BITSAT 2015 Question Paper with Answer Key pdf is available for download. BITSAT 2015 was conducted in online CBT mode by BITS Pilani. BITSAT 2015 Question Paper had 150 questions to be attempted in 3 hours.
BITSAT 2015 Question Paper with Answer Key PDF
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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height \(h\) of the satellite above the earth’s surface is (Take radius of earth as \(R_e\)):
In the figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block \(A\) weighs 400 N, Block \(B\) weighs 300 N, and the strut \(AB\) weighs 200 N. If \(\mu = 0.25\) under \(B\), determine the minimum coefficient of friction under \(A\) to prevent motion.
Two tuning forks with natural frequencies 340 Hz each move relative to a stationary observer. One fork moves away from the observer while the other moves towards the observer with the same speed. The observer hears beats of frequency 3 Hz. Find the speed of the tuning forks.
The displacement of a particle is given as a function of time \(t\) by: \[ x = A\sin(2\omega t) + B\sin^2(\omega t) \]
Then,
A ray parallel to the principal axis is incident at \(30^\circ\) from the normal on a concave mirror having radius of curvature \(R\). The point on the principal axis where rays are focused is \(O\) such that \(PQ\) is:
A solid sphere of radius \(R\) has a charge \(Q\) distributed in its volume with a charge density \(\rho = kr\), where \(k\) and \(r\) are constants and \(r\) is the distance from its centre. If the electric field at \(r=\dfrac{R}{2}\) is \(\dfrac{1}{8}\) times that at \(r=R\), the value of \(a\) is:
A charged particle moving in a uniform magnetic field loses \(4%\) of its kinetic energy. The radius of curvature of its path changes by:
Calculate the wavelength of light used in an interference experiment from the following data: Fringe width \(=0.03\) cm. Distance between the slits and eyepiece through which interference pattern is observed is 1 m. Distance between the images of the two virtual sources when a convex lens of focal length 16 cm is used at a distance of 80 cm from the eyepiece is 0.8 cm.
The masses of blocks \(A\) and \(B\) are \(m\) and \(M\) respectively. Between \(A\) and \(B\) there is a constant frictional force \(F\). Block \(B\) can slide on a smooth horizontal surface. \(A\) is set in motion with velocity \(v_0\) while \(B\) is at rest. What is the distance moved by \(A\) relative to \(B\) before they move with the same velocity?
An elastic string of unstretched length \(L\) and force constant \(k\) is stretched by a small length \(x\). It is further stretched by another small length \(y\). The work done in the second stretching is:
A body is thrown vertically upwards from point \(A\), the top of a tower, and reaches the ground in time \(t_1\). If it is thrown vertically downwards from \(A\) with the same speed, it reaches the ground in time \(t_2\). If it is allowed to fall freely from \(A\), the time it takes to reach the ground is given by:
\(0.5\) mole of an ideal gas at constant temperature \(27^\circC\) is kept inside a cylinder of length \(L\) and cross-sectional area \(A\), closed by a massless piston. The cylinder is attached to a conducting rod of length \(L\), cross-sectional area \((1/9)\,m^2\) and thermal conductivity \(k\), whose other end is maintained at \(0^\circC\). The piston is moved such that heat flow through the conducting rod is constant. Find the velocity of the piston when it is at a height \(L/2\) from the bottom of the cylinder. (Neglect any loss of heat from the system.)
A conducting square loop is placed in a magnetic field \(B\) with its plane perpendicular to the field. The sides of the loop are shrinking at a constant rate \(\alpha\). The induced emf in the loop at an instant when its side is \(a\) is:
The beam of light has wavelengths \(4144\)\AA, \(4972\)\AA\ and \(6216\)\AA\ with a total intensity of \(3.6\times10^{-3}\,W m^{-2}\) equally distributed amongst the three wavelengths. The beam falls normally on an area of \(1\,cm^2\) of a clean metallic surface of work function \(2.3\,eV\). Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in \(2\,s\).
A square gate of size \(1\,m \times 1\,m\) is hinged at its mid-point. A fluid of density \(\rho\) fills the space to the left of the gate. The force \(F\) required to hold the gate stationary is:
When \(0.5\)\AA\ X-rays strike a material, the photoelectrons from the K-shell are observed to move in a circular radius \(23\,mm\) in a magnetic field of \(2\times10^{-2}\,T\) perpendicular to the direction of emission of photoelectrons. What is the binding energy of K-shell electrons?
