BITSAT 2023

Select the sentence that means same as the given sentence. Sohan was too weak to play.

How many triangles are there in the following figure?

Select the correct mirror image of the given combination when the mirror is placed at $$\mathrm{MN}$$ as shown below.

A boat crosses a river from part $$A$$ to part $$B$$, which are just on the opposite side. The speed of the water. $$v_\omega$$ and the of boat is $$v_B$$ relative to still water. Assume $$v_B=\sqrt{2} v_\omega$$. What is the time taken by the boat, if it has to cross the river directly on the $$A B$$ line ($$D=$$ width of the river) ?

A charged particle moving in a uniform magnetic field and losses $$16 \%$$ of its kinetic energy. The radius of curvature of its path changes by

Two rings of radius $$R$$ and $$n R$$ made of same material have the ratio of moment of inertia about an axis passing through centre is $$1: 64$$. The value of $$n$$ is

The masses of block $$A$$ and $$B$$ are $$m$$ and $$M$$, respectively. Between $$A$$ and $$B$$, there is a constant frictional force $$F$$ and $$B$$ can slide on a smooth horizontal surface. A is set in motion with velocity $$3 v_0$$ while $$B$$ is at rest. What is the distance moved by $$A$$ relative to $$B$$ before they move with the same velocity?

The potential energy for a force field $$\mathbf{F}$$ is given by $$u(x, y)=\cos (x+y)$$. The force acting on a particle at position given by co-ordinates $$(0, \pi / 6)$$ is

A thin but rigid semicircular wire frame of radius $$r$$ is hinged at $$O$$ and can rotate in its own vertical plane. A smooth peg $$P$$ starts from $$O$$ and moves horizontally with constant speed $$2 v_0$$ lifting the frame upward as shown in figure. Find the angular velocity $$\omega$$ of the frame when its diameter makes an angle of $$60^{\circ}$$ with vertical.

A man of mass $m$ starts falling towards a planet of mass $$M$$ and radius $$R$$. As he reaches near to the surface, he realizes that will pass through a small role in the planet. As he enters the role, we sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass $$3 M / 4$$ and a point mass $$M / 4$$ at the centre. Change in the force of gravity experienced by the man is

Water is flowing on a horizontal fixed surface such that its flow velocity varies with $$y$$ (vertical direction) as $$v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$$. If coefficient of viscosity for water is $$2 \eta$$. What will the shear stress between layers of water at $$y=a$$ ?

The $$x$$-$$t$$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $$t=2. \mathrm{~s}$$ is

When a string is divided into four segments of $$l_1, l_2, l_3$$ and $$l_4$$. The fundamental frequencies of these three segments are $$v_1, v_2, v_3$$ and $$v_4$$, respectively. The original fundamental frequency $$(v)$$ of the string is

For a constant hydraulic stress on an object, the fractional change in the object's volume $$(\Delta V / V)$$ and its bulk modulus $$B$$ are related as

The fundamental frequency of an open organ pipe is $$600 \mathrm{~Hz}$$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $$330 \mathrm{~m} / \mathrm{s}$$, then the length of a closed organ pipe is

The wavelength of two waves are 40 and $$42 \mathrm{~cm}$$ respectively. If the temperature of the room is $$20^{\circ} \mathrm{C}$$ then what will be the number of beats produced per second by these waves. When the speed of sound at $$0^{\circ} \mathrm{C}$$ is $$332 \mathrm{~m} / \mathrm{s}$$ ?

A Carnot's heat engine works between the temperature $$527^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$. What amount of heat should it consume per second to deliver mechanical work at the rate of $$1.0 \mathrm{~kW}$$ ?

