Aptitude
1. From the given options, choose the correct one that will replace the question mark(?) in the following series.
$$2,0,3,2 2. In a certain code language, 'RUBBER' is coded as '102' and 'JELLY' is coded as '76'. How will 'LABEL' be coded in the sa 3. Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the lette 4. In a code language, 'SAUCE' is written as 'ASVEC'. How will 'MEANT' be written as in that language? 5. Select the number from among the given options that can replace the question mark (?) in the following series.
$$3,10,24 6. What is the average income of the company over the years? 7. Which of the following pairs of years, shows the equal expenditure of the company? 8. Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even 9. How is P related to R?
I. $$Q$$ is the son of $$R$$.
II. $$\mathrm{Q}$$ is the brother of $$\mathrm{P}$$. 10. 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
Chemistry
1. In context of the lanthanoides, which of the following statements is not correct? 2. The number of peptide bonds in a linear tetrapeptide (made of different amino acids) are 3. The uncertainty in the momentum of an electron is $$2.0 \times 10^{-8} \mathrm{~kg} \mathrm{~ms}^{-1}$$. The uncertainty 4. 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 5. $$\mathrm{MnO}_4^{-}$$ is good oxidising agent in different medium changing to $$\mathrm{MnO}_4^{-} \rightarrow \mathrm{ 6. In the reaction, $$\mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI}$$.
In a 4L flask, 0.8 mole of each $$\math 7. The ionic conductance of following cation in a given concentration are in the order. 8. $$\mathrm{H}$$-bonding is maximum in 9. The stability of dihalides of $$\mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}$$ and decreases gradually in the sequence. 10. The structure of $$\mathrm{XeOF}_4$$ is 11. $$\mathrm{PH}_3$$ has much lower boiling point than $$\mathrm{NH}_3$$ because : 12. Match the following Column I and Column II
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.tg td{border-color:black; 13. ortho-silicate ion is 14. Which is correct about zero order reaction? 15. Which of the following compounds is used as the starting material for the preparation of potassium dichromate? 16. The total number of metal-metal bond present in $$\left[\mathrm{Co}_2(\mathrm{CO})_8\right]$$ is 17. Which of the following is an intensive property? 18. Plot of $$\log x / m$$ against $$\log p$$ is a straight line inclined at an angle of $$45^{\circ}$$. When the pressure i 19. The value of $$\Delta E$$ for combustion of $$32 \mathrm{~g}$$ of $$\mathrm{CH}_4$$ is $$-1770778 \mathrm{~J}$$ at $$298 20. The standard $$E_{\text {red }}^{\circ}$$ values of $$A, B$$ and $$C$$ are $$+0.52 \mathrm{~V},-23.6 \mathrm{~V},-0.44 \ 21. Addition of water to butyne occurs in acidic medium and in the presence of $$\mathrm{Hg}^{2+}$$ ions as a catalyst. The 22. The reaction,
is called 23. Which of the following products is formed in the given reaction?
24. The acidic strength of following compounds are in the order 25. Consider the following cell reaction.
$$\begin{aligned}
& 2 \mathrm{Fe}(s)+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longri 26. In a set of reactions acetophenone gave a product $$B$$. Identify the product $$B$$.
$$\mathrm{C}_6 \mathrm{H}_5 \mathrm 27. Glucose contains $$-\mathrm{CHO}$$ group and
Which of the following solution or reagent can be used to distinguish the 28. In the given reaction,
The product P is 29. Which one of the following concentration terms is/are independent of temperature? 30. In a set of reactions nitrobenzene gave a product $$C$$. Identify the product $$C$$.
$$\mathrm{C}_6 \mathrm{H}_5 \mathrm 31. Which one of the following compounds is formed in the laboratory from benzene by a substitution reaction? 32. Atomic number of $$\mathrm{Mn}, \mathrm{Fe}$$ and $$\mathrm{Co}$$ are 25, 26 and 27 respectively. Which of the following 33. Arrhenius equation may not be represented as 34. Match the Column I with Column II.
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.tg td{border-color:black;border-s 35. Choose the wrong statements.
