Determinants Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The value of the determinant
 is equal to
(a) –2
(b) –1
(c) 0
(d) 1
2. If a be a repeated root of the quadratic equation f(x) = 0 and A(x), B(x),
C(x) be polynomials of degrees 3, 4 and 5 respectively, then 
(a) is divisible by f(x) for all x
(b) is not divisible by f(x) for all x
(c) is equal to 0
Page 2


PART-I (Single Correct MCQs)
1. The value of the determinant
 is equal to
(a) –2
(b) –1
(c) 0
(d) 1
2. If a be a repeated root of the quadratic equation f(x) = 0 and A(x), B(x),
C(x) be polynomials of degrees 3, 4 and 5 respectively, then 
(a) is divisible by f(x) for all x
(b) is not divisible by f(x) for all x
(c) is equal to 0
(d) None of these
3. If in a triangle ABC,  then the triangle is
(a) equilateral or isosceles
(b) equilateral or right-angled
(c) right angled or isosceles
(d) None of these
4. If [ ] denotes the greatest integer less than or equal to the real number
under consideration and –1 < x < 0; 0 < y < 1;1 < z < 2 , then the value
of the determinant
 is
(a) [z]
(b) [y]
(c) [x]
(d) None of these
5. If x, y, z are complex numbers, and
 then ? is
(a) purely real
(b) purely imaginary
(c) complex
(d) 0
6. If the system of linear equations :
x
1
 + 2x
2
 + 3x
3 
= 6
x
1
 + 3x
2
 + 5x
3
 = 9
2x
1
 + 5x
2 
+ ax
3
 = b
Page 3


PART-I (Single Correct MCQs)
1. The value of the determinant
 is equal to
(a) –2
(b) –1
(c) 0
(d) 1
2. If a be a repeated root of the quadratic equation f(x) = 0 and A(x), B(x),
C(x) be polynomials of degrees 3, 4 and 5 respectively, then 
(a) is divisible by f(x) for all x
(b) is not divisible by f(x) for all x
(c) is equal to 0
(d) None of these
3. If in a triangle ABC,  then the triangle is
(a) equilateral or isosceles
(b) equilateral or right-angled
(c) right angled or isosceles
(d) None of these
4. If [ ] denotes the greatest integer less than or equal to the real number
under consideration and –1 < x < 0; 0 < y < 1;1 < z < 2 , then the value
of the determinant
 is
(a) [z]
(b) [y]
(c) [x]
(d) None of these
5. If x, y, z are complex numbers, and
 then ? is
(a) purely real
(b) purely imaginary
(c) complex
(d) 0
6. If the system of linear equations :
x
1
 + 2x
2
 + 3x
3 
= 6
x
1
 + 3x
2
 + 5x
3
 = 9
2x
1
 + 5x
2 
+ ax
3
 = b
is consistent and has infinite number of solutions, then :
(a) a = 8, b can be any real number
(b) b = 15, a can be any real number
(c) and 
(d) a = 8, b = l5
7. The determinant  vanishes for
(a) 3 values of x
(b) 2 values of x
(c) 1 values of x
(d) no value of x
8. If  b
2
 – ac < 0, a < 0 then the value of
 is
(a) Zero
(b) Positive
(c) Negative
(d) b
2
 + ac
9. Suppose a, ß, ? ?R are such that  and
 then ? cannot exceed
(a) 1
(b) 0
(c) (d)  None of these
10. The number of distinct real roots of
Page 4


