BITSAT 2024
Chemistry
1
The degeneracy of hydrogen atom that has energy equal to $ \frac{-R_{\mathrm{H}}}{9} $ is (where, $ R_{\mathrm{H}}= $ Rydberg constant)
2
The final product in following reaction $ Y $ is, $ \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2} \xrightarrow[\text { (ii) } \mathrm{NaBH}_{4}]{\text { (i) }\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2} \mathrm{Hg}, \mathrm{CH}_{3} \mathrm{OH}} Y $
3
A dimolar solution potassium ferrocyanide is $ 50 \% $ dissociated at 300 K . The osmotic pressure of solution is $ \left(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right) $
4
What would be the amount of heat absorbed in the cyclic process shown below?
5
What is the stoichiometric coefficient of $ \mathrm{SO}_{2} $ in the following balance reaction?
$ \mathrm{MnO}_{4}^{-}(a q)+\mathrm{SO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{Mn}^{2+}(a q)^{-}+\mathrm{HSO}_{4}^{-}(a q) $
(in acidic solution)
6
If the de-broglie wavelength of a particle of mass $ (m) $ is 100 times its velocity. Then, its value in terms of its mass $ (m) $ and plank constant $ (h) $ is
7
Electron affinity is positive, when
8
The bond dissociation energy of $ X_{2}, Y_{2} $ and $ X Y $ are in the ratio of $ 1: 0.5: 1 . \Delta H $ for the formation of $ X Y $ is $ -200 \mathrm{~kJ} / \mathrm{mol} $. The bond dissociation energy of $ X_{2} $ will be
9
The pH of 1 N aqueous solutions of HCl , $ \mathrm{CH}_{3} \mathrm{COOH} $ and HCOOH follows the order:
10
The ionic radii in $ \mathring{A} $ of $ \mathrm{N}^{3-}, \mathrm{O}^{2-} $ and $ \mathrm{F}^{-} $are respectively.
11
20 mL of 0.1 M acetic acid is mixed with 50 mL of potassium acetate. $ K_{\alpha} $ of acetic acid $ =1.8 \times 10^{-5} $ at $ 27^{\circ} \mathrm{C} $. Calculate the concentration of potassium acetate if pH of mixture is 4.8 .
12
58.5 g of NaCl and 180 g of glucose were separately dissolved in 1000 mL of water. Identify the correct statement regarding the elevation of boiling point of the resulting solution.
13
The number of geometrical isomers possible for the compound, $ \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} $ is
14
The major product $ X $ in the following given reaction is
15
The pH of 0.5 L of 1.0 M NaCl solution after .electrolysis for 965 s using 5.0 A current is,
16
Intramolecular hydrogen bonding is found in
17
Calculate the molarity of a solution containing 5 g of NaOH dissolved in the product of $ \mathrm{H}_{2}-\mathrm{O}_{2} $ fuel cell operated at 1 A current for 595.1 hours. (Assume $ \mathrm{F}=96500 \mathrm{C} / \mathrm{mol} $ of electron and molecular weight of NaOH as $ 40 \mathrm{~g} \mathrm{~mol}^{-1} $ ).
18
The hybridisation scheme for the central atom includes a $ d $-orbital contribution in
19
Which of the following compounds will undergo self aldol condensation in the presence of cold dilute alkali?
20
Volume of $ M / 8 \mathrm{KMnO}_{4} $ solution required to react completely with $ 25.0 \mathrm{~cm}^{3} $ of $ \mathrm{M} / 4 \mathrm{FeSO}_{4} $ in acidic medium is.
21
Cheilosis and digestive disorders are due to deficiency of
22
In $ S_{N} 2 $ substitution reaction of the type
$ R-\mathrm{Br}+\mathrm{Cl}^{-} \xrightarrow[\mathrm{BMF}]{ } R-\mathrm{Cl}+\mathrm{Br}^{-} $
Which one of the following has highest relative rate?
23
For the reaction $ 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3} $, the rate of disappearance of $ \mathrm{O}_{2} $ is $ 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}{ }^{-1} $ $ \mathrm{s}^{-1} $. The rate appearance of $ \mathrm{SO}_{3} $ is
24
If for a first order reaction, the value of $ A $ and $ E_{a} $ are $ 4 \times 10^{13} \mathrm{~s}^{-1} $ and $ 98.6 \mathrm{~kJ} \mathrm{~mol}^{-1} $ respectively, then at what temperature will its half life period be 10 minutes?
