Chemistry
1. Which one of the following decreasing orders of stability is correct? 2. Glucose and mannose are related as 3. Which of the following is added to remove permanent hardness of water? 4. $$10 \mathrm{~g}$$ each of $$\mathrm{CH}_4$$ and $$\mathrm{O}_2$$ are kept in cylinders of same volume under same temper 5. A certain compound gives negative test with ninhydrin and positive test with Benedict's solution, it is 6. Which of the following is cross-linked polymer? 7. The complex showing a spin-only magnetic moment of $$2.82 \mathrm{~BM}$$ is 8. In $$\mathrm{BrF}_3$$ molecule, the lone pairs occupy equatorial positions to minimise 9. In electrophilic aromatic substitution reaction, the nitro group is meta-directing because it 10. Which of the following acts as interstitial hydride? 11. Match the following columns.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:s 12. Which one of the following is/are linear structure?
I. $$\mathrm{I}_3^{-}$$
II. $$\mathrm{NO}_2^{-}$$
III. $$\mathrm{I}_ 13. The correct statement with respect to the complexes $$\mathrm{Ni}(\mathrm{CO})_4$$ and $$[\mathrm{Ni}(\mathrm{CN})_4]^{2 14. The decreasing order of nucleophilicity among the following nucleophiles is
15. Identify product $$(Z)$$ in the series, of reaction
$$\mathrm{CH}_2=\mathrm{CH}_2 \xrightarrow{\mathrm{HBr}} X \xrightar 16. Sulphur does not exist as $$\mathrm{S}_2$$ molecule because 17. A compound formed by elements A and B crystallises in the cubic structure where A atoms are at the corners of a cube and 18. The concentration of hydrogen ion in a sample of soft drink is $$3.8 \times 10^{-3} \mathrm{M}$$. What is its $$\mathrm{ 19. Anti-Markownikoff's addition of $$\mathrm{HBr}$$ is observed in 20. Which of the following oxides is amphoteric in character? 21. The temperature of $$K$$ at which $$\Delta G=0$$, for a given reaction with $$\Delta H=-20.5 \mathrm{~kJ} \mathrm{~mol}^ 22. A mixture of two moles of carbon monoxide and one mole of oxygen, in a closed vessel is ignited to convert the carbon mo 23. Which of the following statements does not form a part of Bohr's model of hydrogen atom? 24. The equilibrium constant of the reaction
$$A(s)+2 B^{+}(a q) \rightleftharpoons A^{2+}(a q)+2 B(s)$$
$$E_{\text {cell }} 25. The value of enthalpy change $$(\Delta H)$$ for the reaction $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)+3 \mathrm{O}_2(\ 26. The volume-temperature graphs of a given mass of an ideal gas at constant pressures are shown below. What is the correct 27. In acetylene molecule between the carbon atoms there are 28. If the ionic product of $$\mathrm{Ni}(\mathrm{OH})_2$$ is $$1.9 \times 10^{-15}$$, then the molar solubility of $$\mathr 29. If two compounds have the same empirical formula but different molecular formulae, they must have 30. If $$20 \mathrm{~g}$$ of $$\mathrm{CaCO}_3$$ is treated with $$100 \mathrm{~mL}$$ of $$20 \%$$ $$\mathrm{HCl}$$ solution
English Proficiency
1. The discovery of treasure under the Bermuda Triangle is probably a $$\underline {hoax} $$. 2. He gave a large amount of donation for flood victims and everyone appreciated his $$\underline{magnanimous}$$ act. 3. Select the one which best expresses the same sentence in Passive/Active voice.
Did everybody miss the first bus? 4. Wither 5. Culmination 6. Critical explanation or interpretation of a text, especially of scripture 7. Destruction or slaughter on a mass scale. 8. Select the sentence that means same as the given sentence. Sohan was too weak to play. 9. A. Most of these superpowers are not rich in natural resources and have faced political turmoil.
B. Human capital ultima 10. A. There are other who claim that they have never been so well connected.
B. However, such social networking sites help
Logical Reasoning
1. Four options have been given, out of which three are alike in some manner and one is different. Select the option that i 2. Which number will replace the question mark (?) in the given series?
$$61,73,99,141,201, ?$$ 3. Select the figure that will replace the question mark (?) in the following figure series.
