If $\tan^{-1}\left(\dfrac{1-x}{1+x}\right)=\dfrac{1}{2}\tan^{-1}x$, then $x$ is

1

The projections of a line segment on the $X,Y,Z$ axes are $12,4,3$ respectively. The length and direction cosines are

Topic: MAH MCA CET 2025 (Shift 1)

2

The perpendicular distance of the point $P(1,2,3)$ from the line $\dfrac{x-6}{3}=\dfrac{y-7}{2}=\dfrac{z-7}{-2}$ is

Topic: MAH MCA CET 2025 (Shift 1)

3

The valid range of $x$ for which $\cos^{-1}(2x-3)$ is defined is

Topic: MAH MCA CET 2025 (Shift 1)

4

Given $,\dfrac{dy}{dx}+y=1,$ with $y(0)=2$, find $y(1)$.

Topic: MAH MCA CET 2025 (Shift 1)

5

The number of real solutions of $\sqrt{1+\cos 2x}=\sqrt{2},\cos^{-1}(\cos x)$ in $\left[\frac{\pi}{2},\pi\right]$ is

Topic: MAH MCA CET 2025 (Shift 1)

6

In $\triangle ABC$, sides are $a=9$, $b=7$, $c=12$. Find angle $C$ (opposite side $c$) using the Law of Cosines.

Topic: MAH MCA CET 2025 (Shift 1)

7

The equation of a parabola is $y^2=4x$. Which of the following points lies on the parabola?

Topic: MAH MCA CET 2025 (Shift 1)

8

The coefficient of $x^{n}$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ are in the ratio

Topic: MAH MCA CET 2025 (Shift 1)

9

A family of parabolas $y=ax^{2}$ $(a>0)$ has vertices on the $x$–axis and axis parallel to $y$–axis. The differential e…

Topic: MAH MCA CET 2025 (Shift 1)

10

A company models the rate of change of concentration by $(y^2+3xy),dx+(x^2+xy),dy=0$, with $y=1$ when $x=1$. Find $y$ a…

Topic: MAH MCA CET 2025 (Shift 1)

1

Find the total number of ways to put $20$ balls into $5$ boxes so that the first box contains only one ball.

Topic: MAH MCA CET 2025 (Shift 1)

2

Find the number of arrangements of the letters of the word $,\text{INDEPENDENCE},$ such that(i) the words start with $I…

Topic: MAH MCA CET 2025 (Shift 1)

3

The number of parallelograms formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines is

Topic: MAH MCA CET 2025 (Shift 1)

4

A study finds that employees working fewer hours per week are more productive during their working hours and concludes …

Topic: MAH MCA CET 2025 (Shift 1)

5

A study found that employees who worked fewer hours per week were more productive. Which of the following, if true, wea…

Topic: MAH MCA CET 2025 (Shift 1)

6

In a certain code “SAND” is written as “UCPF”. How is “STONE” written in that code?

Topic: MAH MCA CET 2025 (Shift 1)

7

Three of the following four words are alike in a certain way and one is different. Select the odd one.

Topic: MAH MCA CET 2025 (Shift 1)

8

Look at this series: $53,53,40,40,27,27,\ldots$ What number should come next?

Topic: MAH MCA CET 2025 (Shift 1)

9

In a certain language, “BOOK” is written as $4300$, “MATE” as $3900$. Then $1600$ represents which word?

Topic: MAH MCA CET 2025 (Shift 1)

10

If CLAUSE is coded as ECSLUA, then the code of UMPIRE will be

Topic: MAH MCA CET 2025 (Shift 1)