ

b) (3, 4)

c) (4, ∞)

d) (0, 3)

Solve the inequality
 

a)

b) (0, log₃4)

c)

d)

Solve the inequality
 

a) (– 4, 2) 

b) (– 4, 8)

c) (2, 8)

d) (– 4, 2) ∪ (2, 8)

Solve the equation
 

a) No solution

b) – 99

c) 1

d) 100

Solve the equation
 

a) 3

b) – 2

c) (3, - 2)

d) Φ

Solve
3^x + 4^x = 5^x

a) Φ

b) 2

c) 4

d) 100

Solve the equation
 

a) Φ

b) 2

c) 4

d) 100

Multiple choices

Let g(x) be a function defined on  If the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g (x)) is   then the function g (x) is

a)

b)

c)

d)

If w ( ≠1 ) is cube root of unity, then
 

a) 0

b) 1

c) - 1

d) w

The determinant
 = 0 if

a) x, y, z are in arithmetic progression

b) x, y, z are in geometric progression

c) x, y, z are in harmonic progression

d) xy, yz, zx are in arithmetic progression

If = x + iy then

a) x = 3, y = 1

b) x = 1, y = 3

c) x = 0, y = 3

d) x = 0, y = 0

If f(x) =
then f(100) equals

a) 0

b) 1

c) 100

d) −100

If the system of equations

x – ky – z = 0

kx – y –z = 0

x + y –z = 0

has a non zero solution then possible values of k are

a) −1, 2

b) 1, 2

c) 0, 1

d) −1, 1

The number of distinct roots of
 = 0
in the interval   ≤ x ≤   is

a) 0

b) 2

c) 1

d) 3

If the system of equations

x + ay = 0

az + y = 0

ax + z = 0

has infinite solutions then the value of a is

a) −1

b) 1

c) 0

d) No real values