4. Flourine is related to Halogen in the same way as Helium is related to _________. 5. Select the number that is related to the third number in the same way as the second number is related to the first numbe 6. Select the word-pair in which the two words are related in the same way as are the two words in the following word-pair. 7. Select the option in which the numbers are related in the same way as are the numbers of the following set.
$$29: 36: 39 8. 'A # B' means 'A is the husband of B'.
'A @ B' means 'A is the daughter of B'.
'A & B' means 'A is the sister of B'.
If 9. Select the option that is not embedded in the given figure as its part (rotation is not allowed).
10. Which letter-cluster will replace the question mark (?) in the given series?
KLIMC, JJFIX, IHCES, HFZAN, ? 11. Among five persons P, Q, R, S and T, T is older than $$\mathrm{P}, \mathrm{Q}$$ is younger than $$\mathrm{T}, \mathrm{S} 12. Two different positions of the same dice are shown below. Select the number that will be at the top if ' 6 ' is at the b 13. How many triangles are there in the following figure?
14. Statement In a one day cricket match, the total runs made by a team were 200. Out of these, 160 runs were made by spinne 15. Statement The old order changed yielding place to new
Conclusions
I. Change is the law of nature.
II. Discard old ideas 16. ₹ 5110 is to be divided among Rajesh, Vivek and Kripal in such a way that Rajesh gets double the amount that Vivek gets 17. A paper is folded and cut as shown below. How will it appear when unfolded?
18. Six friends, A, B, C, D, E and F are sitting around a circular table facing the centre of the table. A is to the immedia 19. In a code language, if 'FORTUNE' is written as '716192122156', then how will 'OCTOBER' be written in the same language? 20. Select the correct mirror image of the given combination when the mirror is placed at $$\mathrm{MN}$$ as shown below.
Mathematics
1. If $$\alpha 2. If $$A=\{x: x$$ is a multiple of 8$$\}$$ and $$B=\{x: x$$ is a multiple of 12$$\}$$, then $$A \cap B$$ consists of multi 3. Number of solutions of the equation $$z^2+|z|^2=0$$ and $$z \neq 0$$ is 4. The value of $$\lim _\limits{x \rightarrow 0} \frac{8}{x^8}\left(1-\cos \frac{x^2}{2}-\cos \frac{x^2}{4}+\cos \frac{x^2} 5. Let $$\frac{1}{16}, a$$ and $$b$$ be in GP and $$\frac{1}{a}, \frac{1}{b}, 6$$ be in AP, where $$a, b>0$$. Then, $$72(a+ 6. The sum of the coefficients of all odd degree terms in the expansion of $$\left(x+\sqrt{x^3-1}\right)^5 +\left(x-\sqrt{x 7. The number of different 6-digit numbers in which only and all the five digits $$1,3,5,7$$ and 9 appear is 8. If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\la 9. Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{c 10. If $$\cot ^{-1} \sqrt{\cos \alpha}-\tan ^{-1} \sqrt{\cos \alpha}=x$$, then $$\sin x$$ is equal to 11. A cylindrical tank of radius $$10 \mathrm{~m}$$ is being filled with wheat at the rate of $$200 \pi$$ cubic metre per ho 12. If $$\left(1+x^2\right) d y+2 x y d x=\cot x d x$$, then the general solution be 13. If the straight line $$y=m x+c$$, touches the circle $$x^2+y^2=a^2$$ at a point, then $$c^2$$ is 14. A normal is drawn at the point $$P$$ to the circle $$x^2+y^2=25$$, which is inclined at $$45^{\circ}$$ with the straight 15. The value of integral $$\int \frac{d x}{(1+x)^{3 / 4}(x-2)^{5 / 4}}$$ is is equal to 16. The area of the region bounded by the parabola $$y=x^2+1$$ and lines $$y=x+1, y=0, x=\frac{1}{2}$$ and $$x=2$$ is 17. Let $$\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}$$ and $$a$$ unit vect 18. A six faced die is a biased once. It is thrice more likely to show an odd number, then show an even number. It is thrown 19. If $$n$$ is the number of solutions of the equation $$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac 20. The upper $$(\frac{3}{4})$$ th portion of a vertical pole subtends an angel $$\tan ^{-1}\left(\frac{3}{5}\right)$$ at a 21. If $$y=m_1 x+c_1$$ and $$y=m_2 x+c_2, m_1 \neq m_2$$ are two common tangents of circle $$x^2+y^2=2$$ and parabola $$y^2= 22. The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowe 23. If $$a_1, a_2, \ldots, a_n$$ are in HP, then the expression $$a_1 a_2+a_2 a_3+\ldots+a_{n-1} a_n$$ is equal to 24. The equation of the line passing through $$(-4,3,1)$$ parallel to the plane $$x+2 y-z-5=0$$ and intersecting the line $$ 25. Let $$\alpha, \beta$$ be the roots of the equation $$x^2-p x+r=0$$ and $$\frac{\alpha}{2}, 2 \beta$$ be the roots of the 26. $$
\text { If } A=\left[\begin{array}{cc}
\sin \theta & -\cos \theta \\
\cos \theta & \sin \theta
\end{array}\right] \te 27. $$
\text { The value of } \lim _\limits{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}} \text { equals to }
$ 28. If a tangent to the circle $$x^2+y^2=1$$ intersect the co-ordinate axes at distinct points $$P$$ and $$Q$$, then the loc 29. Let $$f(x)=\int \frac{\sqrt{x}}{(1+x)^2} d x$$, where $$x \geq 0$$. Then, $$f(3)-f(1)$$ is equal to 30. The mean and variance of the data $$4,5,6,6,7,8, x, y$$, where $$x 31. Given, a sequence of 4 numbers, first three of which are in GP and the last three are in AP with common difference 6. If 32. If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ 33. If $$f(x)=x^2-2 x+1$$ and $$f \circ g(x)=x^2+2 x+1$$, then $$g(x)$$ is equal to 34. If $$z_1$$ and $$z_2$$ be nth root of unity which subtend a right angled at the origin. Then, $$n$$ must be of the form 35. A tower $$T_1$$ of the height $$60 \mathrm{~m}$$ is located exactly opposite to a tower $$T_2$$ of height $$80 \mathrm{~ 36. Water is being filled at the rate of $$1 \mathrm{~cm}^3 / \mathrm{s}$$ in a right circular conical vessel (vertex downwa 37. Let $$\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$$, where $$A, B$$ and $$C$$ are angles of a $$\triangle A B C$ 38. $$\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j$$ is equal to 39. Let the functions $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=e^{x-1}-e^{-|x-1|}$$ and $$g(x) 40. If $$A, B, C \in[0, \pi]$$ and if $$A, B, C$$ are in $$\mathrm{AP}$$, then $$\frac{\sin A+\sin C}{\cos A+\cos C}$$ is eq
Physics
1. For a constant hydraulic stress on an object, the fractional change in the object's volume $$(\Delta V / V)$$ and its bu 2. When 0.25$$\mathop A\limits^o $$ X-Rays strike a material, the photoelectrons from the $$K$$ shell are observed to more 3. A common emitter amplifier has a voltage gain of 50 an input impedance of 100 $$\Omega$$ and an output impedance of 400 4. In an electron gun the potential difference between the filament and plate is $$4000 \mathrm{~V}$$. What will be the vel 5. A man of mass $m$ starts falling towards a planet of mass $$M$$ and radius $$R$$. As he reaches near to the surface, he 6. A vessel containing 1 mole of $$\mathrm{O}_2$$ gas (molar mass 32) at temperature $$T$$. The pressure of the gas is $$p$ 7. The fundamental frequency of an open organ pipe is $$600 \mathrm{~Hz}$$. The first overtone of this pipe has same freque 8. A Carnot's heat engine works between the temperature $$527^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$. What amo 9. The total energy of an electron in the second excited state of hydrogen atom is about $$-1.51 \mathrm{~eV}$$. Its kineti 10. The masses of block $$A$$ and $$B$$ are $$m$$ and $$M$$, respectively. Between $$A$$ and $$B$$, there is a constant fric 11. Magnetic moment of bar magnet is $$2 M$$. The work done to turn the magnet by $$90^{\circ}$$ of magnet in direction of m 12. The wavelength of two waves are 40 and $$42 \mathrm{~cm}$$ respectively. If the temperature of the room is $$20^{\circ} 13. A resistance $$R$$ and inductance $$L$$ and a capacitor $$C$$ all are connected in series with an $$\mathrm{AC}$$ supply 14. Truth table for system of four NAND gate and one NOT gate as shown in figure is.