25
A tetrapeptide is made of naturally occuring alanine, serine, glycine and valine. If the $ C $-terminal amino acid is alanine and N-terminal amino acid is chiral, the number of possible sequence of the tetrapeptide is
26
In the following species, how many species have same magnetic moment?
(i) $ \mathrm{Cr}^{2+} $ (ii) $ \mathrm{Mn}^{3+} $ (iii) $ \mathrm{Ni}^{3+} $ (iv) $ \mathrm{Sc}^{2+} $ (v) $ \mathrm{Zn}^{2+} $ (vi) $ \mathrm{V}^{3+} $ (vii) $ \mathrm{Ti}^{+} $
27
The spin only magnetic moment of $ \mathrm{Fe}^{3+} $ ion (in BM) is approximately.
28
Hybridisation and geometry of $ \left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-} $ are
29
Match List I with List II.
| List I $($ Complex) | List II (Oxidation number of metal) |
| A. $\mathrm{Ni}(\mathrm{CO})_4$ | I. +1 |
| B. $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right]^{2+}$ | II. Zero |
| C. $\left[\mathrm{Co}(\mathrm{CO})_5\right]^{2-}$ | III. -1 |
| D. $\left[\mathrm{Cr}_2(\mathrm{CO})_{10}\right]^{2-}$ | IV. -2 |
Choose the correct answer from the options given below:
30
The major product of the reaction between $ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{ONa} $ and $ \left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCl} $ in ethanol is
English Proficiency
1
Directions Choose the word which best expresses the meaning of the underlined word. The soldiers showed fortitude and resilience while facing the opponents.
2
Directions Choose the word which best expresses the meaning of the underlined word. As the effect of anesthesia dissipated, the patient regained consciousness.
3
Select the one which best expresses the same sentence in Passive/Active Voice. It is your duty to help the poor people in your parish.
4
Directions Choose the word opposite in meaning to the given word.
Jeopardy
5
Directions Choose the word opposite in meaning to the given word.
Cacophony
6
Directions In the following questions, choose the one which can be substituted for the given words/ sentences. A formal statement testifying to someone's character and qualifications.
7
Directions In the following questions, choose the one which can be substituted for the given words/ sentences. Symbols of royalty
8
Choose the sentence that means the same as the given sentence. I woke up early lest I should be late for office.
9
Directions Given below are four jumbled sentences. Select the option that gives their correct order forming a meaningful and coherent paragraph.
A. Unfortunately, it is narrowly defined as protecting water sources in the immediate vicinity.
B. The larger dimensions are often left out.
C. Source sustainability also needs to be made a convergence priority.
D. Prioritising drinking water source sustainability is one of the essential priorities identified.
10
Directions Given below are four jumbled sentences. Select the option that gives their correct order forming a meaningful and coherent paragraph.
A. Green managements are about the environment and sustainability.
B. Adopting green innovation by companies and organisations keeps the environment healthy and clean.
C. It can cause enormous changes in companies operations to green their products, operations, and facilities.
D. It can change their sustainability business to competitive advantages.
Logical Reasoning
1
Four options have been given, out of which three are alike in some manners and one is different. Select the option that is different.
2
Select the figure that will replace the question mark (?) in the following figure series. Question Figure
3
Which number will replace the question mark (?) in the given series?
$ 47,51,55,63,87,? $
4
Select the number that is related to the third number in the same way as the second number is related to the first number.
$ 19: 12:: 23: ? $
5
'Bat' is related to 'Mammal' in the same way as 'Spiders' is related to $ \qquad $
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. Grapes - Bunch
7
Select the option in which the number are related in the same way as are the number in the following set. $ 47: 56: 39 $
8
Which letter-cluster will replace the question mark (?) in the given series.
ZKPE, BOVM, DSBU, FWHC, ?
9
Select the option that is embedded in the given figure as its part (rotation is not allowed).
Question Figure
10
'P # $ Q $ ' means ' $ P $ ' is the brother of ' $ Q $ '. 'P@ $ Q $ ' means ' $ P $ ' is the daughter of ' $ Q $ '.
' $ \mathrm{P} \% \mathrm{Q} $ ' means ' $ P $ ' is the father of ' Q '.
' $ P $ \& $ Q $ ' means ' $ P $ ' is the mother of ' $ Q $ '.
If 'A @ B # C \& E @ F \% R, then which of the following statement is correct.
11
How many triangles are there in the following figure?
12
Three different positions of the same dice are shown below. Select the symbol that will be at the top if ' $ \% $ ' is at the bottom.
13
In a row all the women are facing South, Monika is 29 th from the left end and in the right side of Monika, there are only 19 women. Find the total number of women in this queue?
