VITEEE 2023
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Aptitude

From the given options, choose the correct one that will replace the question mark(?) in the following series. $$2,0,3,2
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In a certain code language, 'RUBBER' is coded as '102' and 'JELLY' is coded as '76'. How will 'LABEL' be coded in the sa
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Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the lette
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In a code language, 'SAUCE' is written as 'ASVEC'. How will 'MEANT' be written as in that language?
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Select the number from among the given options that can replace the question mark (?) in the following series. $$3,10,24
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What is the average income of the company over the years?
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Which of the following pairs of years, shows the equal expenditure of the company?
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Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even
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How is P related to R? I. $$Q$$ is the son of $$R$$. II. $$\mathrm{Q}$$ is the brother of $$\mathrm{P}$$.
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Six persons A, B, C, D, E and F are sitting in a row. A and F are sitting at two extreme ends of the row. B is to the im
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Chemistry

In context of the lanthanoides, which of the following statements is not correct?
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The number of peptide bonds in a linear tetrapeptide (made of different amino acids) are
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The uncertainty in the momentum of an electron is $$2.0 \times 10^{-8} \mathrm{~kg} \mathrm{~ms}^{-1}$$. The uncertainty
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A metal has bcc structure and the edge length of its unit cell is $$8 \mathop A\limits^o$$. The volume of the unit cell
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$$\mathrm{MnO}_4^{-}$$ is good oxidising agent in different medium changing to $$\mathrm{MnO}_4^{-} \rightarrow \mathrm{
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In the reaction, $$\mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI}$$. In a 4L flask, 0.8 mole of each $$\math
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The ionic conductance of following cation in a given concentration are in the order.
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$$\mathrm{H}$$-bonding is maximum in
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The stability of dihalides of $$\mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}$$ and decreases gradually in the sequence.
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The structure of $$\mathrm{XeOF}_4$$ is
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$$\mathrm{PH}_3$$ has much lower boiling point than $$\mathrm{NH}_3$$ because :
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Match the following Column I and Column II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;
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ortho-silicate ion is
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Which is correct about zero order reaction?
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Which of the following compounds is used as the starting material for the preparation of potassium dichromate?
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The total number of metal-metal bond present in $$\left[\mathrm{Co}_2(\mathrm{CO})_8\right]$$ is
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Which of the following is an intensive property?
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Plot of $$\log x / m$$ against $$\log p$$ is a straight line inclined at an angle of $$45^{\circ}$$. When the pressure i
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The value of $$\Delta E$$ for combustion of $$32 \mathrm{~g}$$ of $$\mathrm{CH}_4$$ is $$-1770778 \mathrm{~J}$$ at $$298
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The standard $$E_{\text {red }}^{\circ}$$ values of $$A, B$$ and $$C$$ are $$+0.52 \mathrm{~V},-23.6 \mathrm{~V},-0.44 \
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Addition of water to butyne occurs in acidic medium and in the presence of $$\mathrm{Hg}^{2+}$$ ions as a catalyst. The
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The reaction, is called
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Which of the following products is formed in the given reaction?
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The acidic strength of following compounds are in the order
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Consider the following cell reaction. $$\begin{aligned} & 2 \mathrm{Fe}(s)+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longri
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In a set of reactions acetophenone gave a product $$B$$. Identify the product $$B$$. $$\mathrm{C}_6 \mathrm{H}_5 \mathrm
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Glucose contains $$-\mathrm{CHO}$$ group and Which of the following solution or reagent can be used to distinguish the
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In the given reaction, The product P is
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Which one of the following concentration terms is/are independent of temperature?
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In a set of reactions nitrobenzene gave a product $$C$$. Identify the product $$C$$. $$\mathrm{C}_6 \mathrm{H}_5 \mathrm
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Which one of the following compounds is formed in the laboratory from benzene by a substitution reaction?
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Atomic number of $$\mathrm{Mn}, \mathrm{Fe}$$ and $$\mathrm{Co}$$ are 25, 26 and 27 respectively. Which of the following
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Arrhenius equation may not be represented as
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Match the Column I with Column II. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-s
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Choose the wrong statements. I. $$\mathrm{CO}_2$$ is responsible for greenhouse effect. II. Acid rain contains mainly $$
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English

