Chemistry
1. The degeneracy of a hydrogen atom whose energy equals $-R_{\mathrm{H}}$ / 16
2. A 1 molar aqueous solution of magnesium nitrate is $40 \%$ dissociated at 298 K . Calculate the osmotic pressure of the 3. $$ \text { The product } Z \text { formed in the given reaction is } $$
4. In a cyclic $p V$ process forming $A$ square loop from $(p=1 \mathrm{~atm}, V=2 \mathrm{~L})$ to $(p=3 \mathrm{~atm}$, $ 5. Balance the following redox reaction in acidic medium and determine the stoichiometric coefficient of $\mathrm{H}_2 \mat 6. If the de-Broglie wavelength of a particle is equal to $10 \sqrt{h / m}$, then what is the ratio of its speed to mass?
7. Electron affinity is maximum when
8. The bond dissociation energies of $A_2, B_2$ and $A B$ are in the ratio $1: 4: 2$. If $\Delta H$ for formation of $A B$ 9. Among aqueous 1 N solutions, the pH of HCl , $\mathrm{HNO}_2$ and $\mathrm{CH}_3 \mathrm{COOH}$ follows the order
10. The ionic radii of $\mathrm{N}^{3-}, \mathrm{O}^{2-}$ and $\mathrm{F}^{-}$follow the trend
11. 30 mL of 0.1 M acetic acid is mixed with 60 mL of 0.1 M sodium acetate. If $K_a=1.8 \times 10^{-5}$ what will be the pH 12. 0.1 m of urea and 0.05 m of $\mathrm{CaCl}_2$ are dissolved separately in equal volumes of water. Which solution will ha 13. How many geometrical (cis-trans) isomers are possible for the compound?
$$ \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm 14. $$ \text { The product } X \text { and } Y \text { respectively are } $$
15. A current of 4.0 A is passed through 0.5 L of 0.2 M NaCl solution for 1200 s . Calculate the pH of the solution after el 16. Intramolecular hydrogen bonding is predominantly observed in
17. The approximate time duration in hours to electroplate 20 g of calcium from molten calcium chloride using a current of 4 18. The central atom shows $d$-orbital participation in hybridisation in
19. Identify the compound that undergoes self-aldol condensation in the presence of cold dilute alkali, forming a $\beta$-hy 20. Calculate the volume of $M / 10 \mathrm{KMnO}_4$ needed to react with 20 mL of $M / 2 \mathrm{FeSO}_4$ in acidic medium. 21. Angular stomatitis and cracked lips are caused by deficiency of
22. $$ \text { The major product formed in the given reaction is } $$
23. For the reaction,
$$ 2 \mathrm{SO}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{SO}_3 $$
if the rate of disappearance of 24. If for a first-order reaction, the frequency factor $A=4 \times 10^{13} \mathrm{~s}^{-1}$ and activation energy $E_a=98. 25. A tetrapeptide is formed from four amino acids: alanine, serine, glycine, and valine. The C-terminal is fixed as alanine 26. Among the following transition metal ions, how many have the same number of unpaired electrons, and thus approximately t 27. The $\mathrm{Fe}^{3+}$ ion, having five unpaired electrons, shows a spin-only magnetic moment closest to
28. The hybridisation and geometry of the complex $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are
29. Match List-I with List-II for oxidation number of central metal atom.
$$ \begin{array}{llcc} \hline \begin{array}{c} \t 30. The major product of the reaction between $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{ONa}$ and $\left(\mathrm{CH}_3\right)_3 \
English Proficiency
1. Select the most appropriate option that can substitute the underlined segment in the given sentence.
They had eaten an a 2. Select the most appropriate option to fill in the blank.
Though he is stout, he runs $\_\_\_\_$
3. Select the option that expresses the given sentence in active voice.
The door was opened by the children for their fathe 4. Select the most appropriate antonym of the given word.
Famous
5. Select the most appropriate synonym of the given word. Austere
6. Select the option that can be used as a one-word substitute for the given group of words. One thing that can be divided
7. Unselfish interest in the welfare of others
8. Select the most appropriate meaning of the highlighted idiom.
The actress' daughter is just a chip off the old block.
9. Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningf 10. Select the option that expresses the given sentence in passive voice.
