List of top Questions asked in JEE Main

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

Match List-I with List-II

The metal salts formed during softening of hardwater using Clark's method are :

Stearic acid and polyethylene glycol react to form which one of the following soaps/detergents ?

Drugs used to bind to receptors, inhibiting its natural function and blocking a message are called :

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time The ratio of their initial velocities is

Refining using liquation method is the most suitable for metals with :

Which of the following can be used to prevent the decomposition of $H _2 O _2$ ?

Which technique among the following, is most appropriate in separation of a mixture of $100\, mg$ of $p$-nitrophenol and picric acid ?

The force required to stretch a wire of cross-section $1 cm ^2$ to double its length will be: (Given Yong's modulus of the wire $=2 \times 10^{11} N / m ^2$ )

The photochemical smog does not generally contain :

Choose the correct order of density of the alkali metals :

In two different experiments, an object of mass $5\, kg$ moving with a speed of $25 \,ms ^{-1}$ hits two different walls and comes to rest within
(i) 3 second, 
(ii) 5 seconds, respectively.
Choose the correct option out of the following :

Given below are two statements :
Statement I: In polluted water values of both dissolved oxygen and BOD are very low.
Statement II: Eutrophication results in decrease in the amount of dissolved oxygen.
In the light of the above statements, choose the most appropriate answer from the options given below :

 NCC parade is going at a uniform speed of $9\, km / h$ under a mango tree on which a monkey is sitting at a height of $196\, m$ At any particular instant, the monkey drops a mango A cadet will receive the mango whose distance from the tree at time of drop is : (Given g= 9.8 m/s²)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Lithium salts are hydrated.
Reason (R) : Lithium has higher polarising power than other alkali metal group members.
In the light of the above statements, choose the most appropriate answer from the options given below :

The \( \text{Eu}^{2+} \) ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number of Eu = 63]

Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is __________

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

Let \(\binom{n}{k}\) denote \(^nC_k\).
If \(A_k = \sum_{i=0}^{9} \binom{9}{i} \binom{12}{12-k+i} + \sum_{i=0}^{8} \binom{8}{i} \binom{13}{13-k+i}\) and \(A_4 - A_3 = 190 p\), then p is equal to ___________.

If \({}^{20}C_r\) is the co-efficient of \(x^r\) in the expansion of \((1+x)^{20\), then the value of \(\sum_{r=0}^{20} r^2 \cdot {}^{20}C_r\) is equal to :}

\(3 \times 7^{22} + 2 \times 10^{22} - 44\) when divided by 18 leaves the remainder _________.