14
In a code language, if 'VERTEX' is written as ' $ 3-20-7-5-20-1 $ ', then how will 'CONDUCT' be written in same language.
15
Pritam, Queen, Rani, Sachin, Tinu, Uri, Vineet and Sohan are sitting round the circular table, all are facing the centre. Pritam is second to the right of Tinu who is the neighbour of Rani and Vineet. Sachin is not the neighbour of Pritam. Vineet is the neighbour of Uri. Queen is not between Sachin and Sohan.Sohan is not between Uri and Sachin. Who is sitting immediate right to the Vineet?
16
Select the correct mirror image of the given combination when the mirror is placed at $ A B $ as shown below.
Question Figures
17
In the given question below are given some statements followed by two conclusions numbered
I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow.
Statements
All facebook are whatsapp.
Some whatsapp are Paytm.
No Paytm is Telegram.
Conclusions
Some Telegram is a Facebook.
Some Whatapp is not Telegram.
18
A paper is folded and cut as shown below. How will it appear when unfolded?
Question Figure
19
In the given question a statement is followed by two conclusions I and II. Taking the statement to be true decide which of the given conclusions definitely follows from the given statement. .
Statement The team manager humiliated Satish in front of his colleagues on a Monday Morning.
Conclusions
I. The team manager did not like Satish.
II. Satish was not as popular as his other colleagues.
20
The product of the ages of Anil and Bishnu is 240. If twice the age of Bishnu is more than Anil's age by 4 yr . What was Bishnu's age 2 years ago?
Mathematics
1
Number of solutions of equations $ \sin 9 \theta=\sin \theta $ in the interval $ [0,2 \pi] $ is
2
The probability of getting 10 in a single throw of three fair dice is
3
Roots of the equation $ x^{2}+b x-c=0(b, c > 0) $ are
4
If $ a > 0, b > 0, c > 0 $ and $ a, b, c $ are distinct, then $ (a+b)(b+c)(c+a) $ is greater than
5
The locus of the point of intersection of the lines $ x=a\left(\frac{1-t^{2}}{1+t^{2}}\right) $ and $ y=\frac{2 a t}{1+t^{2}} $ represent $ (t $ being a parameter)
6
Let $ A, B $ and $ C $ are the angles of a triangle and $ \tan \frac{A}{2}=\frac{1}{3}, \tan \frac{B}{2}=\frac{2}{3} $. Then, $ \tan \frac{C}{2} $ is equal to
7
If $ A=\frac{1}{3}\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right] $ is an orthogonal matrix, then
8
The points represented by the complex number $ 1+i,-2+3 i, \frac{5}{3} i $ on the argand plane are
9
Let $ \mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{k}}, \mathbf{b}=x \hat{\mathbf{i}}+\hat{\mathbf{j}}+(1-x) \hat{\mathbf{k}} $ and $ \mathbf{c}=y \hat{\mathbf{i}}+x \hat{\mathbf{j}}+(1+x-y) \hat{\mathbf{k}} $. Then, $ [\mathbf{a} \mathbf{b} \mathbf{c}] $ depends on
10
The magnitude of projection of line joining ( 3,4 , $ 5) $ and $ (4,6,3) $ on the line joining $ (-1,2,4) $ and $ (1,0,5) $ is
11
The Boolean expression $ \sim(p \vee q) \vee(\sim p \wedge q) $ is equivalent to
12
If $ \sum\limits_{k=1}^{n} k(k+1)(k-1)=p n^{4}+q n^{3}+t n^{2}+s n $, where $ p, q, t $ and $ s $ are constants, then the value of $ s $ is equal to
13
In a binomial distribution, the mean is 4 and variance is 3 . Then, its mode is
14
The maximum area of rectangle inscribed in a circle of diameter $ R $ is
15
In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a TV, 794 families has a radio and 187 has TV. The number of families in that group having both a radio and a TV is
16
The foci of hyperbola $ 4 x^{2}-9 y^{2}-1=0 $ are
17
Let $ [x] $ denote the greatest integer $ \leq x $. If $ f(x)=[x] $ and $ g(x)=|x| $, then the value of $ f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right) $ is
18
Let $ f $ be the function defined by
$ f(x)=\left\{\begin{array}{cc} \frac{x^{2}-1}{x^{2}-2|x-1|-1}, & x \neq 1 \\ \frac{1}{2}, & x=1 \end{array}\right. $
19
If $ x \sqrt{1+y}+y \sqrt{1+x}=0 $, then $ \frac{d y}{d x}= $
20
Consider the function $ f(x)=\frac{|x-1|}{x^{2}} $, then $ f(x) $ is
21
There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6 . If the first and the last numbers are equal, then two other numbers are
22
$ \int_{0}^{\infty} \frac{d x}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)} $ is
23
The line $ y=m x $ bisects the area unclosed by lines $ x=0, y=0 $ and $ x=\frac{3}{2} $ and the curve $ y=1+4 x-x^{2} $. Then, the value of $ m $ is
24
The solution of the differential equation
$ (x+1) \frac{d y}{d x}-y=e^{3 x}(x+1)^{2} $ is
25
Number of real solution of $ \sqrt{5-\log _{2}|x|} $ $ =3-\log _{2}|x| $ is equal to
26
The value of definite integral $ \int_{0}^{\pi / 2} \log (\tan x) d x $ is .