I am going to ask all employees about the incident
Logical Reasoning
1. Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd l 2. Which figure from the given options would replace the question mark (?) if the following figure series were to be contin 3. Which of the following numbers will replace the question mark (?) in the given series? 270, 241, 212, ?, 154, 125
4. Select the option that is related to the third term in the same way as the second term is related to the first term and 5. Select the option that is related to the third word in the same way as the second word is related to the first word.
Pre 6. Select the option figure in which the given figure is embedded as its part (Rotation is not allowed.)
7. Select the set in which the numbers are related in the same way as are the numbers of the following sets.
$$ (112,327,21 8. Which letter-cluster will replace the question mark (?) to complete the given series?
BRCQ, EPFO, ?, KLLK, NJOI
9. Select the option in which the given figure is embedded (Rotation is not allowed).
10. $\mathrm{Q}+\mathrm{J}$ means " Q is the Husband of J "
Q - J means "Q is the Father of J"
$\mathrm{Q} \times \mathrm{J} 11. When the following figure is folded to form a cube, which letter-number will be on the face opposite to the face showing 12. Six characters A, B, C, 1, 2 and 3 are written on different faces of a dice. Two positions of this dice are shown in the 13. Stanley starts cycling from point $A$. He cycles $x$ km towards the West and then turns right and cycles 3 km . He again 14. In a certain code language, 'SPAM' is coded as ' 36 ' and 'JUG' is coded as ' 27 '. How will 'FROCK' be coded in that la 15. Six students Meera, Jigyasa, Tarun, Naina, Shambhavi and Avni are sitting around a circular table facing the centre (Not 16. In a certain code language, 'BLOCK' is coded as LBCON and 'CABIN' is coded as ACIBQ. How will 'SUITE' be coded in the sa 17. Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even 18. A paper is folded and cut as shown below. How will it appear when unfolded?
19. Which of the following numbers will replace the question mark (?) in the given series?
$$ 69,65,67,63, ?, 61 $$
20. Which of the following numbers will replace the question mark (?) in the given series?
$5,20,60,240,720$, ?
Mathematics
1. If $f: X \rightarrow Y$ be a function defined by $f(x)=a \sin \left(x+\frac{\pi}{4}\right)+b \cos x+c$ and $f$ is biject 2. The value of $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ is
3. The function $f(x)=\frac{x}{\sin x}$ is strictly increasing in the interval.
4. The value of integral $\int_a^b e^x d x$ as limit of sums is
5. For what values of the parameter ' $a$ ' does the function $f(x)=x^3+3(a-7) x^2+3\left(a^2-9\right) x-1$ have a positive 6. The solution of the differential equation $\frac{d y}{d x}+x \sin 2 y=x^3 \cos ^2 y$ is
7. If ' $a$ ' is a complex number such that $|a|=1$. Find the value of $a$, so that the equation $a z^2+z+1=0$ has one pure 8. If $\mathbf{a , b , c}$ are vectors such that $|\mathbf{b}|=|\mathbf{c}|$ then $\{(\mathbf{a}+\mathbf{b}) \times(\mathbf 9. For what value of $a, 6$ lies between the roots of the equation $x^2+2(a-3) x+9=0$.
10. What is the probability of getting a sum of 9 in a single throw of three fair dice?
11. The coefficient of $x^n$ in the expansion of $\frac{1-a x-x^2}{e^x}$ is
12. The locus of the middle points of chords of the circle $x^2+y^2=25$ which are parallel to the line $x-2 y+3=0$ is
13. What is the value of the definite integral $\int_0^\pi \log (\sin x) d x$ ?
14.
If $p, q, r$ are in GP and the line $p x+q y+r=0$ forms a triangle with the coordinate axes, what is the area of the tr 15. What is the area enclosed by the curves $y=x^4$ and $y=x^{\frac{1}{3}}$
16. The number of real solution of $\sqrt{\left(7-\log _3|x|\right)}=4-\log _3|x|$ is equal to
17. For three numbers $a, b, c$ between 2 and 18 such that their sum is 25 , the numbers $2, a, b$ are in AP and the numbers 18. If ${ }^n C_{n-r}+3 \cdot{ }^n C_{n-r+1}+3 \cdot{ }^n C_{n-r+2} +{ }^n C_{n-r+3}={ }^x C_r$, then the value of $x$ is
19.
