Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits are allowed to repeat any number of times, is equal to
Previous 10 Questions — NIMCET 2025
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Given the equation $x+y =1$, $x^2+y^2 =2$, $x^5 +y^5 =A$. Let N be the number
of solution pairs (x,y) to this system of…
Topic: NIMCET 2025
The area enclosed between the curve y = sin x, y = cosx, $0\leq x\leq\frac{\pi}{2}$ is
Topic: NIMCET 2025
Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}+\lambda \hat…
Topic: NIMCET 2025
The circle $x^2 + y^2+ \alpha x+ \beta y+ \gamma=0$ is the image of the circle $x^2 + y^2- 6x- 10y+ 30=0$ across
the li…
Topic: NIMCET 2025
The number of 3-digit integers that are multiple of 6 which can be formed by using the
digits 1,2,3,4,5,6 without repet…
Topic: NIMCET 2025
Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}…
Topic: NIMCET 2025
The maximum value of $\sin x+\sin(x+1)$ is $k \cos \frac{1}{2}$. Then the value of k is
Topic: NIMCET 2025
If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic r…
Topic: NIMCET 2025
A circle with its center in the first quadrant touches both the coordinate axes and the line
x-y-2=0. Then the area of …
Topic: NIMCET 2025
Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be…
Topic: NIMCET 2025
Next 10 Questions — NIMCET 2025
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Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = s…
Topic: NIMCET 2025
An airplane, when 4000m high from the ground, passes vertically above another airplane at
an instant when the angles of…
Topic: NIMCET 2025
Suppose $t_1, t_2, ...t_5$ are in AP such that $\sum ^{18}_{l=0}{{t}}_{3l+1}=1197$ and ${{t}}_7+{{3}}t_{22}=174$. …
Topic: NIMCET 2025
Let E and F be two events such that P(E) > 0 and P(F) > 0. Which one of the
following is NOT equivalent to the co…
Topic: NIMCET 2025
What is the general solution of the equation $\tan \theta + \cot \theta = 2$ ?
Topic: NIMCET 2025
If $\cos^2(10°)\cos(20°)\cos(40°)\cos(50°) \cos(70°) = \alpha+\frac{\sqrt{3}}{16} \cos(10°)$, then $3\alpha^{-1}$ is eq…
Topic: NIMCET 2025
The slope of the normal line to the curve $x = t^2 + 3t - 8$ and $y = 2t^2 - 2t - 5$ at the point
(2,-1) is
Topic: NIMCET 2025
A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a
second point h meters…
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There are 40 female and 20 male students in a class. If the average heights of female and
male students are 5.15 feet a…
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Let $x$ be a positive real number such that $x^{(8\log_5x-24)}=5^{-4}$. Then the product of all possible values of x is…
Topic: NIMCET 2025