In a CE transistor amplifier, the audio signal voltage across the collector resistance of \(2\,k\Omega\) is \(2\,V\). If the base resistance is \(1\,k\Omega\) and the current amplification of the transistor is \(100\), the input signal voltage is:
At the three vertices of an equilateral triangle of side \(a\), three point charges are placed (each of \(0.1\,C\)). If this system is supplied energy at the rate of \(1\,kW\), calculate the time required to move one of the charges to the mid-point of the line joining the other two.
A vessel of volume \(20\,L\) contains a mixture of hydrogen and helium at temperature \(27^\circC\) and pressure \(2\,atm\). The mass of the mixture is \(5\,g\). Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the mixture is:
The resistance of a wire is \(R\). It is bent at the middle by \(180^\circ\) and the ends are twisted together to make a shorter wire. The resistance of the new wire is:
In a YDSE, light of wavelength \(\lambda = 5000\,\AA\) is used, which emerges in phase from two slits at a distance \(d = 3\times10^{-7}\,m\) apart. A transparent sheet of thickness \(t = 1.5\times10^{-7}\,m\) and refractive index \(\mu = 1.17\) is placed over one of the slits. What is the angular position of the central maxima of the interference pattern from the centre of the screen? Find the value of \(y\).
The position of a projectile launched from the origin at \(t=0\) is given by \[ \vec{r} = (40\hat{i}+50\hat{j})\,m \quad at t=2\,s. \]
If the projectile was launched at an angle \(\theta\) from the horizontal (take \(g=10\,m s^{-2}\)), then \(\theta\) is:
Water is flowing on a horizontal fixed surface such that its flow velocity varies with \(y\) (vertical direction) as \[ v = k\!\left(\frac{2y^2}{a^2}-\frac{y^3}{a^3}\right). \]
If coefficient of viscosity for water is \(\eta\), what will be the shear stress between layers of water at \(y=a\)?
A load of mass \(m\) falls from a height \(h\) onto the scale pan hung from a spring of mass \(m\) and force constant \(k\). If the spring constant is such that the scale pan is zero and the mass does not bounce relative to the pan, then the amplitude of vibration is:
In an ore containing uranium, the ratio of \(^{238}U\) to \(^{206}Pb\) is \(3:1\). Calculate the age of the ore, assuming that all the lead present in the ore is the final stable product of \(^{238}U\). Take the half-life of \(^{238}U\) to be \(4.5\times10^9\) yr.
A direct current of \(5 A\) is superposed on an alternating current \(I=10\sin\omega t\) flowing through the same wire. The effective value of the resulting current will be:
A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices \(\mu_1\) and \(\mu_2\) and \(R\) is the radius of curvature of the curved surfaces of the lenses, then the focal length of the combination is:
A thin rod of length \(4l\) and mass \(M\) is bent at the points as shown in the figure. What is the moment of inertia of the rod about an axis passing through point \(O\) and perpendicular to the plane of the paper?
One of the lines in the emission spectrum of \(Li^{2+}\) has the same wavelength as that of the second line of the Balmer series in hydrogen spectrum. The Balmer transition corresponds to \(n=4\rightarrow2\). If the corresponding transition in \(Li^{2+}\) is \(n=12\rightarrow x\), find the value of \(x\).
Two particles \(X\) and \(Y\) having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii \(R_1\) and \(R_2\) respectively. The ratio of masses of \(X\) and \(Y\) is:
A glass capillary tube of internal radius \(r = 0.25\,mm\) is immersed in water. The top end of the tube is projected by \(2\,cm\) above the surface of the water. At what angle does the liquid meet the tube? (Surface tension of water \(=0.7\,N/m\)).