27
If the number of available constraints is 3 and the number of parameters to be optimise is 4 , then
28
The locus of the mid-point of a chord of the circle $ x^{2}+y^{2}=4 $, which subtends a right angle at the origin is
29
A person invites a party of 10 friends at dinner and place so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is
30
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be $ 30^{\circ} $ and $ 45^{\circ} $. The height of tower is
31
If $ y=\tan ^{-1}\left(\frac{\sqrt{x}-x}{1+x^{\frac{3}{2}}}\right) $, then $ y^{\prime}(1) $ is equal to
32
The coefficient of $ x^{2} $ term in the binomial expansion of $ \left(\frac{1}{3} x^{\frac{1}{2}}+x^{\frac{-1}{4}}\right)^{10} $ is
33
If $ a, c, b $ are in GP, then the area of the triangle formed by the lines $ a x+b y+c=0 $ with the coordinates axes is equal to
34
Suppose $ p, q, r \neq 0 $ and system of equation $ (p+a) x+b y+c z=0 $, $ a x+(q+b) y+c z=0 $, $ a x+b y+(r+c) z=0 $, has a non-trivial solution, then the value of $ \frac{a}{p}+\frac{b}{q}+\frac{c}{r} $ is
35
The coefficient of $ x^{n} $ in the expansion of $ \frac{e^{7 x}+e^{x}}{e^{3 x}} $ is
36
The modulus of the complex number $ z $ such that $ |z+3-i|=1 $ and $ \arg (z)=\pi $ is equal to
37
$ A B C $ is a triangular park with $ A B=A C=100 \mathrm{~m} $. A TV tower stands at the mid-point of $ B C $. The angles of elevation of the top of the tower at $ A $, $ B, C $ are $ 45^{\circ}, 60^{\circ}, 60^{\circ} $ respectively. The height of the tower is
38
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions
39
If matrix $ A=\left[\begin{array}{ccc}3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1\end{array}\right] $ and $ A^{-1}=\frac{1}{k} \operatorname{adj}(A) $,
40
The area enclosed by the curves $ y=x^{3} $ and $ y=\sqrt{x} $ is
Physics
1
A body which is initially at rest at a height $ R $ above the surface of the Earth of radius $ R $, falls freely towards the Earth, then its velocity on reaching the surface of the Earth is
2
Find the average value of current shown graphically from $ t=0 $ to $ t=2 \mathrm{~s} $.
3
A force of $ F=0.5 \mathrm{~N} $ is applied on lower block as shown in figure. The work done by lower block on upper block for a displacement of 3 m of the upper block with respect to ground is (Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ )
4
Two wires of the same material (Young's modulus $ =Y $ ) and same length $ L $ but radii $ R $ and $ 2 R $ respectively, are joined end to end and a weight $ w $ is suspended from the combination as shown in the figure. The elastic potential energy in the system is
5
A parallel plate capacitor consists of two circular plates of radius $ R=0.1 \mathrm{~m} $. They are separated by a short distance. If electric field between the capacitor plates changes as $ \frac{d E}{d t}=6 \times 10^{13} \frac{\mathrm{~V}}{\mathrm{~m} \times \mathrm{s}} $, then the value of displacement current is
6
Power of biconvex lens is $ P $ diopter. When it is cut into two symmetrical halves by a plane containing the principal axis. The ratio of power of two halves is
7
In the given cycle $ A B C D A $, the heat required for an ideal monoatomic gas will be
8
The straight wire $ A B $ carries a current $ I $. The ends of the wire subtend angles $ \theta_{1} $ and $ \theta_{2} $ at the point $ P $ as shown in figure. The magnetic field at the point $ P $ is
9
Inside a solenoid of radius 0.5 m , magnetic field is changing at a rate of $ 50 \times 10^{-6} \mathrm{~T} / \mathrm{s} $. Acceleration of an electron placed at a distance of 0.3 m from axis of solenoid will be
10
Which of the following transitions of $ \mathrm{He}^{+} $ion will give rise to spectral line which has same wavelength as the spectral line in hydrogen atom?
