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JEE Questions for Maths Equations And Inequalities Quiz 15 - MCQExams.com
JEE
Maths
Equations And Inequalities
Quiz 15
If (1 + i) is a root of the equation x
2
– x + (1 – i) = 0 then the other root is
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0%
1 – i
0%
i
0%
–i
0%
2i
0%
–2i
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0%
4
0%
2
0%
1
0%
None of these
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0%
0%
2)
0%
0%
None of these
The values of a for which 2x
2
– 2(2a)x + a(a += 0 may have one root less than a and other root greater than a are given by
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0%
1 > a > 0
0%
–1 < a < 0
0%
a ≥ 0
0%
a < 0 or a < –1
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
6, 4, –1
0%
6, 4, 1
0%
–6, 4, 1
0%
–6, –4, 1
If 3 ≤ 3t – 18 ≤ 18, then which one of the following is true?
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0%
0%
2)
0%
0%
0%
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0%
a and b
0%
a and c
0%
b and c
0%
a and d
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0%
a and b
0%
a and d
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c and d
0%
c and b
Read the following statements carefully to the correct option out of the options given below:
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0%
Statement 1 is true, statement 2 is true; statement 2 is correct explanation for statement 1
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Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
0%
Statement 1 is true, statement 2 is false
0%
Statement 1 is false, statement 2 is true.
If |x
2
– x – 6| = x + 2, then the values of x are
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0%
–2, 2, –4
0%
–2, 2, 4
0%
3, 2, –2
0%
4, 4, –3
The positive value of k for which ke
x
– x = 0 has only one root is
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0%
1/e
0%
1
0%
e
0%
loge2
The number of integral values of b, for which the equation x
2
+ bx – 16 = 0 has integral roots, is
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0%
2
0%
3
0%
4
0%
5
0%
6
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0%
Both negative
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Both positive
0%
Both real
0%
One negative and one positive
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0%
0%
0
0%
0%
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0%
A.P
0%
G.P
0%
H.P
0%
None of these
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
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0%
0%
2)
0%
0%
None of these
Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x
2
correctly as –6 and 1 respectively. The correct roots are
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0%
3, –2
0%
–3, 2
0%
–6, –1
0%
6, –1
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
0%
All of these
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All real and equal
0%
All real and distinct
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One real and two imaginary
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All real and two equal
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4, –2
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–4, –2
0%
4, 2
0%
–4, 2
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a = 3, b = 12
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a = 12, b = 3
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a = 2, b = 32
0%
a = 4, b = 16
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0%
3
0%
4
0%
5
0%
None of these
If 2 + i is a root of the equation x
2
–5x
2
+ 9x – 5 = 0, then the other roots are
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0%
1 and 2 – i
0%
–1 and 3 + i
0%
0 and 1
0%
–1 and i – 2
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0%
–1, 2
0%
–1, 1
0%
0, –1
0%
0, 1
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0%
0%
2)
0%
0%
None of these
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0%
0%
2)
0%
0%
The condition that x
3
– 3px + 2q may be divisible by a factor of the form x
2
+ 2ax + a
2
is
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0%
0%
2)
0%
0%
The diagram shows the graph of y =ax
2
+ bx + c. Then a > 0 b < 0 c > 0 b
2
– 4ac = 0
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0%
b and c
0%
a and b
0%
a and c
0%
a and d
The number of values of k for which the equation x
2
– 3x + k = 0 has two real and distinct roots lying in the interval (0,are
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0%
0
0%
2
0%
3
0%
Infinitely many
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0%
–3q
0%
–p
0%
–pq
0%
3pq
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0%
1
0%
2
0%
3
0%
4
Number of solution of |x – 1| = cosx is
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0%
2
0%
3
0%
4
0%
None of these
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0%
E → (i); B → (ii); D → (iii); F → (iv)
0%
E → (i); B → (ii); A → (iii); D → (iv)
0%
E → (i); D → (ii); B → (iii); F → (iv)
0%
E → (i); B → (ii); D → (iii); A → (iv)
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0%
b and d
0%
b and c
0%
b and a
0%
a and c
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0%
0%
2)
0%
0%
0%
Let a, b, c be three numbers such that a + 2b + 4c = 0. Then the equation ax
2
+ bx + c = 0
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0%
Has both the roots complex
0%
Has its roots lying within –1 < x < 0
0%
Has one of the roots equal to 1/2
0%
Has its roots lying within 2 < x < 6
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