I. $$\mathrm{CO}_2$$ is responsible for greenhouse effect.
II. Acid rain contains mainly $$
English
1. Fill in the blank with most suitable word. I ............. for forty minutes to see the doctor before my name was announ 2. Pick out the correct synonym of the word-'Prerogative'. 3. Select the antonym for the word 'Dishevelled' 4. What is '$$\mathrm{I}$$' in the above lines? 5. The rain calls itself the 'dotted silver threads' as
Mathematics
1. 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 $$\log _2\ 2. The value of $$\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}\ 3. Out of 9 consonants and 4 vowels, how many words of 4 consonants and 3 vowels can be formed? 4. Last three digits in $$(9)^{50}$$ be 5. The minium value of $$\left[2-\cos \theta+\sin ^2 \theta\right]$$ is 6. If $$z_1, z_2$$ and $$z_3$$ are the vertices $$A, B$$ and $$C$$ respectively of an isosceles right angled triangle with 7. The line $$a x+b y+c=0$$ will be a tangent to the circle $$x^2+y^2=r^2$$, then 8. The image of the point $$(2,3,7)$$ in the plane $$2 x+5 y-3 z-19=0$$, is 9. The distance between the point $$(7,2,4)$$ and the plane determined by the points $$(2,5,-3),(-2,-3,5)$$ and $$(5,3,-3)$ 10. The value of $$\int_\lambda^{\lambda+\pi / 2}\left(\cos ^4 x+\sin ^4 x\right) d x$$ is 11. If matrix $$A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]$$ is given to be symme 12. If the 4th term in the expansion of $$\left(p x+\frac{1}{x}\right)^n, n \in N$$ is $$\frac{5}{2}$$ and three normals to 13. The area of the region containing the points $$(x, y)$$ satisfying $$4 \leq x^2+y^2 \leq 2|x|+|y|$$, is 14. If $$\alpha$$ is a non -real fifth root of unity, then the value of $$3^{\left|1+\alpha+\alpha^2+\alpha^{-2}-\alpha^{-1 15. If $$\alpha, \beta$$ and $$\gamma$$ are the cube roots of $$P,(P 16. If $$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 17. 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, 18. If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2 19. If $$\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2$$, then the range of $$a$$ is 20. The equation $$3 \cos ^{-1} x-\pi x-\pi / 2=0$$ has 21. The area enclosed by $$y=x^3+1$$ and $$y=x+2$$ in first quadrant, is 22. If $$R$$ is a relation from a finite set A having $$m$$ elements to finite set $$B$$ having $$n$$ elements, then the num 23. If $$\sin A, \sin B$$ and $$\cos A$$ are in GP, then the roots of $$x^2+2 x \cot B+1=0$$ are always 24. The determinant of the matrix $$\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]$$ is 25. Let $$A$$ and $$B$$ be two independent events such that the odds in favour of $$A$$ and $$B$$ are $$1: 1$$ and $$3: 2$$, 26. The plane is perpendicular to the planes $$x-y+2 z-4=0$$ and $$2 x-2 y+z=0$$ and passes through $$(1,-2,1)$$ is 27. If $$\theta_1, \theta_2$$ and $$\theta_3$$ are the angles made by a line with the positive direction of $$X, Y$$ and $$Z 28. 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 29. 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 30. The solution of $$d y / d x=1+x+y+x y$$ is 31. A unit vector perpendicular to both the vectors $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathb 32. If $$\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)$$, then the value of $$y$$ is 33. $$\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\le 34. If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to 35. The sum of all the numbers of four different digits that can be made using the digits 0, 1, 2 and 3 is 36. 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 37. The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\le 38. For $$x \in R, f(x)=|\log 2-\sin x|$$ and $$g(x)=f(f(x))$$, then 39. $$\lim _\limits{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \ldots 3 n}{n^{2 n}}\right)^{1 / n}$$ is equal to 40. Let $$a, b$$ and $$c$$ be three unit vectors such that $$a \times(b \times c)=\frac{\sqrt{3}}{2}(b+c)$$. If $$b$$ is not
Physics
1. The upper end of a wire of diameter $$24 \mathrm{~mm}$$ and length $$1 \mathrm{~m}$$ is damped and its other end is twis 2. What is the voltage gain in a common emitter amplifier, where input resistance is $$6 \Omega$$ and load resistance $$48 3. When $${ }_{92} \mathrm{U}^{235}$$ undergoes fission, $$0.1 \%$$ of its original mass is changed into energy. How much e 4. A copper sphere cools from $$82^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 10 minutes and to $$42^{\circ} \mat 5. Two gases occupy two containers $$A$$ and $$B$$. The gas in $$A$$ of volume $$0.20 \mathrm{~m}^3$$, exerts a pressure of 6. Assuming the diodes to be of silicon with forward resistance zero, the current $$i$$ in the following circuit is
