CUET PG MCA Mathematics Previous Year Questions (PYQs) – Page 1 of 17
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Showing 165 questions
| 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 |
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 |
