If $\cos^2(10°)\cos(20°)\cos(40°)\cos(50°) \cos(70°) = \alpha+\frac{\sqrt{3}}{16} \cos(10°)$, then $3\alpha^{-1}$ is equal to

1

What is the general solution of the equation $\tan \theta + \cot \theta = 2$ ?

Topic: NIMCET 2025

2

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

3

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

4

An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of…

Topic: NIMCET 2025

5

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

6

Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits are allowed to repeat any nu…

Topic: NIMCET 2025

7

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

8

The area enclosed between the curve y = sin x, y = cosx, $0\leq x\leq\frac{\pi}{2}$ is

Topic: NIMCET 2025

9

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

10

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

1

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

2

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…

Topic: NIMCET 2025

3

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…

Topic: NIMCET 2025

4

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

5

The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is

Topic: NIMCET 2025

6

What is the value of $\lim _{{x}\rightarrow\infty}-(x+1)\Bigg{(}{e}^{\frac{1}{x+1}}-1\Bigg{)}$?

Topic: NIMCET 2025

7

The value of $\int ^{\frac{\pi}{2}}_0\frac{(1+2\cos x)}{({2+\cos x)}^2}dx$ lies in the interval

Topic: NIMCET 2025

8

Read definition and all four choices carefully, and find the answer that provides the best example of the given definit…

Topic: NIMCET 2025

9

In a certain code language, the word "REASON" is encoded as TDDQSK. Using the same rule, how is the word PRAYER coded?

Topic: NIMCET 2025

10

Four people (P,Q,R & S) are standing in a queue. Q is ahead of P. R is between P and S. If S is at the end of the q…

Topic: NIMCET 2025