Fill in the blank with most suitable word. I ............. for forty minutes to see the doctor before my name was announ
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Pick out the correct synonym of the word-'Prerogative'.
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Select the antonym for the word 'Dishevelled'
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What is '$$\mathrm{I}$$' in the above lines?
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The rain calls itself the 'dotted silver threads' as
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Mathematics

Let $$a_n$$ be a sequence of numbers which is defined by relation $$a_1=2, \frac{a_n}{a_{n+1}}=3^{-n}$$, then $$\log _2\
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The value of $$\frac{1}{2}\left(\frac{1}{5}\right)^2+\frac{2}{3}\left(\frac{1}{5}\right)^3+\frac{3}{4}\left(\frac{1}{5}\
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Out of 9 consonants and 4 vowels, how many words of 4 consonants and 3 vowels can be formed?
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Last three digits in $$(9)^{50}$$ be
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The minium value of $$\left[2-\cos \theta+\sin ^2 \theta\right]$$ is
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If $$z_1, z_2$$ and $$z_3$$ are the vertices $$A, B$$ and $$C$$ respectively of an isosceles right angled triangle with
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The line $$a x+b y+c=0$$ will be a tangent to the circle $$x^2+y^2=r^2$$, then
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The image of the point $$(2,3,7)$$ in the plane $$2 x+5 y-3 z-19=0$$, is
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The distance between the point $$(7,2,4)$$ and the plane determined by the points $$(2,5,-3),(-2,-3,5)$$ and $$(5,3,-3)$
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The value of $$\int_\lambda^{\lambda+\pi / 2}\left(\cos ^4 x+\sin ^4 x\right) d x$$ is
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If matrix $$A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]$$ is given to be symme
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If the 4th term in the expansion of $$\left(p x+\frac{1}{x}\right)^n, n \in N$$ is $$\frac{5}{2}$$ and three normals to
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The area of the region containing the points $$(x, y)$$ satisfying $$4 \leq x^2+y^2 \leq 2|x|+|y|$$, is
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If $$\alpha$$ is a non -real fifth root of unity, then the value of $$3^{\left|1+\alpha+\alpha^2+\alpha^{-2}-\alpha^{-1
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If $$\alpha, \beta$$ and $$\gamma$$ are the cube roots of $$P,(P
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If $$x+\frac{1}{x}=1$$ and $$p=x^{4000}+\frac{1}{x^{4000}}$$ and $$q$$ is the digit at unit place in the number $$2^{2 n
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Let $$z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots \ldots \ldots$$ 9,
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If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2
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If $$\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2$$, then the range of $$a$$ is
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The equation $$3 \cos ^{-1} x-\pi x-\pi / 2=0$$ has
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The area enclosed by $$y=x^3+1$$ and $$y=x+2$$ in first quadrant, is
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If $$R$$ is a relation from a finite set A having $$m$$ elements to finite set $$B$$ having $$n$$ elements, then the num
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If $$\sin A, \sin B$$ and $$\cos A$$ are in GP, then the roots of $$x^2+2 x \cot B+1=0$$ are always
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The determinant of the matrix $$\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]$$ is
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Let $$A$$ and $$B$$ be two independent events such that the odds in favour of $$A$$ and $$B$$ are $$1: 1$$ and $$3: 2$$,
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The plane is perpendicular to the planes $$x-y+2 z-4=0$$ and $$2 x-2 y+z=0$$ and passes through $$(1,-2,1)$$ is
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If $$\theta_1, \theta_2$$ and $$\theta_3$$ are the angles made by a line with the positive direction of $$X, Y$$ and $$Z
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Suppose, $$A=\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$$ is an adj
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The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x+7$$ occurs at the point
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The solution of $$d y / d x=1+x+y+x y$$ is
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A unit vector perpendicular to both the vectors $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathb
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If $$\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)$$, then the value of $$y$$ is
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$$\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\le
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If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to
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The sum of all the numbers of four different digits that can be made using the digits 0, 1, 2 and 3 is
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If $$x^n=a_0+a_1(1+x)+a_2(1+x)^2+\ldots \ldots \ldots+ a_n(1+x)^n=b_0+b_1(1-x)+b_2(1-x)^2+\ldots . .+ b_n(1-x)^n$$, then
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The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\le
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For $$x \in R, f(x)=|\log 2-\sin x|$$ and $$g(x)=f(f(x))$$, then
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$$\lim _\limits{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \ldots 3 n}{n^{2 n}}\right)^{1 / n}$$ is equal to
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Let $$a, b$$ and $$c$$ be three unit vectors such that $$a \times(b \times c)=\frac{\sqrt{3}}{2}(b+c)$$. If $$b$$ is not
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Physics

