List of top Questions asked in JEE Main

\( 2.5 \, \text{g} \) of a non-volatile, non-electrolyte is dissolved in \( 100 \, \text{g} \) of water at \( 25^\circ \text{C} \). The solution showed a boiling point elevation by \( 2^\circ \text{C} \). Assuming the solute concentration is negligible with respect to the solvent concentration, the vapour pressure of the resulting aqueous solution is ______ mm of Hg (nearest integer).
(Given: Molal boiling point elevation constant of water (\( K_b \)) = \( 0.52 \, \text{K} \cdot \text{kg} \cdot \text{mol}^{-1} \),1 atm pressure = \( 760 \, \text{mm of Hg} \), molar mass of water = \( 18 \, \text{g mol}^{-1} \))

If \(a=sin^{-1}(sin\ 5)\) and \(b=cos^{-1}(cos\ 5)\), then \(a^2+b^2=\)

If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.

Let \( x_1, x_2, x_3, x_4 \) be the solution of the equation \[ 4x^4 + 8x^3 - 17x^2 - 12x + 9 = 0 \] and \[ \left(4 + x_1^2\right)\left(4 + x_2^2\right)\left(4 + x_3^2\right)\left(4 + x_4^2\right) = \frac{125}{16} m.\] Then the value of \( m \) is ______.

Which one the following compounds will readily react with dilute NaOH?

The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).

One of the commonly used electrode is calomel electrode. Under which of the following categories calomel electrode comes ?

If the system of equations
\( 2x + 3y - z = 5 \)  
\( x + \alpha y + 3z = -4 \)  
\( 3x - y + \beta z = 7 \)  
has infinitely many solutions, then \( 13 \alpha \beta \) is equal to:  

Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:

10 mL of gaseous hydrocarbon on combustion gives 40 mL of CO\(_2\)(g) and 50 mL of water vapour. The total number of carbon and hydrogen atoms in the hydrocarbon is ______ .

Let \( A = \{1, 3, 7, 9, 11\} \) and \( B = \{2, 4, 5, 7, 8, 10, 12\} \). Then the total number of one-one maps \( f: A \to B \), such that \( f(1) + f(3) = 14 \), is:

A vector has magnitude same as that of A = \(-3\hat{i} + 4\hat{j}\) and is parallel to B = \(4\hat{i} + 3\hat{j}\). The x and y components of this vector in the first quadrant are x and y respectively where:

\(x = \_\_\_\_\).

Suppose \( 2 - p \), \( p \), \( 2 - \alpha \), \( \alpha \) are the coefficients of four consecutive terms in the expansion of \( (1 + x)^n \). Then the value of \( p^2 - \alpha^2 + 6\alpha + 2p \) equals

The correct sequence of acidic strength of the following aliphatic acids in their decreasing order is: $CH_3CH_2COOH$, $CH_3COOH$, $CH_3CH_2CH_2COOH$, $HCOOH$

A capacitor of capacitance \( C \) and potential \( V \) has energy \( E \). It is connected to another capacitor of capacitance \( 2C \) and potential \( 2V \). Then the loss of energy is \( \frac{x}{3} E \), where \( x \) is \( \_\_\_\_ \).

A planet at distance r from the sun takes 200 days to complete one revolution around the sun. What will be the time period for a planet at distance \(\frac{r}{4}\) from the sun?

The molecular formula of second homologue in the homologous series of monocarboxylic acid is

A force is represented by \( F = ax^2 + b t^{1/2} \) Where \( x = \) distance and \( t = \) time. The dimensions of \( \frac{b^2}{a} \) are:

Let \( r \) and \( \theta \) respectively be the modulus and amplitude of the complex number \( z = 2 - i \left( 2 \tan \frac{5\pi}{8} \right) \), then \( (r, \theta) \) is equal to

Given below are two statements:
Statement I: Bromination of phenol in a solvent with low polarity such as CHCl\(_3\) or CS\(_2\) requires a Lewis acid catalyst.
Statement II: The Lewis acid catalyst polarizes the bromine to generate \( \text{Br}^+ \).
In light of the above statements, choose the correct answer from the options given below:

Two resistances of 100Ω and 200Ω are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across the 100Ω resistance, which gives a reading of 1V. The resistance of the voltmeter must be _____ Ω.