Question 1: Palette 1/12

BITSAT 2025 MCQ

For what value of $a, 6$ lies between the roots of the equation $x^2+2(a-3) x+9=0$.

A

$\left(\frac{-3}{4}, \infty\right)$

B

$\left(-\infty, \frac{-3}{4}\right) \cup(2, \infty)$

C

$\left(-\infty, \frac{-3}{4}\right)$

D

$\left(\frac{3}{4}, \infty\right)$

Question 2: Palette 2/12

BITSAT 2025 MCQ

Roots of the equation $a x^2+b x+c=0(a, b, c>0)$ are

A

Both positive

B

Both negative

C

Of opposite sign

D

depends on the values of $a, b$ and $c$

Question 3: Palette 3/12

BITSAT 2024 MCQ

Roots of the equation $ x^{2}+b x-c=0(b, c > 0) $ are

A

both positive

B

both negative

C

of opposite sign

D

None of the above

Question 4: Palette 4/12

BITSAT 2024 MCQ

Number of real solution of $ \sqrt{5-\log _{2}|x|} $ $ =3-\log _{2}|x| $ is equal to

A

1

B

2

C

3

D

4

Question 5: Palette 5/12

BITSAT 2023 MCQ

If $\alpha<1$ be a root of the equation $2 x^2-5 x+2=0$, then the other root of the equation is

A

$4 \alpha^2+4 \alpha$

B

$4 \alpha^3+3 \alpha$

C

$4 \alpha^3-3 \alpha$

D

$4 \alpha^2-2 \alpha$

Question 6: Palette 6/12

BITSAT 2023 MCQ

Let $\alpha, \beta$ be the roots of the equation $x^2-p x+r=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the equation $x^2-q x+r=0$. Then, the value of $r$ is equal to

A

$\frac{2}{9}(p-q)(2 q-p)$

B

$\frac{2}{9}(q-2 p)(2 q-p)$

C

$\frac{2}{9}(q-p)(2 p-q)$

D

$\frac{2}{9}(2 p-q)(2 q-p)$

Question 7: Palette 7/12

BITSAT 2022 MCQ

If $\alpha$ be a root of the equation $4{x^2} + 2x - 1 = 0$, then the other root of the equation is

A

4$\alpha$² + 2$\alpha$

B

4$\alpha$² $-$ 2$\alpha$

C

4$\alpha$³ $-$ 3$\alpha$

D

4$\alpha$³ + 3$\alpha$

Question 8: Palette 8/12

BITSAT 2022 MCQ

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solution of x² + qx + 1 = 0. If (a $-$ c) (b $-$ c) and (a + d)(b + d) are the solution of x² + ax + $\beta$ = 0, then $\beta$ is equal to

A

p + q

B

p $-$ q

C

p² + q²

D

q² $-$ p²

Question 9: Palette 9/12

BITSAT 2021 MCQ

If a$\in$R, b$\in$R, then the equation x² $-$ abx $-$ a² = 0 has

A

one positive root and one negative root

B

Both positive roots

C

Both negative roots

D

Non-real roots

Question 10: Palette 10/12

BITSAT 2021 MCQ

The solution of the inequality ${4^{ - x + 0.5}} - {7.2^{ - x}} < 4$, x $\in$R is

A

$( - 2,\infty )$

B

$( 2,\infty )$

C

$\left( {2,{7 \over 2}} \right)$

D

None of these

Question 11: Palette 11/12

BITSAT 2020 MCQ

Let x₁ and x₂ be the real roots of the equation ${x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0$, then maximum value of $x_1^2 + x_2^2$ is

A

19

B

22

C

18

D

17

Question 12: Palette 12/12

BITSAT 2020 MCQ

When x¹⁰⁰ is divided by x² $-$ 3x + 2, the remainder is (2^{k + 1} $-$ 1)x $-$(2^k $-$ 1), then k is

A

97

B

99

C

100

D

101