CUET PG MCA 2023 Previous Year Questions (PYQs) – Page 1 of 10
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Ajay said, “This girl is the wife of the grandson of my mother”. Who is Ajay to the girl?
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Solution
Grandson of my mother” = Ajay’s son (a male grandchild of Ajay’s mother).
The girl is the wife of Ajay’s son ⇒ the girl is Ajay’s daughter-in-law.
So, Ajay is the girl’s Father-in-law.
An athlete takes as much time in running 200 m as a car takes in covering 500 m. The distance covered by the athlete during the time the car covers 2 km is
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Solution
Let the speed of the athlete be $v_a$ and the speed of the car be $v_c$.
Given time is equal:
$\dfrac{200}{v_a} = \dfrac{500}{v_c}$
$\Rightarrow \dfrac{v_a}{v_c} = \dfrac{200}{500} = \dfrac{2}{5}$
So, the athlete’s speed is $\dfrac{2}{5}$ of the car’s speed.
When the car covers $2$ km $= 2000$ m,
distance covered by the athlete
$= \dfrac{2}{5} \times 2000 = 800$ m
| List I | List II | ||
|---|---|---|---|
| A. | Kailash Satyarthi | I. | Chemistry |
| B. | Abhijit Banerjee | II. | Peace |
| C. | Vinkatraman Ramakrishnan | III. | Physics |
| D. | Subrahmanyan Chandrasekhar | IV. | Economics |
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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 |
Two boys and two girls are playing cards and are seated at North, East, South and West of a table. No boy is facing East. Persons sitting opposite to each other are not of the same sex. One girl is facing South. Which directions are the boys facing?
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Solution
If they are seated at North, East, South, West of a table (facing the centre), then:
North seat → faces South
East seat → faces West
South seat → faces North
West seat → faces East
One girl is facing South ⇒ she is sitting at North.
So, South (opposite North) must be a boy.
Remaining seats East and West must be one boy and one girl (opposite sexes).
“No boy is facing East” ⇒ no boy can sit at West (because West seat faces East).
So the second boy sits at East (faces West).
Thus, boys are facing North (boy at South) and West (boy at East).
If $ \cot^2 45^\circ - \sin^2 45^\circ = K \sin^2 30^\circ \times \tan^2 45^\circ \times \sec^2 45^\circ $, then the value of $K$ is
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Solution
$ \cot 45^\circ = 1 \Rightarrow \cot^2 45^\circ = 1 $
$ \sin 45^\circ = \dfrac{1}{\sqrt{2}} \Rightarrow \sin^2 45^\circ = \dfrac{1}{2} $
LHS:
$ \cot^2 45^\circ - \sin^2 45^\circ = 1 - \dfrac{1}{2} = \dfrac{1}{2} $
Now,
$ \sin 30^\circ = \dfrac{1}{2} \Rightarrow \sin^2 30^\circ = \dfrac{1}{4} $
$ \tan 45^\circ = 1 \Rightarrow \tan^2 45^\circ = 1 $
$ \sec 45^\circ = \sqrt{2} \Rightarrow \sec^2 45^\circ = 2 $
RHS:
$ K \times \dfrac{1}{4} \times 1 \times 2 = \dfrac{K}{2} $
Equating LHS and RHS:
$ \dfrac{1}{2} = \dfrac{K}{2} \Rightarrow K = 1 $
Which of the following is true:
A. Two vectors are said to be identical if their difference is zero.
B. Velocity is not a vector quantity.
C. Projection of one vector on another is not an application of dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
Choose the most appropriate answer from the options given below:
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Solution
Statement A is true because if the difference of two vectors is zero, then both vectors are equal in magnitude and direction.
Statement B is false because velocity is a vector quantity.
Statement C is false because projection of one vector on another is an application of dot product.
Statement D is true because gradient gives the direction and maximum rate of increase of a scalar function.
Correct answer: (3) A and D only
The unit vectors orthogonal to the vector $- \hat{i} + 2\hat{j} + 2\hat{k}$ and making equal angles with the x and y axis is (are)
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Solution
Let required unit vector be $\vec{a}=l\hat{i}+m\hat{j}+n\hat{k}$.
Equal angles with x and y axis $\Rightarrow l=m$.
Orthogonal condition:
$\vec{a}\cdot(-\hat{i}+2\hat{j}+2\hat{k})=0$
$-l+2m+2n=0$
Since $l=m$:
$-l+2l+2n=0 \Rightarrow l+2n=0 \Rightarrow n=-\dfrac{l}{2}$
So vector $\propto (l,l,-\dfrac{l}{2}) \Rightarrow (2,2,-1)$
Unit vector:
$\pm \dfrac{1}{3}(2\hat{i}+2\hat{j}-\hat{k})$
| 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 |
Commented Feb 03, 2024
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