CUET PG MCA Quadratic Equations Previous Year Question Paper and Solution with PDF

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations

CUET PG MCA
Previous Year Questions

CUET PG MCA
Previous Year Questions
CUET PG MCA

CUET PG MCA Previous Year Questions (PYQs)

CUET PG MCA Quadratic Equations PYQ

Qus : 1 CUET PG MCA PYQ

List I		List II
A.	Kailash Satyarthi	I.	Chemistry
B.	Abhijit Banerjee	II.	Peace
C.	Vinkatraman Ramakrishnan	III.	Physics
D.	Subrahmanyan Chandrasekhar	IV.	Economics

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2023 PYQ

Solution

List I		List II
A.	Kailash Satyarthi	II.	Peace
B.	Abhijit Banerjee	IV.	Economics
C.	Venkatraman Ramakrishnan	I.	Chemistry
D.	Subrahmanyan Chandrasekhar	III.	Physics

Qus : 2 CUET PG MCA PYQ

List I		List II
A.	Dog : Rabies :: Mosquito :	I.	Bacteria
B.	Amnesia : Memory :: Paralysis :	II.	Liver
C.	Meningitis : Brain :: Cirrhosis :	III.	Movement
D.	Influenza : Virus :: Typhoid :	IV.	Malaria

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQCUET PG MCA CUET 2023 PYQ

Solution

Dog causes Rabies, Mosquito causes Malaria → A-IV

Amnesia affects Memory, Paralysis affects Movement → B-III

Meningitis affects Brain, Cirrhosis affects Liver → C-II

Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I

Correct matching: A-IV, B-III, C-II, D-I

Qus : 3 CUET PG MCA PYQ

Given below are two statements:

Statement I: If the roots of the quadratic equation

$x^2 - 4x - \log_3 a = 0$ are real, then the least value of $a$ is $\dfrac{1}{81}$.

Statement II: The harmonic mean of the roots of the equation

$(5+\sqrt{2})x^2 - (4+\sqrt{5})x + (8+2\sqrt{5}) = 0$ is $2$.

In the light of the above statements, choose the correct answer from the options given below:

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2023 PYQ

Solution

For Statement I:

For real roots, discriminant $\ge 0$

$(-4)^2 - 4(1)(-\log_3 a) \ge 0$

$16 + 4\log_3 a \ge 0$

$\log_3 a \ge -4$

$a \ge 3^{-4} = \dfrac{1}{81}$

So Statement I is true.

For Statement II:

Harmonic mean of roots $= \dfrac{2\alpha\beta}{\alpha+\beta}$

Here,

$\alpha+\beta = \dfrac{4+\sqrt{5}}{5+\sqrt{2}}$

$\alpha\beta = \dfrac{8+2\sqrt{5}}{5+\sqrt{2}}$

So,

HM $= \dfrac{2(8+2\sqrt{5})}{4+\sqrt{5}} = 4 \ne 2$

So Statement II is false.

Qus : 4 CUET PG MCA PYQ

If every pair from among the equations $x^2 + px + qr = 0$, $x^2 + qx + rp = 0$ and $x^2 + rx + pq = 0$ has a common root, then the product of the three common roots is ______.

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2023 PYQ

Solution

Let the common roots be $\alpha,\beta,\gamma$ respectively. From the first equation, common root $\alpha$ satisfies $\alpha^2 + p\alpha + qr = 0$ Similarly, $\alpha^2 + q\alpha + rp = 0$ Subtracting, $(p-q)\alpha + (qr-rp)=0$ $\Rightarrow (p-q)(\alpha - r)=0$ So $\alpha = r$. Similarly, $\beta = p$ and $\gamma = q$. Hence product of the three common roots $= pqr$

Qus : 5 CUET PG MCA PYQ

If $x=(2+\sqrt{3})^{\frac{1}{3}}+(2+\sqrt{3})^{-\frac{1}{3}}$ and $x^{3}-3x+k=0$, then the value of k is:

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2025 PYQ

Solution

Find k given $x=(2+\sqrt{3})^{1/3}+(2+\sqrt{3})^{-1/3}$ and $x^{3}-3x+k=0$

Let $a=2+\sqrt{3}\Rightarrow a^{-1}=2-\sqrt{3}$. Define $u^3=a,\;v^3=a^{-1}$ so that $uv=\big(a\cdot a^{-1}\big)^{1/3}=1$ and $x=u+v$.
Use $(u+v)^3=u^3+v^3+3uv(u+v)$:
\[ x^3=u^3+v^3+3uv(u+v)=(2+\sqrt{3})+(2-\sqrt{3})+3x=4+3x. \]
Rearrange: $\;x^3-3x-4=0$. Comparing with $x^{3}-3x+k=0$ gives $\;k=-4$.

Final answer: $\boxed{k=-4}$

Qus : 6 CUET PG MCA PYQ

If (x -1) is a factor of $2x^2-5x +k = 0$, then the value of k is:

1. 2

2. 5

3. 3

4. 4

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2025 PYQ

Solution

Given: Polynomial $$f(x) = 2x^2 - 5x + k$$ and $(x-1)$ is a factor.

Step 1: Apply factor theorem.
If $(x-1)$ is a factor, then $f(1) = 0$.

Step 2: Substitute $x=1$.
$$f(1) = 2(1)^2 - 5(1) + k = 2 - 5 + k = -3 + k$$

Step 3: Solve for $k$.
$$-3 + k = 0 \quad \Rightarrow \quad k = 3$$

Value of k: 3

Answer: Option 3

Qus : 7 CUET PG MCA PYQ

If ${x}^2+\frac{1}{{x}^2}=2$ then the value of ${x}^{256}+\frac{1}{{x}^{256}}$

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2024 PYQ

Solution

Given $x^2+\dfrac{1}{x^2}=2$. Let $t=x+\dfrac{1}{x}$. Then $x^2+\dfrac{1}{x^2}=t^2-2$, so $t^2-2=2 \Rightarrow t^2=4 \Rightarrow t=\pm2$.

From $x+\dfrac{1}{x}=2 \Rightarrow x=1$ and from $x+\dfrac{1}{x}=-2 \Rightarrow x=-1$.

Hence $x^{256}+\dfrac{1}{x^{256}}= \begin{cases} 1+1=2,& x=1\\ (-1)^{256}+(-1)^{-256}=1+1=2,& x=-1 \end{cases}$.

Final Answer: $2$.

Qus : 8 CUET PG MCA PYQ

If the roots of the equation $x^2+4x+a^2-3a$ are real then the value of a (is / are)

1
2
3
4
Go to Discussion

CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2024 PYQ

Solution

CUET PG MCA

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

CUET PG MCA

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Ask Your Question or Put Your Review.

Please provide more information - at least 10 characters

Feedback

Info.

Information

Aspire's Library

CUET PG MCA Previous Year Questions (PYQs)

CUET PG MCA Quadratic Equations PYQ

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

CUET PG MCA

CUET PG MCA

Info.

Confirm Delete

Edit