If the sum of two roots of the equation $$\displaystyle x^3 px^2 + qx r = 0$$ is zero , then
60%
pq = r
20%
qr = p
0%
pr = q
20%
pqr = 1
Q.2.
If $$f(x)={ 4x }^{ 4 }-{ ax }^{ 3 }+{ bx }^{ 2 }-cx+5$$ (a, b, c $$\in $$ R) has four positive real zeros $${ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 },{ r }_{ 4 }$$ such that $$\frac { { r }_{ 1 } }{ 2 } +\frac { { r }_{ 2 } }{ 4 } +\frac { { r }_{ 3 } }{ 5 } +\frac { { r }_{ 4 } }{ 8 } =1$$, then a is equal to
The roots of the equation $$ax^3 + bx^2 - x + 1=0$$ are real, distinct and are in H.P., then
0%
$$b$$ $$\epsilon$$ $$(-\infty,\frac{1}{3})$$
60%
$$a$$ $$\epsilon$$ $$(-\frac{1}{27},\infty)$$
0%
$$27a + 9b=2$$
40%
None of these
Q.5.
The roots of $$6x^{4}-35x^{3}+62^{2}-35x+6=0$$ are.......
5%
2,-1/2,-1/3,3
37%
2,1/2,3,1/3
26%
-2,-1/2,-3,-1/3
32%
2,1/2,-3,-1/3
Q.6.
If $$p,\quad q,\quad r,\quad s\quad \in R$$, then equation $$({ x }^{ 2 }+{ px }+{ 3 }q)({ -x }^{ 2 }+rx+q)({ -x }^{ 2 }+sx-2q)=0$$ has
22%
6 real roots
28%
atleast two real roots
33%
2 real and 4 imaginary roots
17%
4 real and 2 imaginary roots
Q.7.
The sum of the roots of the equation $$cot-1x-1(x+2)=150$$ is
33%
0
0%
1
33%
2
33%
-2
Q.8.
If $$1,-2,3$$ are the roots of $${ x }^{ 3 }-b{ x }^{ 2 }+ax+6=0$$, then a=
33%
$$-5$$
33%
$$5$$
33%
$$2$$
0%
none of these
Q.9.
The expansion $$\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x - 1} }}{2}} \right]}^7}} \right]$$ is a polynomial in x of degree
100%
7
0%
6
0%
4
0%
3
Q.10.
If roots of equation $$8x^3 -14x^2+7x-1 =0$$ are in geometric progression, then roots are
50%
$$3,6,8$$
0%
$$1,2,4$$
0%
$$2,4,8$$
50%
$$1,1/2,1/4$$
Q.11.
If $$a,\beta ,y$$ are the roots of equation $${ x }^{ 3 }+2x-5=0$$ and if equation $${ x }^{ 3 }+{ bx }^{ 2 }+cx+d=0\quad has\quad roots\quad 2a+1.\quad 2\beta +1,\quad 2y+1.$$ then value of $$\left| b+c+d \right| $$ is (where b,c,dd are coprime ) -
0%
41
50%
39
50%
40
0%
43
Q.12.
The expression $${ \left[ x+{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }$$ is a polynomial of degree
50%
5
50%
6
0%
7
0%
8
Q.13.
If a is a non-real root of $${ x }^{ 6 }=1$$, then $$\dfrac { { a }^{ 5 }{ a }^{ 3 }+a+1 }{ { a }^{ 2 }+1 } $$ is
50%
$${ a }^{ 2 }$$
50%
0
0%
$${ -a }^{ 2 }$$
0%
a
Q.14.
If one root of $$32 x ^ { 3 } - 48 x ^ { 2 } + 22 x - 3 = 0$$ is equal to half of the sum of the other two roots , then the roots are
50%
$$1 / 4,1 / 2,3 / 4$$
50%
$$4,2,4 / 3$$
0%
$$3,4,5$$
0%
$$2.3 .5/2$$
Q.15.
The expression $$(x+(x^4-1)^{1/2})^4 + (x-(x^4-1)^{1/2})^4$$ is a polynomial of degree
50%
8
0%
6
50%
4
0%
2
Q.16.
number of real roots of the equation $$\sqrt { x } +\sqrt { x-\sqrt { 1-x } } =1\quad is$$
100%
0
0%
1
0%
2
0%
3
Q.17.
Find the value of $$\dfrac { 10.5 \times 10.5 - 15 \times 10.5 + 7.5 \times 7.5 } { 10.5 - 7.5 }.$$
0%
$$17$$
100%
$$3$$
0%
$$6$$
0%
$$22$$
Q.18.
If $$\alpha ,\beta ,\gamma $$ are roots of $$7{ x }^{ 3 }-x-2=0$$ then find the value of $$\sum { \left( \dfrac { \alpha }{ \beta } +\dfrac { \beta }{ \alpha } \right) } $$
50%
1
50%
2
0%
-3
0%
-4
Q.19.
The HCF of two ploynomials $$A$$ and $$B$$ using long division method was found to be $$2x + 1$$ after two steps . The fisrt two quotient obtained are $$x$$ and $$(x + 1)$$ . Find $$A$$ and $$B$$ . Given that degree of $$A$$ > degree of $$B$$ is