PART-I (Single Correct MCQs)
1. The value of the determinant
 is equal to
(a) –2
(b) –1
(c) 0
(d) 1
2. If a be a repeated root of the quadratic equation f(x) = 0 and A(x), B(x),
C(x) be polynomials of degrees 3, 4 and 5 respectively, then 
(a) is divisible by f(x) for all x
(b) is not divisible by f(x) for all x
(c) is equal to 0
(d) None of these
3. If in a triangle ABC,  then the triangle is
(a) equilateral or isosceles
(b) equilateral or right-angled
(c) right angled or isosceles
(d) None of these
4. If [ ] denotes the greatest integer less than or equal to the real number
under consideration and –1 < x < 0; 0 < y < 1;1 < z < 2 , then the value
of the determinant
 is
(a) [z]
(b) [y]
(c) [x]
(d) None of these
5. If x, y, z are complex numbers, and
 then ? is
(a) purely real
(b) purely imaginary
(c) complex
(d) 0
6. If the system of linear equations :
x
1
 + 2x
2
 + 3x
3 
= 6
x
1
 + 3x
2
 + 5x
3
 = 9
2x
1
 + 5x
2 
+ ax
3
 = b
is consistent and has infinite number of solutions, then :
(a) a = 8, b can be any real number
(b) b = 15, a can be any real number
(c) and 
(d) a = 8, b = l5
7. The determinant  vanishes for
(a) 3 values of x
(b) 2 values of x
(c) 1 values of x
(d) no value of x
8. If  b
2
 – ac < 0, a < 0 then the value of
 is
(a) Zero
(b) Positive
(c) Negative
(d) b
2
 + ac
9. Suppose a, ß, ? ?R are such that  and
 then ? cannot exceed
(a) 1
(b) 0
(c) (d)  None of these
10. The number of distinct real roots of
 in the interval  is
(a) 0
(b) 2
(c) 1
(d) 3
11. For what value of p, is the system of equations :
p
3
x + (p + 1)
3
 y = (p + 2)
3
px + (p + 1) y = p + 2
x + y = 1
consistent ?
(a) p = 0
(b) p = 1
(c) p = – 1
(d) For  all p > 1
12. The value of
 is
(a) 0
(b) 2abc
(c)
(d) None of these
13. Value of the determinant (when n ? N)
D =   is
(a)
Page 5


PART-I (Single Correct MCQs)
1. The value of the determinant
 is equal to
(a) –2
(b) –1
(c) 0
(d) 1
2. If a be a repeated root of the quadratic equation f(x) = 0 and A(x), B(x),
C(x) be polynomials of degrees 3, 4 and 5 respectively, then 
(a) is divisible by f(x) for all x
(b) is not divisible by f(x) for all x
(c) is equal to 0
(d) None of these
3. If in a triangle ABC,  then the triangle is
(a) equilateral or isosceles
(b) equilateral or right-angled
(c) right angled or isosceles
(d) None of these
4. If [ ] denotes the greatest integer less than or equal to the real number
under consideration and –1 < x < 0; 0 < y < 1;1 < z < 2 , then the value
of the determinant
 is
(a) [z]
(b) [y]
(c) [x]
(d) None of these
5. If x, y, z are complex numbers, and
 then ? is
(a) purely real
(b) purely imaginary
(c) complex
(d) 0
6. If the system of linear equations :
x
1
 + 2x
2
 + 3x
3 
= 6
x
1
 + 3x
2
 + 5x
3
 = 9
2x
1
 + 5x
2 
+ ax
3
 = b
is consistent and has infinite number of solutions, then :
(a) a = 8, b can be any real number
(b) b = 15, a can be any real number
(c) and 
(d) a = 8, b = l5
7. The determinant  vanishes for
(a) 3 values of x
(b) 2 values of x
(c) 1 values of x
(d) no value of x
8. If  b
2
 – ac < 0, a < 0 then the value of
 is
(a) Zero
(b) Positive
(c) Negative
(d) b
2
 + ac
9. Suppose a, ß, ? ?R are such that  and
 then ? cannot exceed
(a) 1
(b) 0
(c) (d)  None of these
10. The number of distinct real roots of
 in the interval  is
(a) 0
(b) 2
(c) 1
(d) 3
11. For what value of p, is the system of equations :
p
3
x + (p + 1)
3
 y = (p + 2)
3
px + (p + 1) y = p + 2
x + y = 1
consistent ?
(a) p = 0
(b) p = 1
(c) p = – 1
(d) For  all p > 1
12. The value of
 is
(a) 0
(b) 2abc
(c)
(d) None of these
13. Value of the determinant (when n ? N)
D =   is
(a)
(b)
(c)
(d) None of these
14. Let , then
 is equal to
(a) S
6
(b) S
5
 – S
3
(c) S
6
 – S
4
(d) None of these
15. Let A, B and C be n × n matrices. Which one of the following is a
correct statement?
(a) If AB = AC, then B = C
(b) If ; then A is invertible.
(c) If , then A = 0
(d) None of these
16. If a, b, c are sides of a triangle and
, then
(a) ?ABC cannot be equilateral triangle
(b) ?ABC is a right angled isosceles triangle
(c) ?ABC is an isosceles triangle
(d) None of these