15. A boat crosses a river from part $$A$$ to part $$B$$, which are just on the opposite side. The speed of the water. $$v_\ 16. Two rings of radius $$R$$ and $$n R$$ made of same material have the ratio of moment of inertia about an axis passing th 17. When a string is divided into four segments of $$l_1, l_2, l_3$$ and $$l_4$$. The fundamental frequencies of these three 18. A charged particle moving in a uniform magnetic field and losses $$16 \%$$ of its kinetic energy. The radius of curvatur 19. A thin but rigid semicircular wire frame of radius $$r$$ is hinged at $$O$$ and can rotate in its own vertical plane. A 20. After two hours one-eight of the starting amount of a certain radioactive isotope remained undecayed. The half-life of t 21. A thin plano-convex lens of focal length $$f$$ is split into two halves one of the halves is shifted along the optical a 22. The potential energy for a force field $$\mathbf{F}$$ is given by $$u(x, y)=\cos (x+y)$$. The force acting on a particle 23. A direct current of $$10 \mathrm{~A}$$ is superimposed on an alternating current $$i=10 \sin \omega t$$ flowing through 24. The $$x$$-$$t$$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the pa 25. A vessel is half filled with a liquid of refractive index $$\mu$$. The other half of the vessel is filled with an immisc 26. Water is flowing on a horizontal fixed surface such that its flow velocity varies with $$y$$ (vertical direction) as $$v 27. The power dissipated in the circuit shown in the figure $$40 \mathrm{~W}$$. The value of $$R$$ is.
28. In a YDSE, the light of wavelength $$\lambda=5000\mathop A\limits^o $$ is used, which emerges in phase from two slits at 29. The electric and the magnetic field associated with an E.M. wave, propagating along the $$\mathrm{Z}$$-axis can be repre 30. An electron of mass $$m$$ and charge $$e$$ initially at rest gets accelerated by a constant field $$2 E$$. The rate of c
1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1
Let $$\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$$, where $$A, B$$ and $$C$$ are angles of a $$\triangle A B C$$. If the lengths of the sides opposite these angles are $$a, b$$ and $$c$$ respectively, then
A
$$b^2-a^2=a^2+c^2$$
B
$$b^2, c^2, a^2$$ are in AP
C
$$c^2, a^2, b^2$$ are in AP
D
$$a^2, b^2, c^2$$ are in AP
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1
$$\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j$$ is equal to
A
$$2^{2 n}-{ }^{2 n} C_n$$
B
$$2^{2 n-1}-{ }^{2 n-1} C_{n-1}$$
C
$$2^{2 n}-\frac{1}{2}\left({ }^{2 n} C_n\right)$$
D
$$2^{n-1}+2\left({ }^{2 n-1} C_n\right)$$
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1
Let the functions $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=e^{x-1}-e^{-|x-1|}$$ and $$g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$$. Then, the area of the region in the first quadrant bounded by the curves $$y=f(x), y=g(x)$ and $x=0$$ is.
A
$$(2-\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$$
B
$$(2+\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$$
C
$$(2-\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$$
D
$$(2+\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$$
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1
If $$A, B, C \in[0, \pi]$$ and if $$A, B, C$$ are in $$\mathrm{AP}$$, then $$\frac{\sin A+\sin C}{\cos A+\cos C}$$ is equal to
A
$$\sin B$$
B
$$\cos B$$
C
$$\cot B$$
D
$$\tan B$$
Paper analysis
Total Questions
Chemistry
30
English Proficiency
10
Logical Reasoning
20
Mathematics
40
Physics
30
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