A vessel containing 1 mole of $$\mathrm{O}_2$$ gas (molar mass 32) at temperature $$T$$. The pressure of the gas is $$p$$. An identical vessel containing one mole of He gas (molar mass 4) at temperature $$4 T$$ has a pressure of

In a YDSE, the light of wavelength $$\lambda=5000\mathop A\limits^o $$ is used, which emerges in phase from two slits at $$a$$ distance $$d=3 \times 10^{-7} \mathrm{~m}$$ apart. A transparent sheet of thickness $$t=1.5 \times 10^{-7} \mathrm{~m}$$ and refractive index $$\mu=1.25$$ is placed over one of the slits. What is the new angular position of the central maxima of the interference pattern, from the centre of the screen? Find the value of $$y$$.

Magnetic moment of bar magnet is $$2 M$$. The work done to turn the magnet by $$90^{\circ}$$ of magnet in direction of magnetic field $$B / 2$$ will be

A resistance $$R$$ and inductance $$L$$ and a capacitor $$C$$ all are connected in series with an $$\mathrm{AC}$$ supply. The resistance of $$R$$ is $$24 \mathrm{~ohm}$$ and for a given frequency, the inductive reactance of $$L$$ is 36 ohm and capacitive reactance of $$C$$ is $$24 \mathrm{~ohm}$$. If the current in the circuit is $$5 \mathrm{~amp}$$. Find the potential difference across $$R, L$$ and $$C$$.

A vessel is half filled with a liquid of refractive index $$\mu$$. The other half of the vessel is filled with an immiscible liquid of refractive index $$2 \mu$$. The apparent depth of the vessel is $$50 \%$$ of the actual depth. Then $$\mu$$ is

A thin plano-convex lens of focal length $$f$$ is split into two halves one of the halves is shifted along the optical axis. The separation between object and image formed by one of the half-lenses is 2.4 and the magnification of same lens is 2. If $$f$$ and $$d$$ be the focal length of the lens and separation between the two halves respectively then

The power dissipated in the circuit shown in the figure $$40 \mathrm{~W}$$. The value of $$R$$ is.

In an electron gun the potential difference between the filament and plate is $$4000 \mathrm{~V}$$. What will be the velocity of electron emitting from the gain?

The total energy of an electron in the second excited state of hydrogen atom is about $$-1.51 \mathrm{~eV}$$. Its kinetic energy in this state is

The electric and the magnetic field associated with an E.M. wave, propagating along the $$\mathrm{Z}$$-axis can be represented by

After two hours one-eight of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is

When 0.25$$\mathop A\limits^o $$ X-Rays strike a material, the photoelectrons from the $$K$$ shell are observed to more in a circle of radius $$23 \mathrm{~mm}$$ in magnetic field of $$4 \times 10^{-2}$$ tesla active perpendicularly to the direction of emission of photoelectrons. What is the Binding energy of $$K$$ shell electrons?

A direct current of $$10 \mathrm{~A}$$ is superimposed on an alternating current $$i=10 \sin \omega t$$ flowing through the wire. The effective value of the resulting current will be.

Which of the following statements does not form a part of Bohr's model of hydrogen atom?

If $$20 \mathrm{~g}$$ of $$\mathrm{CaCO}_3$$ is treated with $$100 \mathrm{~mL}$$ of $$20 \%$$ $$\mathrm{HCl}$$ solution, the amount of $$\mathrm{CO}_2$$ produced is

Truth table for system of four NAND gate and one NOT gate as shown in figure is.

A common emitter amplifier has a voltage gain of 50 an input impedance of 100 $$\Omega$$ and an output impedance of 400 $$\Omega$$. The power gain of the amplifier is

An electron of mass $$m$$ and charge $$e$$ initially at rest gets accelerated by a constant field $$2 E$$. The rate of change of de-Broglie wavelength of this electron at time $$t$$ ignoring relativistic effects is

The volume-temperature graphs of a given mass of an ideal gas at constant pressures are shown below. What is the correct order of pressures?

$$10 \mathrm{~g}$$ each of $$\mathrm{CH}_4$$ and $$\mathrm{O}_2$$ are kept in cylinders of same volume under same temperature, give the pressure ratio of two gases