A particle of mass \(2m\) is projected at an angle of \(45^\circ\) with the horizontal with a velocity \(20\sqrt{2}\,m/s\). After \(1\,s\), an explosion takes place and the particle breaks into two equal pieces. As a result of explosion, one part comes to rest. The maximum height from the ground attained by the other part is:
A \(2\,m\) wide truck is moving with a uniform speed \(v_0 = 8\,m/s\) along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed \(v\) when the truck is \(4\,m\) away from him. The minimum value of \(v\) so that he can cross the road safely is:
A neutron moving with speed \(v\) makes a head-on collision with a hydrogen atom in the ground state kept at rest. The minimum kinetic energy of the neutron for which inelastic collision takes place is:
Vertical displacement of a plank with a body of mass \(m\) on it is varying according to law \[ y=\sin(\omega t)+\sqrt{3}\cos(\omega t). \]
The minimum value of \(\omega\) for which the mass just breaks off from the plank and the moment it occurs is first after \(t=0\), are given by:
A parallel plate capacitor of capacitance \(C\) is connected to a battery and is charged to a potential difference \(V\). Another capacitor of capacitance \(2C\) is similarly charged to a potential difference \(2V\). The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
In the circuit shown below, the AC source has voltage \(V=20\cos(\omega t)\,V\) with \(\omega=2000\,rad/s\). The amplitude of the current will be nearest to:
A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if:
The frequency of a sonometer wire is \(100\,Hz\). When the weights producing the tension are completely immersed in water, the frequency becomes \(80\,Hz\). On immersing the weights in a certain liquid, the frequency becomes \(60\,Hz\). The specific gravity of the liquid is:
A long straight wire along the \(Z\)-axis carries a current \(I\) in the negative \(Z\)-direction. The magnetic vector field \(\vec{B}\) at a point having coordinates \((x,y)\) in the \(Z=0\) plane is:
Which of the following pollutants is the main product of automobile exhaust?
The disease caused by high concentration of hydrocarbon pollutants in atmosphere is/are:
The element with atomic number 118 will be:
Which law of thermodynamics helps in calculating the absolute entropies of various substances at different temperatures?
The colour of \(CoCl_3\cdot5NH_3\cdotH_2O\) is:
View Solution
Step 1: This is a coordination compound of cobalt(III).
Step 2: Its known colour is orange-yellow. Quick Tip: Colour depends on ligand field splitting.
The metal present in vitamin \(B_{12}\) is:
Cobalt (60) isotope is used in the treatment of:
Polymer used in bullet proof glass is:
What is the correct increasing order of Brønsted basic strength?
The boiling points of alkyl halides are higher than those of corresponding alkanes because of:
Some salts containing two different metallic elements give test for only one of them in solution. Such salts are:
The carbylamine reaction is:
Laughing gas is:
The anthracene is purified by:
The common name of \( \mathrm{K[PtCl_3(\eta^2\!-\!C_2H_4)]} \) is:
The by-product of Solvay–ammonia process is:
Semiconductor materials like Si and Ge are usually purified by:
Which of the following is the strong base?
Ordinary glass is:
The prefix \(10^{18}\) is:
Which of the following is the most basic oxide?
Which one of the following does not follow octet rule?
Which of the following according to Le-Chatelier’s principle is correct?
The efficiency of fuel cell is given by the expression \(\eta\) is:
The mass of the substance deposited when one Faraday of charge is passed through its solution is equal to:
The unit of rate constant for reactions of second order is:
In a first order reaction with time the concentration of the reactant decreases:
The P–P angle in \( \mathrm{P_4} \) molecule and S–S–S angle in \( \mathrm{S_8} \) molecule (in degree) respectively are:
The number of elements present in the d-block of the periodic table is:
Which of the following represents hexadentate ligand?
Which one of given elements shows maximum number of different oxidation states in its compounds?
K\(_4\)[Fe(CN)\(_6\)] is used in detecting:
A spontaneous reaction is impossible if:
Which one of the following removes temporary hardness of water?
Graphite is a:
Which of the following ionic substances will be most effective in precipitating the sulphur sol?
Which one of the fluorides of xenon is impossible?
Thomas slag is:
A sequence of how many nucleotides in messenger RNA makes a codon for an amino acid?
Which of the following molecule/ion has all the three types of bonds, electrovalent, covalent and coordinate bond?
Decay is an immutable factor of human life.
It was an ignominious defect for the team.
The attitude of western countries towards the third world countries is rather callous to say the least.
Freedom and equality are the \hspace{1.5cm} rights of every human.
The team was well trained and strong, but some how their \hspace{1.5cm} was low.
His speech was disappointing; it \hspace{1.5cm} all the major issues.
Hydra is biologically believed to be immortal.
The Gupta rulers patronised all cultural activities and thus Gupta period was called the golden era in Indian History.
The General Manager is quite tactful and handles the workers union very effectively.
A person who does not believe in any religion is called:
A person who believes that pleasure is the chief good is called:
A person who is in charge of a museum is called:
Choose the order of the sentences marked A, B, C, D and E to form a logical paragraph.
Sentences:
A. Tasty and healthy food can help you bring out their best.
B. One minute they are toddlers and next you see them in their next adventure.
C. Your young ones seem to be growing so fast.
D. Being their loving custodians you always want to see them doing well.
E. Their eyes sparkle with curiosity and endless questions on their tongues.
Choose the order of the sentences marked A, B, C, D and E to form a logical paragraph.