If $A, B, C$ are the angles of a $\triangle A B C$, then
$$ \Delta=\left|\begin{array}{ccc} \sin 2 A & \sin C & \sin B 20. What is the coefficient of $x^{50}$ in $(1+x)^{41}\left(1-x+x^2\right)^{40}$.
21. If $a, b, c, d$ be four positive unequal quantities and $s=a+b+c+d$, then $(s-a)(s-b)(s-c) (s-d)>k a b c d$. Then, value 22. If four lines $a x \pm b y \pm c=0$ encloses a rhombus, then the area is
23. If the equation $2 h x y+2 g x+2 f y+c=0$ represents two straight lines, then the area of rectangle formed with the coor 24. What is the set of values of a for which the point ( $2 a, a+1$ ) is an interior point of the larger segment of the circ 25. Tangents are drawn to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at points where it is intersected by the line $l x 26. The locus of the mid-point of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9 x^2-16 y^2=14 27. If $A+B=\frac{\pi}{4}$, then $(1+\tan A)(1+\tan B)$ is equal to
28. The angles of a triangle are in the ratio $1: 2: 7$. The ratio of the greatest side to the least side is $(k+1):(k-1)$. 29. Let $A, B$ and $C$ be the angles of a triangle and $\tan \frac{A}{2}=\frac{2}{5}, \tan \frac{B}{2}=\frac{3}{7}$. Then, $ 30. Roots of the equation $a x^2+b x+c=0(a, b, c>0)$ are
31. Consider the function $g(x)$ defined as
$$ g(x)=\left\{\begin{array}{cc} \frac{x^2-4}{x^2-2|x-2|-4}, & x \neq 2 \\ \frac 32. The magnitude projection of line segment joining points $(1,2,3)$ and $(-1,4,2)$ on the line joining points $(-2,3,3)$ a 33. The Boolean expression
$$ \sim(p \wedge q) \vee(p \wedge \sim q) \vee(\sim p \wedge \sim q) $$
is equivalent to
34. In a binomial distribution, the mean is 10 and the variance is 6 . Then, its median is
35. A rectangle is inscribed in an ellipse with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
What is the maximum area of 36. A four digit number is formed with digits $1,3,4$, 5 with no repetition. What is the probability that the number is divi 37. If the function $f: R \rightarrow R$ is defined by $f(x)=x^2+5 x+9$, then $f^{-1}(9)$ is equal to
38. If $\mathop {\lim }\limits_{x \to \infty }\left\{\frac{x^2-1}{x+1}-a x-b\right\}=2$. The value of $a$ is
39. The slope of the curve $2 y^2=a x^2+b$ at $(1,-1)$ is -1 . Then, the value of $b$ is
40. Let $z$ be a complex number for which $\left|2 z \cos \theta+z^2\right|>1$, if $|z|
Physics
1. A beam of light travelling in water strikes a glass plate which is also immersed in water. When the angle of incidence i 2. Consider a hydrogen atom with its electron in the $n$th orbit. An electromagnetic radiation of wavelength 90 nm is used 3. A water film is made between two straight parallel wires of length 10 cm each and at a distance of 0.5 cm from each othe 4. The acceleration versus time graph of a particle moving along a straight line is shown in the figure. Draw the respectiv 5. In given lens combination, each lens is of focal length 10 cm .
Correct ray diagram for this combination is 6. A parallel plate capacitor with plate area $A$ and separation between plates $d$ is charged with constant current $I$. C 7. A body is projected vertically upwards from the surface of Earth with a velocity equal to one third of escape velocity. 8. A current $I=10 \sin (100 \pi t) A$ is passed in the first coil, which induces a maximum emf of $5 \pi \mathrm{~V}$ in s 9. A dielectric slab of dielectric constant $k=3$ is filling $\frac{3}{4}$ th space of the capacitor.