The value of enthalpy change $$(\Delta H)$$ for the reaction $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)+3 \mathrm{O}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_2(\mathrm{~g})+ 3 \mathrm{H}_2 \mathrm{O}(l)$$, at $$27^{\circ} \mathrm{C}$$ is $$-1366 \cdot 5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$. The value of internal energy change for the above reaction at this temperature will be

A mixture of two moles of carbon monoxide and one mole of oxygen, in a closed vessel is ignited to convert the carbon monoxide to carbon dioxide. If $$\Delta H$$ is the enthalpy change and $$\Delta E$$ is the change in internal energy, then

If the ionic product of $$\mathrm{Ni}(\mathrm{OH})_2$$ is $$1.9 \times 10^{-15}$$, then the molar solubility of $$\mathrm{Ni}(\mathrm{OH})_2$$ in $$1.0 \mathrm{~M} \mathrm{~NaOH}$$ is

The concentration of hydrogen ion in a sample of soft drink is $$3.8 \times 10^{-3} \mathrm{M}$$. What is its $$\mathrm{pH}$$ ?

The temperature of $$K$$ at which $$\Delta G=0$$, for a given reaction with $$\Delta H=-20.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$\Delta S=-50.0 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$$ is

A compound formed by elements A and B crystallises in the cubic structure where A atoms are at the corners of a cube and B atoms are at the face centre. The formula of the compound is :

Which one of the following is/are linear structure?

I. $$\mathrm{I}_3^{-}$$

II. $$\mathrm{NO}_2^{-}$$

III. $$\mathrm{I}_3^{+}$$

IV. $$\mathrm{SO}_2$$

V. $$\mathrm{N}_3^{-}$$

Which of the following acts as interstitial hydride?

Which one of the following decreasing orders of stability is correct?

Which of the following is added to remove permanent hardness of water?

In $$\mathrm{BrF}_3$$ molecule, the lone pairs occupy equatorial positions to minimise

The equilibrium constant of the reaction

$$A(s)+2 B^{+}(a q) \rightleftharpoons A^{2+}(a q)+2 B(s)$$

$$E_{\text {cell }}^{\circ}=0.0295 \mathrm{~V} \text { is } \quad\left[\frac{2.303 R T}{F}=0.059\right]$$

Sulphur does not exist as $$\mathrm{S}_2$$ molecule because

Which of the following oxides is amphoteric in character?

The complex showing a spin-only magnetic moment of $$2.82 \mathrm{~BM}$$ is

In electrophilic aromatic substitution reaction, the nitro group is meta-directing because it

The correct statement with respect to the complexes $$\mathrm{Ni}(\mathrm{CO})_4$$ and $$[\mathrm{Ni}(\mathrm{CN})_4]^{2-}$$ is

The decreasing order of nucleophilicity among the following nucleophiles is

Anti-Markownikoff's addition of $$\mathrm{HBr}$$ is observed in

In acetylene molecule between the carbon atoms there are

Glucose and mannose are related as

Identify product $$(Z)$$ in the series, of reaction

$$\mathrm{CH}_2=\mathrm{CH}_2 \xrightarrow{\mathrm{HBr}} X \xrightarrow{a q . \mathrm{KOH}} Y \xrightarrow[\mathrm{I}_2 \text { excess }]{\mathrm{Na}_2 \mathrm{CO}_3} Z$$

If two compounds have the same empirical formula but different molecular formulae, they must have

Which of the following is cross-linked polymer?

If $$\alpha<1$$ be a root of the equation $$2 x^2-5 x+2=0$$, then the other root of the equation is

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 equation $$x^2-q x+r=0$$. Then, the value of $$r$$ is equal to

A certain compound gives negative test with ninhydrin and positive test with Benedict's solution, it is

Match the following columns.

Choose the correct options.