Sentences:
A. It is hoping that overseas friends will bring in big money and lift the morale of the people.
B. But a lot needs to be done to kick start industrial revival.
C. People had big hopes from the new government.
D. So far government has only given an incremental push to existing policies and programmes.
E. Government is to go for big time reforms, which it promised.
Choose the order of the sentences marked A, B, C, D and E to form a logical paragraph.
Sentences:
A. Forecasting the weather has always been a difficult business.
B. During a period of drought, streams and rivers dried up, the cattle died from thirst and were ruined.
C. Many different things affect the weather and we have to study them carefully to make accurate forecast.
D. Ancient Egyptians had no need of weather forecasting in the Nile valley hardly ever changes.
E. In early times, when there were no instruments, such as thermometer or barometer, a man looked for tell tale signs in the sky.
Choose the correct answer figure which will make a complete square on joining with the problem figure.
In the following question, five figures are given. Out of them, find the three figures that can be joined to form a square.
Choose the answer figure which completes the problem figure matrix.
What is the opposite of 3, if four different positions of dice are as shown below?
In the following questions, one or more dots are placed on the figure marked as (A). The figure is followed by four alternatives marked as (a), (b), (c) and (d). One out of these four options contains region(s) common to the circle, square and triangle, similar to that marked by the dot in figure (A).
Complete the series by replacing ‘?’ mark: \[ G4T, J9R, M20P, P43N, S90L \]
Neeraj starts walking towards South. After walking 15 m, he turns towards North. After walking 20 m, he turns towards East and walks 10 m. He then turns towards South and walks 5 m. How far is he from his original position and in which direction?
The average age of 8 men is increased by 2 years when one of them whose age is 20 years is replaced by a new man. What is the age of the new man?
Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. How is Shikha related to Ankit?
In a queue of children, Arun is fifth from the left and Suresh is sixth from the right. When they interchange their places among themselves, Arun becomes thirteenth from the left. Then, what will be Suresh’s position from the right?
\(\displaystyle \lim_{x\to\infty}\frac{\int_{0}^{2x} x e^{x^{2}}\,dx}{e^{4x^{2}}}\) equals
If \(\omega\) is the complex cube root of unity, then the value of \[ \omega+\omega\!\left(\frac12+\frac38+\frac{9}{32}+\frac{27}{128}+\cdots\right) \]
is
The root of the equation \[ 2(1+i)x^2-4(2-i)x-5-3i=0 \]
which has greater modulus is
The value of \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots up to n terms is \]
The period of \(\tan 3\theta\) is
If a function \(f(x)\) is given by \[ f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2x+1)}+\frac{x}{(2x+1)(3x+1)}+\cdots+\infty, \]
then at \(x=0\), \(f(x)\)
If \(g\) is the inverse of function \(f\) and \(f'(x)=\sin x\), then \(g'(x)\) is equal to
A bag contains \((2n+1)\) coins. It is known that \(n\) of these coins have a head on both sides, whereas the remaining \((n+1)\) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is \(\frac{31}{42}\), then \(n\) is equal to
If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \]
is
The area of the region \(R=\{(x,y):|x|\le |y| and x^2+y^2\le1\}\) is
Universal set, \[ U=\{x\mid x^5-6x^4+11x^3-6x^2=0\}; \quad A=\{x\mid x^2-5x+6=0\}; \quad B=\{x\mid x^2-3x+2=0\}. \]
What is \((A\cap B)'\)?
