List of top Questions asked in JEE Main, KCET

In a screw gauge, when the circular scale is given five complete rotations, it moves linearly by \(2.5\,\text{mm\). If the circular scale has 100 divisions, the least count of the screw gauge is:}
Let in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :
Calculate the number of molecules and moles of \( \text{SO_2 \) in its 1.479 liters at STP.}
A particle is moving along the \(x\)-axis where the speed varies as \[ v^2 = 100 - x^2 \] Determine the time period.
(A) Bond angle Cr–O–Cr in \( \text{CrO}_7^{2-} \) is 126° (B) \( \text{Na}_2\text{Cr}_2\text{O}_7 \) is used as primary standard solution in titration. (C) \( \text{K}_2\text{Cr}_2\text{O}_7 \) oxidises \( \text{Fe}^{2+} \) into \( \text{Fe}^{3+} \) in acidic medium. (D) \( \text{CrO}_4^{2-} \) and \( \text{Cr}_2\text{O}_7^{2-} \) are interconvertible by changing pH.
Two blocks \(A\) and \(B\) are released from rest on two inclined planes of the same inclination. One inclined plane is smooth while the other is rough as shown in the figure. If block \(B\) takes \(50\%\) more time to reach the bottom than block \(A\), find the coefficient of friction \((\mu)\). The inclination of the plane is \(45^\circ\).
If \( L_1 : x - y = 0 \), \( L_2 : y = -3x \), \( L_3 \) is the obtuse angle bisector of \( L_1 \) and \( L_2 \), and \( L_4 : x + 3 = 0 \). Let \( A \) be the point of intersection of \( L_4 \) and \( L_1 \), \( B \) be the point of intersection of \( L_4 \) and \( L_2 \), and \( C \) be the point of intersection of \( L_4 \) and \( L_3 \). Then the value of \( \dfrac{(BC)^2}{(AC)^2} \) is:
Nuclei \(A\) and \(B\) form a nucleus \(C\). Binding energy per nucleon for \(A, B\) and \(C\) are \(3\,\text{MeV}, 7\,\text{MeV}\) and \(6\,\text{MeV}\) respectively. Find the energy produced in the reaction: \[ 2A^{3} + B^{4} \rightarrow C^{10} \]
The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is
Let $A$ is a matrix of order 3 such that $|A| = -4$, then the value of $|\text{adj}(\text{adj}(2\text{adj} A)^{-1})|$ is
An ideal gas is placed in a container at \( (P_1, V_1, T_1) \) and another ideal gas is placed in a different container at \( (P_2, V_2, T_2) \) are mixed at final pressure of \( P \) and final volume of \( V \). Calculate the final temperature.
If $S = \{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, A^2 - 4A + 3I = \text{Null matrix}, a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } \text{Tr}(A) = 4 \}$. Then the number of elements of set $S$ is/are
In an A.P. first term is $\frac{10}{3}$ and first 30 terms are non-negative such that sum of first 30 terms = $(T_{30})^3$, then d is equal to (where $T_n$ is $n^{\text{th}}$ term of A.P., and d is the common difference of A.P.)
Choose the correct match.
Match the column:
} Match correct reagents with given reactions:
Arrange the following groups according to their decreasing order of electron withdrawing nature – \( \text{COOH} \), \( \text{CN} \), \( I \), and \( \text{NO}_2 \).
Soluble in aqueous NaOH
Statement-1: Maltose is a non-reducing sugar.
Statement-2: Lactose is a reducing sugar.
Match the column-I with column-II:
Choose the correct match.
IUPAC Name of the formed compound:
Statement-1: Under certain conditions, the covalency of oxygen can be up to 4. In \( \text{SO}_2 \), the oxidation state of oxygen is \( -2 \) and in \( \text{OF}_2 \), the oxidation state of oxygen is \( +2 \). Statement-2: The anomalous behaviour of oxygen in the 16th group is due to its small size and high electronegativity.
In an AC circuit a resistor \(100\Omega\), inductor \(0.1\,\text{mH}\) and a capacitor are connected in series across an AC source of \(220\,\text{V},\,50\,\text{Hz}\). If the power factor of the circuit is \( \frac{1}{2} \) and \( |X_L - X_C| = \alpha\sqrt{3}\,\Omega \), find \(\alpha\).
Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.
Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :
Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c\}$ then total number of functions from $A$ to $B$ which are not onto are