List of top Questions asked in VITEEE- 2015

Let \( f(x) = 25x^{24}(1 - x)^{75} \), on the interval \( [0, 1] \), then \[ f'(x) = 25x^{24}(1 - x)^{75} - 75x^{25}(1 - x)^{74} = 25x^{24}(1 - x)^{74}[(1 - x) - 3x] \]
If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is
If \( l = x^2 + y^2 + z^2 \) is a normal to the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1, \] then
If \( \text{line} \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \] then \( c^2 \) is equal to
Correct result is as follows: \[ P \, (\neg \, Q) \, \equiv (P \, \vee \, Q) \, \implies (P \, \vee \, Q) \, \implies \, R \, \implies \, S \]
The correct result of the equation \( 3x^2 + 2x + 7y^2 - 14y + 4 \) is
The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).
The integral \( \int \frac{dx}{\cos x + \sqrt{5} \sin x} \) equals
The differential equation \( (3x + 4y + 1) dx + (4x + 5y + 1) dy = 0 \) represents a family of
If \( \Delta r = \left| \sum_{r=1}^{n} r \right| \), then \( \sum_{r=1}^{n} \Delta r \) is equal to
If \( A, B, C \) are three events associated with a random experiment, then \( P(A \,|\, B) \) is
If \( A = \begin{pmatrix} 1 & 2
3 & 1 \end{pmatrix} \), then rank \( A \) is
The probability of getting a double six in one throw of two dice
The rate constant of the reaction \( A \rightarrow B \) at different times are given below: \[ \text{Concentration (M)} \quad \text{Time (Minutes)}
0.069 \quad 0 \quad 0.052 \quad 17 \quad 0.035 \quad 34 \quad 0.018 \quad 51 \] The rate constant of the reaction according to the correct order of reaction is
If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius
A compound which gives a negative test with ninhydrin, it cannot be a protein or an amino acid. As, it gives a positive test with Benedict’s solution. The compound is
The compound used for making super glue or crazy glue is
\( X' \) and \( Y' \) respectively are
In the Cannizzaro reaction given below: \[ 2Ph - CHO \xrightarrow{\text{NaOH}} Ph - CH_2OH + Ph - CO_2 \] the slowest step is
The reaction of 1-bromo-3-chlorocyclobutane with metallic sodium in dioxane under reflux conditions gives
Identify \( Z \) in the following reaction sequence \[ CH_3CH_2CH_2OH \xrightarrow{H_2SO_4, 160^\circ C} CH_3CH_2CH = CH_2 \xrightarrow{NaNH_2} Z \]
Which of the following reactions is used to prepare isobutane?
The concentrations of the reactant A in the reaction \( A \rightarrow B \) at different times are given below Concentration (M) \quad Time (Minutes) \[ 0.069 \quad 0 \quad 0.052 \quad 17 \quad 0.035 \quad 34 \quad 0.018 \quad 51 \] The rate constant of the reaction according to the correct order of reaction is
The ratio of slopes of \( K_{\text{max}} \) vs \( V \) and \( V_0 \) vs \( v \) curves in the photoelectric effect gives
With excess of water, both \( P_2O_5 \) and \( PCl_5 \) give