7. With increasing temperature, the angle of contact, 8. In a $$n$$-$$p$$-$$n$$ transistor $$10^{10}$$ electrons enter the emitter in $$10^{-6}$$ s. $$6 \%$$ of the other electr 9. The position of a projectile launched from the origin at $$t=0$$ is given $$\mathbf{r}=(40 \hat{\mathbf{i}}+50 \hat{\mat 10. Electric field in the region is given by $$\mathbf{E}=\left(M / x^4\right) \hat{\mathbf{i}}$$, then the correct expressi 11. The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} 12. Two parallel conductors carry current in opposite directions as shown in the figure. One conductor carries a current of 13. The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ co 14. A ball is allowed to fall from a height of $$10 \mathrm{~m}$$. If there is $$30 \%$$ loss of energy due to impact, then 15. The elastic limit of $$1 \mathrm{~kg}$$ mass is $$3.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$$. Find the maximum load 16. The focal length of thin convex lens for red and blue rays are $$100 \mathrm{~cm}$$ and $$98.01 \mathrm{~cm}$$, respecti 17. The ratio of the acceleration for a solid sphere (mass $$m$$ and radius $$R$$) rolling down an incline of angle '$$\thet 18. The de-Broglie wavelength of a proton $$\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$$ acclerated through a potentia 19. The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immerse 20. A particle of mass $m$ is projected with a velocity $$v$$ making an angle of $$45^{\circ}$$ with the horizontal. The mag 21. A parallel plate capacitor with air between the plates has a capacitance of $$15 \mathrm{~pF}$$. the separation between 22. A constant voltage is applied between the two ends of a uniform metallic wire, Some heat is developed in it. The heat de 23. The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The 24.
A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to 25. Susceptibility of ferromagnetic substance is 26. A particle of mass $$10 \mathrm{~kg}$$ moving eastwards with a speed $$10 \mathrm{~m} / \mathrm{s}$$ collides with anoth 27. A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$ 28. A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil 29. A geostationary satellite is orbiting the Earth at a height of $$4 R$$ above that surface of the Earth. $R$ being the ra 30. Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The ma 31. 0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cr 32. In the formula $$X=3 Y Z^2, X$$ and $$Z$$ have dimensions of capacitance and magnetic induction respectively. The dimens 33. Three blocks of masses $$m_1, m_2$$ and $$m_3$$ are connected by massless strings, as shown, on a frictionless table. Th 34. The susceptibility of a magnetism at $$300 \mathrm{~K}$$ is $$1.5 \times 10^{-5}$$. The temperature at which the suscept 35. A transmitting antenna is kept on the surface of the Earth. The minimum height of receiving antenna required to receive
1
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0
The solution of $$d y / d x=1+x+y+x y$$ is
A
$$x+y=c(1+x y)$$
B
$$\log (1+x)+x+y=c$$
C
$$\log (1+y)=x+\frac{x^2}{2}+C$$
D
None of these
2
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0
A unit vector perpendicular to both the vectors $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathbf{k}}$$ is
A
$$\frac{\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}}{\sqrt{3}}$$
B
$$\frac{-\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}}{\sqrt{3}}$$
C
$$\frac{\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}}{\sqrt{3}}$$
D
$$\frac{\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}}{\sqrt{3}}$$
3
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0
If $$\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)$$, then the value of $$y$$ is
A
$$\frac{3 x-x^3}{3 x^2-1}$$
B
$$\frac{x^3-3 x}{3 x^2-1}$$
C
$$\frac{x^3-3 x}{1+3 x^2}$$
D
$$\frac{3 x+x^3}{1+3 x^2}$$
4
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0
$$\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$$ equals to
A
$$\frac{\pi}{3}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{2 \pi}{3}$$
Paper analysis
Total Questions
Aptitude
10
Chemistry
35
English
5
Mathematics
40
Physics
35
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