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 first and last term of this sequence are equal, then the last term is

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, $$72(a+b)$$ is equal to

The number of different 6-digit numbers in which only and all the five digits $$1,3,5,7$$ and 9 appear is

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

The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is

The sum of the coefficients of all odd degree terms in the expansion of $$\left(x+\sqrt{x^3-1}\right)^5 +\left(x-\sqrt{x^3-1}\right)^5, x>1$$ is

If $$A=\{x: x$$ is a multiple of 8$$\}$$ and $$B=\{x: x$$ is a multiple of 12$$\}$$, then $$A \cap B$$ consists of multiple of

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 twice. The probability that the sum of the number in two throws is odd, is

$$ \text { If } A=\left[\begin{array}{cc} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{array}\right] \text {, then } A(\operatorname{adj} A)^{-1} \text { equals to } $$

Let $$\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}$$ and $$a$$ unit vector $$\mathbf{c}$$ be coplanar. If $$\mathbf{c}$$ is perpendicular to $$\mathbf{a}$$, then c equals to

The equation of the line passing through $$(-4,3,1)$$ parallel to the plane $$x+2 y-z-5=0$$ and intersecting the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$$ is

Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{ccc}1 & 13 & -3 \\ -4 & -3 & 12 \\ \alpha & -11 & -5\end{array}\right]$$ If $$B$$ is the inverse of $$A$$, then the value of $$\alpha$$ is

$$\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j$$ is equal to

If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ has a non-trivial solution, then $$a b+b c+c a$$ equals to

The mean and variance of the data $$4,5,6,6,7,8, x, y$$, where $$x< y$$ are 6 and $$\frac{9}{4}$$, respectively. Then, $$x^2-2 y$$ is equal to

If $$n$$ is the number of solutions of the equation $$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$$ and $$S$$ is the sum of all these solutions, then the ordered pair $$(n, S)$$ is

Number of solutions of the equation $$z^2+|z|^2=0$$ and $$z \neq 0$$ is

A tower $$T_1$$ of the height $$60 \mathrm{~m}$$ is located exactly opposite to a tower $$T_2$$ of height $$80 \mathrm{~m}$$ on a straight road. From the top of $$T_1$$, if the angle of depression of the foot of $$T_2$$ is twice the angle of elevation of the top of $$T_2$$, then the width (in $$\mathrm{m}$$) of the road between the feet of the towers $$T_1$$ and $$T_2$$ is

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

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 $$\lambda$$ equals to

The upper $$(\frac{3}{4})$$ th portion of a vertical pole subtends an angel $$\tan ^{-1}\left(\frac{3}{5}\right)$$ at a point in the horizontal plane through its foot and at a distance $$40 \mathrm{~m}$$ from the foot. A possible height of the vertical is

If $$f(x)=x^2-2 x+1$$ and $$f \circ g(x)=x^2+2 x+1$$, then $$g(x)$$ is equal to

The value of $$\lim _\limits{x \rightarrow 0} \frac{8}{x^8}\left(1-\cos \frac{x^2}{2}-\cos \frac{x^2}{4}+\cos \frac{x^2}{2} \cos \frac{x^2}{4}\right)$$ is

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

If $$\cot ^{-1} \sqrt{\cos \alpha}-\tan ^{-1} \sqrt{\cos \alpha}=x$$, then $$\sin x$$ is equal to

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

$$ \text { The value of } \lim _\limits{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}} \text { equals to } $$

A cylindrical tank of radius $$10 \mathrm{~m}$$ is being filled with wheat at the rate of $$200 \pi$$ cubic metre per hour. Then, the depth of the wheat is increasing at the rate of

Let $$f(x)=\int \frac{\sqrt{x}}{(1+x)^2} d x$$, where $$x \geq 0$$. Then, $$f(3)-f(1)$$ is equal to

If $$\left(1+x^2\right) d y+2 x y d x=\cot x d x$$, then the general solution be

Water is being filled at the rate of $$1 \mathrm{~cm}^3 / \mathrm{s}$$ in a right circular conical vessel (vertex downwards) of height $$35 \mathrm{~cm}$$ and diameter $$14 \mathrm{~cm}$$. When the height of the water levels is $$10 \mathrm{~cm}$$, the rate (in $$\mathrm{cm}^2 / \mathrm{sec}$$) at which the wet conical surface area of the vessel increases is

