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Let and be the roots of equation is equal to:

• Option 1)

6

• Option 2)

-6

• Option 3)

3

• Option 4)

-3

3

All the pairs ( x, y ) that satisfy the inequality

also satisfy the equation :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

=>  &  So, correct option is (4). Option 1) Option 2) Option 3) Option 4)

If  are three consecutive terms of a non-constant

G.P. such that the equations   and

have a common root , then  is equal to :

• Option 1)

0

• Option 2)

• Option 3)

• Option 4)

are in G.P. =>  For equation,                  Hence, roots are equal & equals to  Since, given equation have common roots , hence   must be root of                     Option 1) 0 Option 2) Option 3) Option 4)

Let   with   and  it satisfies

for some natural number n . Then :

• Option 1)

n = 20 and Re(z) = -10

• Option 2)

n = 40 and Re(z) = 10

• Option 3)

n = 40 and Re(z) = -10

• Option 4)

n = 20 and Re(z) = 10

,  ,  Option 1)  n = 20 and Re(z) = -10 Option 2)  n = 40 and Re(z) = 10 Option 3)  n = 40 and Re(z) = -10 Option 4)  n = 20 and Re(z) = 10

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :

• Option 1)

28

• Option 2)

27

• Option 3)

25

• Option 4)

24

atleast one boy & one girl :  ( 1B & 2G) + ( 2B & 1G)   As, n cannot be -ve so, n = 25 Option 1) 28 Option 2) 27 Option 3) 25 Option 4) 24

If  is the inverse of a  matrix A, then the sum of all values of  for which det  is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)

The equation  represents :

• Option 1)

• Option 2)

• Option 3)

the line through the origin with slope

• Option 4)

the line through the origin with slope

The line through the origin with slope 1Option 1)a circle of radius .  Option 2)a circle of radius Option 3)the line through the origin with slope Option 4)the line through the origin with slope

if  are roots of the equation  then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)

Let a,b and c be in G.P. with common ratio r , where  and

. If  3a , 7b and 15c are the first three terms of an A.P.,

then the 4th term of this A.P. is :

• Option 1)

• Option 2)

5 a

• Option 3)

• Option 4)

a

Since a,b,c are in G.P. with common ratio r then  b = ar ,  Also 3a, 7b and 15c are in A.P. =>  =>  =>  =>  =>  =>  =>  So, terms are                         or                         =>    or    So, 4th term     or    So, option (4) is correct.   Option 1) Option 2) 5 a Option 3) Option 4) a

The sum of the real roots of the equation

, is equal to :

• Option 1)

6

• Option 2)

0

• Option 3)

1

• Option 4)

-4

=>  =>  Root of equation (-3,1,2) So, Sum of real root of equation = -3+1+2=0 So, option (2) is correct.Option 1)6Option 2)0Option 3)1Option 4)-4

If  and  are two complex numbers such that

and   then :

• Option 1) • Option 2)

• Option 3)

• Option 4)

and  Let    =>                                                                  Option 1)Option 2)Option 3)Option 4)

If  and  are the roots of the quadratic equation,

, then

is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

and  are the roots of the equation  Now,                                                                                                                                                                   correct option (2) Option 1) Option 2) Option 3) Option 4)

If a>0 and  , has magnitude  ,

then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

given that  Option (1) is correct. Option 1) Option 2) Option 3) Option 4)

Let  be such that . If  ,

then :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1)Option 2)Option 3)Option 4)

If m is chosen in the quadratic equation  such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is  :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

for sum of root to be greatest     should be minimum  now equation         Option 1) Option 2) Option 3) Option 4)

Let  If  is a root of the quadratic equation, then :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Given that one root is  then another root will by  Sum of roots =  Product of roots=  Question is wrong   Option 1)             Option 2)   Option 3) Option 4)

All the points in the set

lie on a :

• Option 1)

straight line whose slope is .

• Option 2)

• Option 3)

• Option 4)

straight line whose slop is

Given ,     Option 1) straight line whose slope is . Option 2) circle whose radius is  Option 3) circle whose radius is  . Option 4) straight line whose slop is

Let  and  be the roots of the equation  Then for  in , is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

are roots of      Option 1)Option 2)Option 3)Option 4)

If three distinct numbers   are in  and the equations  and  have a common root, then which one of the following statements is correct ?

• Option 1)

are in A.P.

• Option 2)

are in A.P.

• Option 3)

are in G.P.

• Option 4)

are in G.P.

Given  are in G.P. roots are =  root of this eq =  or     divide by ac Option 1)   are in A.P. Option 2)  are in A.P. Option 3)  are in G.P.   Option 4)  are in G.P.

The number of integral values of m for which the equation  has no real root is :

• Option 1)

• Option 2)

• Option 3)

infinitely many

• Option 4)

Given equation is  given eq. has no real root Infinite value of m satisfies this.  Option 1) Option 2) Option 3) infinitely many Option 4)
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