The upper end of a wire of diameter $$24 \mathrm{~mm}$$ and length $$1 \mathrm{~m}$$ is damped and its other end is twis
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What is the voltage gain in a common emitter amplifier, where input resistance is $$6 \Omega$$ and load resistance $$48
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When $${ }_{92} \mathrm{U}^{235}$$ undergoes fission, $$0.1 \%$$ of its original mass is changed into energy. How much e
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A copper sphere cools from $$82^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 10 minutes and to $$42^{\circ} \mat
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Two gases occupy two containers $$A$$ and $$B$$. The gas in $$A$$ of volume $$0.20 \mathrm{~m}^3$$, exerts a pressure of
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Assuming the diodes to be of silicon with forward resistance zero, the current $$i$$ in the following circuit is
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With increasing temperature, the angle of contact,
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In a $$n$$-$$p$$-$$n$$ transistor $$10^{10}$$ electrons enter the emitter in $$10^{-6}$$ s. $$6 \%$$ of the other electr
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The position of a projectile launched from the origin at $$t=0$$ is given $$\mathbf{r}=(40 \hat{\mathbf{i}}+50 \hat{\mat
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Electric field in the region is given by $$\mathbf{E}=\left(M / x^4\right) \hat{\mathbf{i}}$$, then the correct expressi
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The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N}
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Two parallel conductors carry current in opposite directions as shown in the figure. One conductor carries a current of
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The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ co
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A ball is allowed to fall from a height of $$10 \mathrm{~m}$$. If there is $$30 \%$$ loss of energy due to impact, then
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The elastic limit of $$1 \mathrm{~kg}$$ mass is $$3.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$$. Find the maximum load
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The focal length of thin convex lens for red and blue rays are $$100 \mathrm{~cm}$$ and $$98.01 \mathrm{~cm}$$, respecti
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The ratio of the acceleration for a solid sphere (mass $$m$$ and radius $$R$$) rolling down an incline of angle '$$\thet
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The de-Broglie wavelength of a proton $$\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$$ acclerated through a potentia
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The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immerse
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A particle of mass $m$ is projected with a velocity $$v$$ making an angle of $$45^{\circ}$$ with the horizontal. The mag
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A parallel plate capacitor with air between the plates has a capacitance of $$15 \mathrm{~pF}$$. the separation between
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A constant voltage is applied between the two ends of a uniform metallic wire, Some heat is developed in it. The heat de
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The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The
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A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to
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Susceptibility of ferromagnetic substance is
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A particle of mass $$10 \mathrm{~kg}$$ moving eastwards with a speed $$10 \mathrm{~m} / \mathrm{s}$$ collides with anoth
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A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$
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A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil
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A geostationary satellite is orbiting the Earth at a height of $$4 R$$ above that surface of the Earth. $R$ being the ra
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Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The ma
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0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cr
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In the formula $$X=3 Y Z^2, X$$ and $$Z$$ have dimensions of capacitance and magnetic induction respectively. The dimens
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Three blocks of masses $$m_1, m_2$$ and $$m_3$$ are connected by massless strings, as shown, on a frictionless table. Th
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The susceptibility of a magnetism at $$300 \mathrm{~K}$$ is $$1.5 \times 10^{-5}$$. The temperature at which the suscept
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A transmitting antenna is kept on the surface of the Earth. The minimum height of receiving antenna required to receive
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