The value of integral $$\int \frac{d x}{(1+x)^{3 / 4}(x-2)^{5 / 4}}$$ is is equal to

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

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 normal is drawn at the point $$P$$ to the circle $$x^2+y^2=25$$, which is inclined at $$45^{\circ}$$ with the straight line $$y=6$$. Then, the point lies on the straight line

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 $$y^2=x$$, then the value of $$8\left|m_1 m_2\right|$$ is equal to

If the straight line $$y=m x+c$$, touches the circle $$x^2+y^2=a^2$$ at a point, then $$c^2$$ is

If a tangent to the circle $$x^2+y^2=1$$ intersect the co-ordinate axes at distinct points $$P$$ and $$Q$$, then the locus of the mid-point of $$P Q$$ is

Select the one which best expresses the same sentence in Passive/Active voice.

Did everybody miss the first bus?

The discovery of treasure under the Bermuda Triangle is probably a $$\underline {hoax} $$.

He gave a large amount of donation for flood victims and everyone appreciated his $$\underline{magnanimous}$$ act.

A. Most of these superpowers are not rich in natural resources and have faced political turmoil.

B. Human capital ultimately makes the difference, both in an enterprise and a nation

C. the new economic superpowers of today amply testify this thesis.

D. Yet, they have achieved economic affluence in a relatively short period.

Culmination

A. There are other who claim that they have never been so well connected.

B. However, such social networking sites help us to keep in touch with old friends or make new ones.

C. Whether or not Facebook friendships are lasting is debatable.

D. Some people believe that real friendships are collapsing in modern times.

Destruction or slaughter on a mass scale.

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.

Growth : Expansion

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 immediate left of $$\mathrm{E}$$. $$\mathrm{B}$$ is to the immediate right of F. D is second to the left of F. A and C have equal number of persons between them from both the ends. Who is sitting between $$\mathrm{A}$$ and $$\mathrm{F}$$ ?

Two different positions of the same dice are shown below. Select the number that will be at the top if ' 6 ' is at the bottom.

Critical explanation or interpretation of a text, especially of scripture

Which letter-cluster will replace the question mark (?) in the given series?

KLIMC, JJFIX, IHCES, HFZAN, ?

Select the number that is related to the third number in the same way as the second number is related to the first number.

$$12: 36:: 18: \text { ? }$$

Select the option in which the numbers are related in the same way as are the numbers of the following set.

$$29: 36: 39$$

Select the figure that will replace the question mark (?) in the following figure series.

Flourine is related to Halogen in the same way as Helium is related to _________.

Four options have been given, out of which three are alike in some manner and one is different. Select the option that is different.

Among five persons P, Q, R, S and T, T is older than $$\mathrm{P}, \mathrm{Q}$$ is younger than $$\mathrm{T}, \mathrm{S}$$ is older than $$\mathrm{R}$$ and $$\mathrm{P}$$ is older than $$\mathrm{S}$$ but younger than $$\mathrm{Q}$$. Who is the oldest among all?

Statement The old order changed yielding place to new

Conclusions

I. Change is the law of nature.

II. Discard old ideas because they are old.

Statement In a one day cricket match, the total runs made by a team were 200. Out of these, 160 runs were made by spinners.

Conclusions

I. $$80 \%$$ of the team consists of spinners.

II. The opening batsmen were spinners.

₹ 5110 is to be divided among Rajesh, Vivek and Kripal in such a way that Rajesh gets double the amount that Vivek gets and Kripal gets double the amount that Rajesh gets. How much money will Kripal get?

'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 'P & Q @ D # K @ S # T', then which of the following statements is not correct?

Which number will replace the question mark (?) in the given series?

$$61,73,99,141,201, ?$$

Select the option that is not embedded in the given figure as its part (rotation is not allowed).

A paper is folded and cut as shown below. How will it appear when unfolded?

In a code language, if 'FORTUNE' is written as '716192122156', then how will 'OCTOBER' be written in the same language?