List of top Questions asked in MHT CET

If $\sin(\theta-\alpha)$, $\sin~\theta$ and $\sin(\theta+\alpha)$ are in H.P., then the value of $\cos~2\theta$ is

The equation \( x^{3} + x - 1 = 0 \) has

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( |\vec{a}+\vec{b}+\vec{c}|=1 \), \( \vec{c}=\lambda(\vec{a}\times\vec{b}) \) and \( |\vec{a}|=\frac{1}{\sqrt{2}} \), \( |\vec{b}|=\frac{1}{\sqrt{3}} \), \( |\vec{c}|=\frac{1}{\sqrt{6}} \), then the angle between \( \vec{a} \) and \( \vec{b} \) is

Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors such that \( |\vec{a}|=\sqrt{3} \), \( |\vec{b}|=5 \), \( \vec{b}\cdot\vec{c}=10 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \frac{\pi}{3} \). If \( \vec{a} \) is perpendicular to the vector \( \vec{b}\times\vec{c} \), then \( |\vec{a}\times(\vec{b}\times\vec{c})| \) is equal to

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

General solution of the differential equation $\cos x(1+\cos y)dx-\sin y(1+\sin x)dy=0$ is

If the line \( x - 2y = m \, (m \in \mathbb{Z}) \) intersects the circle \( x^{2} + y^{2} = 2x + 4y \) at two distinct points, then the number of possible values of \( m \) are

The solution set of the inequalities $4x+3y\le60$, $y\ge2x$, $x\ge3$, $x, y\ge0$ is represented by region

The statement $[(p\rightarrow q)\wedge\sim q]\rightarrow r$ is tautology, when $r$ is equivalent to

The negation of the statement "The number is an odd number if and only if it is divisible by 3."

Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \( \frac{4}{5} \), then the probability that he is unable to solve less than two problems is

A particle executes a simple harmonic motion of time period $ T $ . Find the time taken by the particle to go directly from its mean position to half the amplitude

A ball of mass $ 0.25\, kg $ attached to the end of a string of length $ 1.96\, m $ is moving in a horizontal circle. The string will break if the tension is more than $ 25 \,N $ . What is the maximum speed with which ball can be moved?

A circular disc is to be made by using iron and aluminium, so that it aquires momentum of inertia about its geometrical axis. It is possible with

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

Which one does not show HSK pathway ?

Biennials get changed into annuals by

Pulmonary trunk and aorta are attached by

$ U $ is the $ PE $ of an oscillating particle and $ F $ is the force acting on it at a given instant. Which of the following is true ?

Anticoagulant hirudin is obtained from genetically modified

A hormone delaying senescence is

The increase in pressure required to decrease the $ 200 \,L $ volume of a liquid by $ 0.008\% $ in $ kPa $ is (Bulk modulus of the liquid $ = 2100 \,MPa $ is)

Which ones are gustatoreceptors ?

A nitrogen fixing blue-green alga is