If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then \(4x^2-4xy\cos\alpha+y^2\) is equal to
If \[ \frac{e^x+e^{5x}}{e^{3x}}=a_0+a_1x+a_2x^2+a_3x^3+\cdots, \]
then the value of \(2a_1+2^3a_3+2^5a_5+\cdots\) is
Let \(\vec a,\vec b,\vec c\) be three vectors satisfying \(\vec a\times\vec b=\vec a\times\vec c\), \(|\vec a|=|\vec c|=1\), \(|\vec b|=4\) and \(|\vec b\times\vec c|=\sqrt{15}\). If \(\vec b-2\vec c=\lambda \vec a\), then \(\lambda\) equals
The total number of 4-digit numbers in which the digits are in descending order is
The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) is
In a \(\triangle ABC\), the lengths of the two larger sides are 10 and 9 units respectively. If the angles are in A.P., then the length of the third side can be
The arithmetic mean of the data \(0,1,2,\ldots,n\) with frequencies \(1,{}^nC_1,{}^nC_2,\ldots,{}^nC_n\) is
The mean square deviation of a set of observations \(x_1,x_2,\ldots,x_n\) about point \(c\) is defined as \[ \frac1n\sum_{i=1}^n(x_i-c)^2. \]
The mean square deviations about \(-2\) and \(2\) are 18 and 10 respectively. The standard deviation of the set of observations is
Let \(S\) be the focus of the parabola \(y^2=8x\) and \(PQ\) be the common chord of the circle \(x^2+y^2-2x-4y=0\) and the given parabola. The area of \(\triangle PQS\) is
The number of real roots of the equation \[ e^{x-1}+x-2=0 \]
is
Minimise \( Z=\sum_{i=1}^{n}\sum_{j=1}^{m} c_{ij}x_{ij} \)
subject to \[ \sum_{i=1}^{m} x_{ij}=b_j,\; j=1,2,\ldots,n, \] \[ \sum_{j=1}^{n} x_{ij}=b_i,\; i=1,2,\ldots,m. \]
This is an LPP with number of constraints equal to
A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is
Let \(M\) be a \(3\times3\) non-singular matrix with \(\det(M)=\alpha\). If \(|M^{-1}\operatorname{adj}(M)|=K\), then the value of \(K\) is
Tangents are drawn from the origin to the curve \(y=\cos x\). Their points of contact lie on
The slope of the tangent to the curve \(y=e^x\cos x\) is minimum at \(x=\alpha,\;0\le\alpha\le2\pi\). Then the value of \(\alpha\) is
Two lines \(L_1:\;x=5,\; \dfrac{y}{3-\alpha}=\dfrac{z}{-2}\) \(L_2:\;x=\alpha,\; \dfrac{y}{1}=\dfrac{z}{2-\alpha}\)
are coplanar. Then \(\alpha\) can take value(s)
The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is
The function \(f(x)=\dfrac{x}{2}+\dfrac{2}{x}\) has local minimum at
If \(y=\left(x+\sqrt{1+x^2}\right)^n\), then \((1+x^2)\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}\) is
If \(\displaystyle \lim_{x\to\infty}x\sin\!\left(\frac1x\right)=A\) and \(\displaystyle \lim_{x\to0}x\sin\!\left(\frac1x\right)=B\), then which one of the following is correct?
If \(a\) and \(b\) are non-zero roots of \(6x^2+ax+b=0\), then the least value of \(x^2+ax+b\) is
If \(0
The degree of the differential equation satisfying \[ \sqrt{1-x^2}+\sqrt{1+y^2}=a(x-y) \]
is
Let \(f(x)\) be a polynomial of degree three satisfying \(f(0)=-1\) and \(f'(0)=0\). Also, 0 is a stationary point of \(f(x)\). If \(f(x)\) does not have an extremum at \(x=0\), then the value of \(\displaystyle\int\frac{f(x)}{x^3-1}\,dx\) is
The domain of the function \[ f(x)=\frac{\sin^{-1}(x-3)}{\sqrt{9-x^2}} \]
is
If the lines \(p_1x+q_1y=1\), \(p_2x+q_2y=1\) and \(p_3x+q_3y=1\) are concurrent, then the points \((p_1,q_1), (p_2,q_2)\) and \((p_3,q_3)\) are
Area of the circle in which a chord of length \(\sqrt{2}\) makes an angle \(\pi/2\) at the centre is
If \(\dfrac{\cos A}{\cos B}=n,\ \dfrac{\sin A}{\sin B}=m\), then the value of \(m^2-n^2\) is
If complex numbers \(z_1,z_2\) and \(0\) are vertices of an equilateral triangle, then \(z_1^2+z_2^2-z_1z_2\) is equal to
If \(\rho=\{(x,y)\mid x^2+y^2=1;\ x,y\in\mathbb R\}\), then \(\rho\) is
A line makes the same angle \(\theta\) with each of the X and Z-axes. If the angle \(\beta\) which it makes with Y-axis is such that \(\sin^2\beta=3\sin^2\theta\), then \(\cos^2\theta\) equals
If in a binomial distribution \(n=4\), \(P(X=0)=\frac{16}{81}\), then \(P(X=4)\) equals
Let \(f:\mathbb R\to\mathbb R\) be a function such that \(f(x+y)=f(x)+f(y)\) for all \(x,y\in\mathbb R\).
If \(f(x)\) is differentiable at \(x=0\), then which one of the following is incorrect?
If binomial coefficients of three consecutive terms of \((1+x)^n\) are in H.P., then the maximum value of \(n\) is
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