There are two circles in xy −plane whose equations are $x^2+y^2-2y=0$ and $x^2+y^2-2y-3=0$. A point $(x,y)$ is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is

1

Coordinate of the focus of the parabola $4y^2+12x-20y+67=0$ is

Topic: NIMCET 2022

2

The value of $\int \frac{({x}^2-1)}{{x}^3\sqrt[]{2{x}^4-2{x}^2+1}}dx$

Topic: NIMCET 2022

3

A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equat…

Topic: NIMCET 2022

4

If the roots of the quadratic equation $x^2+px+q=0$ are tan 30° and tan 15° respectively, then the value of 2 + p - q …

Topic: NIMCET 2022

5

In a Harmonic Progression, $p^{th}$ term is $q$ and the $q^{th}$ term is $p$. Then $pq^{th}$ term is

Topic: NIMCET 2022

6

Solutions of the equation ${\tan }^{-1}\sqrt[]{{x}^2+x}+{\sin }^{-1}\sqrt[]{{x}^2+x+1}=\frac{\pi}{2}$ are

Topic: NIMCET 2022

7

If $a_1, a_2, a_3,...a_n$, are in Arithmetic Progression with common difference d, then the sum $(sind) (cosec a_1 . c…

Topic: NIMCET 2022

8

If $\alpha , \beta$ are the roots of $x^2-x-1=0$ and $A_n=\alpha^n+\beta^n$, the Arithmetic mean of $A_{n-1}$ and $A_n$…

Topic: NIMCET 2022

9

If ${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$, $(a{\gt}b)$ and ${x}^2-{y}^2={c}^2$ cut at righ…

Topic: NIMCET 2022

10

The area enclosed within the curve |x|+|y|=2 is

Topic: NIMCET 2022

1

In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half th…

Topic: NIMCET 2022

2

If $x^my^n$=$(x+y)^{m+n}$, then $\frac{dy}{dx}$ is

Topic: NIMCET 2022

3

If $cos^{-1} \frac{x}{2}+cos^{-1} \frac{y}{3}=\phi$, then $9x^2-12xy cos\phi+4y^2$ is

Topic: NIMCET 2022

4

The value of ${3}^{3-\log _35}$ is

Topic: NIMCET 2022

5

There are two sets A and B with |A| = m and |B| = n. If |P(A)| − |P(B)| = 112 then choose the wrong option (where |A|…

Topic: NIMCET 2022

6

The eccentricity of an ellipse, with its center at the origin is $\frac{1}{3}$ . If one of the directrices is $x=9$, …

Topic: NIMCET 2022

7

If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is $\alp…

Topic: NIMCET 2022

8

If $(\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c})$, then

Topic: NIMCET 2022

9

Today is Wednesday. What would be the day after 61 days?

Topic: NIMCET 2022

10

Identify the fifth number in the series: 122, 144, 166, 188, ?

Topic: NIMCET 2022