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CUET PG MCA Previous Year Questions (PYQs)

CUET PG MCA Properties Of Triangle PYQ

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






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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
CUET PG MCA PYQ
The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is $60^\circ$. If the third side is 3, the remaining fourth side is





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

Solution

Opposite angles in a cyclic quadrilateral are supplementary. Using cosine rule in both triangles and equating, the fourth side comes out as 4.
CUET PG MCA PYQ
Which of the following is true
A. If $a\cos A=b\cos B$, then the triangle is isosceles or right angled.
B. If in a triangle $ABC$, $\cos A\cos B+\sin A\sin B\sin C=1$, then the triangle is isosceles right angled.
C. If the ex-radii $r_1,r_2,r_3$ of $\triangle ABC$ are in H.P., then its sides are not in A.P.

Choose the correct answer from the options given below:





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

Solution

A:
$a\cos A=b\cos B \Rightarrow \cos A\cos A=\cos B\cos B$
This holds when $A=B$ (isosceles) or one angle is $90^\circ$
✔ True

B:
Maximum value of $\cos A\cos B+\sin A\sin B\sin C$ is $1$
This occurs when $A=B=45^\circ,\ C=90^\circ$
✔ True

C:
If ex-radii are in H.P., sides cannot be in A.P.
✔ True
CUET PG MCA PYQ
The mean deviation from the mean of the A.P. $a, a+d, a+2d, \ldots, a+2nd$ is





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

Solution

The A.P. is symmetric with $2n+1$ terms. Mean deviation from mean for such A.P. is $\dfrac{n(n+1)d}{2n+1}$.

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