When capacitor is ch 10. A string of length $L$ and force constant $k$ is stretched to obtain extension $l$. It is further stretched to obtain ex 11. A block of mass 10 kg slides down a rough slope which is inclined at an angle of $45^{\circ}$ to the horizontal. The coe 12. In a Young's double slit experiment for a particular wavelength of light the distance between third dark and fifth brigh 13. A mass $M$ is broken into two parts of masses $m_1$ and $m_2$. How are $m_1$ and $m_2$ related, so that force of gravita 14. The frequency of a light wave in a material is $2 \times 10^{14} \mathrm{~Hz}$ and wavelength is $5000 \mathop {\rm{A}}\ 15. A man with a mass of 80 kg is standing on the rim to a circular platform with a mass of 200 kg . The circular platform i 16. Two wires of the same material (Young's modulus $=Y$ ) and same length $L$ but radii $R$ and $2 R$ respectively are join 17. A pure resistive circuit element $X$, when connected to an AC supply of peak voltage 200 V , gives a peak current of 5 A 18. The equivalent resistance of the circuit across $A B$ is given by
19. The fundamental frequency of a closed organ pipe is same as the first overtone frequency of an open organ pipe. If the l 20. A vessel is filled with a gas at a pressure of 76 cm of mercury at a certain temperature. The mass of gas is increased b 21. A cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner 22. The mass of proton is 1.0073 u and that of neutron is $1.0087 \mathrm{u}(\mathrm{u}=$ atomic mass unit). The binding ene 23. In a certain process, 400 cal of heat is supplied to a system and at the same time 105 J of mechanical work was done on 24. A standing wave $y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$ is maintained in a taught string, where $y$ 25. Two rods $P$ and $Q$ have equal lengths. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are 26. A bar magnet has magnetic moment of $0.05 \mathrm{Am}^2$ which is suspended in uniform magnetic field of 0.2 T . Calcula 27. The frequency of oscillation of the spring mass system is
28. A body is projected with a speed $u \mathrm{~ms}^{-1}$ at an angle $\beta$ with the horizontal. The kinetic energy at th 29. The temperature $(T)$ dependence of resistivity ( $\rho$ ) of a semiconductor is represented by 30. A large block of ice 10 cm thick with a vertical hole drilled through it is floating in a lake. The minimum length of th
1
BITSAT 2025
MCQ (Single Correct Answer)
+3
-1
The solution of the differential equation $\frac{d y}{d x}+x \sin 2 y=x^3 \cos ^2 y$ is
A
$\tan y=\left(x^2-1\right) e^{x^2}+C$
B
$e^{x^2}=\frac{1}{2}\left(x^2-1\right) \tan y e^{x^2}+C$
C
$\tan y\left(x^2-1\right)=e^{x^2}+C$
D
$e^{x^2} \tan y=\frac{1}{2}\left(x^2-1\right) e^{x^2}+C$
2
BITSAT 2025
MCQ (Single Correct Answer)
+3
-1
If ' $a$ ' is a complex number such that $|a|=1$. Find the value of $a$, so that the equation $a z^2+z+1=0$ has one purely imaginary root.
A
$\cos \left\{\cos ^{-1}\left(\frac{-\sqrt{5}+1}{4}\right)\right\}$
B
$\cos \left\{\sin ^{-1}\left(\frac{\sqrt{5}+1}{4}\right)\right\}+i \sin \left\{\cos ^{-1}\left(\frac{\sqrt{5}+1}{4}\right)\right\}$
C
$\sin \left\{\cos ^{-1}\left(\frac{\sqrt{5}-1}{4}\right)\right\}+i \sin ^{-1}\left(\frac{-\sqrt{5}+1}{2}\right)$
D
None of the above
3
BITSAT 2025
MCQ (Single Correct Answer)
+3
-1
If $\mathbf{a , b , c}$ are vectors such that $|\mathbf{b}|=|\mathbf{c}|$ then $\{(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}+\mathbf{c})\} \times(\mathbf{b} \times \mathbf{c}) \cdot(\mathbf{b}+\mathbf{c})$ is equal to
A
1
B
4
C
2
D
0
4
BITSAT 2025
MCQ (Single Correct Answer)
+3
-1
For what value of $a, 6$ lies between the roots of the equation $x^2+2(a-3) x+9=0$.
A
$\left(\frac{-3}{4}, \infty\right)$
B
$\left(-\infty, \frac{-3}{4}\right) \cup(2, \infty)$
C
$\left(-\infty, \frac{-3}{4}\right)$
D
$\left(\frac{3}{4}, \infty\right)$
Paper Analysis
Total Questions
Chemistry 30
English Proficiency 10
Logical Reasoning 20
Mathematics 40
Physics 30
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