11
Young's double slit experiment is performed in a medium of refractive index of 1.33 . The maximum intensity is $ I_{0} $. The intensity at a point on the screen, where path difference between the light coming out from slits is $ \frac{\lambda}{4} $, is
12
The magnifying power of a telescope is 9 . When it is adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm . The ratio of focal length of objective lens to focal length of eyepiece is found to be $ m $, then the value of $ m $ is
13
In the given circuit, $ E_{1}=E_{2}=E_{3}=2 \mathrm{~V} $ and $ R_{1}=R_{2}=4 \Omega $, then current flowing through the branch $ A B $ is
14
An oil drop of radius $ 1 \mu \mathrm{~m} $ is held stationary under a constant electric field of $ 3.65 \times 10^{4} \mathrm{~N} / \mathrm{C} $ due to some excess electrons presence on it. If the density of oil drop is $ 1.26 \mathrm{~g} / \mathrm{cm}^{3} $, then number of excess electrons on the oil drop approximately are [Take, $ g=10 \mathrm{~ms}^{-2} $ ]
15
In YDSE, monochromatic light falls on a screen 1.80 m from two slits separated by 2.08 mm . The first and second order bright fringes are separated by 0.553 mm . The wavelength of light used is
16
Identify the correct output signal $ Y $ in the given combination of gates for the given inputs $ A $ and $ B $ shown in the figure.
17
The moment of inertia of a cube of mass $ m $ and side $ a $ about one of its edges is equal to
18
The potential of a large liquid drop when eight liquid drops are combined is 20 V , then the potential of each single drop was
19
Five identical springs are used in the three configurations as shown in figure. The time periods of vertical oscillations in configurations (a), (b) and (c) are in the ratio.
20
A pendulum of mass 1 kg and length $ l=1 \mathrm{~m} $ is released from rest at angle $ \theta=60^{\circ} $. The power delivered by all the forces acting on the bob at angle $ \theta=30^{\circ} $ will be (Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ )
21
A projectile is projected with velocity of $ 40 \mathrm{~m} / \mathrm{s} $ at an angle $ \theta $ with the horizontal. If $ R $ be the horizontal range covered by the projectile and after $ t $ seconds, its inclination with horizontal becomes zero, then the value of $ \cot \theta $ is [Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ ]
22
A dust particle of mass $ 4 \times 10^{-12} \mathrm{mg} $ in suspended in air under the influence of an electric field of $ 50 \mathrm{~N} / \mathrm{C} $ directed vertically upwards. How many electrons were removed from the neutral dust particle? [Take, $ g=10 \mathrm{~m} / \mathrm{s} $ $ { }^{2} $ ]
23
An ideal massless spring $ S $ can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at $ 30^{\circ} $ to the horizontal. A 10 kg block $ M $ is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2 m . If $ g=10 \mathrm{~m} / \mathrm{s}^{2} $, what is the speed of mass just before it touches the spring?
24
You measure two quantities as $ A=1.0 \mathrm{~m} \pm 0.2 \mathrm{~m} $, $ B=2.0 . \mathrm{m} \pm 0.2 \mathrm{~m} $. We should report correct value for $ \sqrt{A B} $ as
25
A rigid body rotates about a fixed axis with variable angular velocity equal to $ \alpha-\beta t $, at the time $ t $, where $ \alpha, \beta $ are constants. The angle through which it rotates before it stops is
26
Electric field at point $ (30,30,0) $ due to a charge of $ 0.008 \mu \mathrm{C} $ placed at origin will be, (coordinates are in cm )
27
In the following circuit diagram, when $ 3 \Omega $ resistor is removed, then equivalent resistance of the network
28
A conducting wire is stretched by applying a deforming force, so that its diameter decreases to $ 40 \% $ of original value. The percentage change in its resistance will be
29
A ball falling freely from a height of $ 4.9 \mathrm{~m} / \mathrm{s} $, hits a horizontal surface. If $ e=\frac{3}{4} $, then the ball will hit the surface, second time after.
30
In a mixture of gases, the average number of degree of freedoms per molecule is 6 . The rms speed of the molecule of the gas is $ c $, then the velocity of sound in the gas is