Chemistry
1. The degeneracy of hydrogen atom that has energy equal to $ \frac{-R_{\mathrm{H}}}{9} $ is (where, $ R_{\mathrm{H}}= $ Ry 2. The final product in following reaction $ Y $ is, $ \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2} \xrightarrow[\text { (ii 3. A dimolar solution potassium ferrocyanide is $ 50 \% $ dissociated at 300 K . The osmotic pressure of solution is $ \lef 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 6. If the de-broglie wavelength of a particle of mass $ (m) $ is 100 times its velocity. Then, its value in terms of its ma 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 format 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} 12. 58.5 g of NaCl and 180 g of glucose were separately dissolved in 1000 mL of water. Identify the correct statement regard 13. The number of geometrical isomers possible for the compound, $ \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\math 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} 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{ 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 23. For the reaction $ 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3} $, the rate of disappearance of 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 \ma 25. A tetrapeptide is made of naturally occuring alanine, serine, glycine and valine. If the $ C $-terminal amino acid is al 26. In the following species, how many species have same magnetic moment? (i) $ \mathrm{Cr}^{2+} $ (ii) $ \mathrm{Mn}^{3+} $ 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. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:sol 30. The major product of the reaction between $ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{ONa} $ and $ \left(\mathrm{CH}_{3}\r
English Proficiency
1. Directions Choose the word which best expresses the meaning of the underlined word. The soldiers showed fortitude and re 2. Directions Choose the word which best expresses the meaning of the underlined word. As the effect of anesthesia dissipat 3. Select the one which best expresses the same sentence in Passive/Active Voice. It is your duty to help the poor people i 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 7. Directions In the following questions, choose the one which can be substituted for the given words/ sentences. Symbols o 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 10. Directions Given below are four jumbled sentences. Select the option that gives their correct order forming a meaningful
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 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 numbe 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. 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 $ '.' $ \ 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 a 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 on 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 16. Select the correct mirror image of the given combination when the mirror is placed at $ A B $ as shown below.Question Fi 17. In the given question below are given some statements followed by two conclusions numbered I and II. You have to take th 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 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
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 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} $. 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 matr 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} 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 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 th 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, 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( 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{ 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 . I 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} $ 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 tab 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^{\c 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}}\righ 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 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 $, h 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 angl 38. How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd 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} 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 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 blo 4. Two wires of the same material (Young's modulus $ =Y $ ) and same length $ L $ but radii $ R $ and $ 2 R $ respectively, 5. A parallel plate capacitor consists of two circular plates of radius $ R=0.1 \mathrm{~m} $. They are separated by a shor 6. Power of biconvex lens is $ P $ diopter. When it is cut into two symmetrical halves by a plane containing the principal 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} $ 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} 10. Which of the following transitions of $ \mathrm{He}^{+} $ion will give rise to spectral line which has same wavelength a 11. Young's double slit experiment is performed in a medium of refractive index of 1.33 . The maximum intensity is $ I_{0} $ 12. The magnifying power of a telescope is 9 . When it is adjusted for parallel rays, the distance between the objective and 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 14. An oil drop of radius $ 1 \mu \mathrm{~m} $ is held stationary under a constant electric field of $ 3.65 \times 10^{4} \ 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 b 16. Identify the correct output signal $ Y $ in the given combination of gates for the given inputs $ A $ and $ B $ shown in 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 dr 19. Five identical springs are used in the three configurations as shown in figure. The time periods of vertical oscillation 20. A pendulum of mass 1 kg and length $ l=1 \mathrm{~m} $ is released from rest at angle $ \theta=60^{\circ} $. The power d 21. A projectile is projected with velocity of $ 40 \mathrm{~m} / \mathrm{s} $ at an angle $ \theta $ with the horizontal. I 22. A dust particle of mass $ 4 \times 10^{-12} \mathrm{mg} $ in suspended in air under the influence of an electric field o 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 th 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 25. A rigid body rotates about a fixed axis with variable angular velocity equal to $ \alpha-\beta t $, at the time $ t $, w 26. Electric field at point $ (30,30,0) $ due to a charge of $ 0.008 \mu \mathrm{C} $ placed at origin will be, (coordinates 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 va 29. A ball falling freely from a height of $ 4.9 \mathrm{~m} / \mathrm{s} $, hits a horizontal surface. If $ e=\frac{3}{4} $ 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
1
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
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
A
2
B
-2
C
1
D
-1
2
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
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. $
A
The function is continuous for all values of $ x $
B
The function is continuous only for $ x > 1 $
C
The function is continuous at $ x=1 $
D
The function is not continuous at $ x=1 $.
3
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
If $ x \sqrt{1+y}+y \sqrt{1+x}=0 $, then $ \frac{d y}{d x}= $
A
$ \frac{x+1}{x} $
B
$ \frac{1}{1+x} $
C
$ \frac{-1}{(1+x)^{2}} $
D
$ \frac{x}{1+x} $
4
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
Consider the function $ f(x)=\frac{|x-1|}{x^{2}} $, then $ f(x) $ is
A
increasing in $ (0,1) \cup(2, \infty) $
B
increasing in $ (-\infty, 0) \cup(0,1) $
C
decreasing in $ (-\infty, 0) \cup(2, \infty) $
D
decreasing in $ (0,1) \cup(2, \infty) $
Paper analysis
Total Questions
Chemistry
30
English Proficiency
10
Logical Reasoning
20
Mathematics
40
Physics
30
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