SRMJEEE UG Model Question Paper with Solutions

The density of a metal is calculated as follows. The weight of \(57.4\) grams is divided by the volume \(6.2\ \text{cm}^3\). Using the approximate rule for significant figures in this calculation, the value of the density, in \(\text{g/cm}^3\), should be reported as:

• (A) \(9\)
• (B) \(9.3\)
• (C) \(9.26\)
• (D) \(9.258\)

If the Reynolds number is less than \(2000\), the flow in a pipe is

• (A) Turbulent
• (B) Laminar
• (C) Transition
• (D) None of the above

Maximum load a structure can bear before its failure is called

• (A) Normal Load
• (B) Shear load
• (C) Ultimate load
• (D) Safety load

Three point charges \(q+Q,\ q,\ q-Q\) are enclosed by the surface \(S\). What net flux crosses \(S\)?

• (A) \(3q\)
• (B) \(2q\)
• (C) \(3q-Q\)
• (D) cannot be determine based on the data given in question

Number of electrons in one coulomb of charge will be

• (A) \(5.46\times10^{23}\)
• (B) \(5.25\times10^{18}\)
• (C) \(1.6\times10^{-19}\)
• (D) \(9\times10^{11}\)

Choose the vector physical quantity

• (A) Electric flux
• (B) Electric potential
• (C) Electric potential energy
• (D) Electric intensity

The voltage is a form of

• (A) Kinetic energy
• (B) Potential energy
• (C) Mechanical energy
• (D) Both kinetic and potential energy

A charge of \(60\ \text{C}\) passes through an electric lamp in \(2\) minutes. Then the current in the lamp is

• (A) \(30\ \text{A}\)
• (B) \(1\ \text{A}\)
• (C) \(0.5\ \text{A}\)
• (D) \(5\ \text{A}\)

Four wires of equal length and of resistance \(3\ \Omega\) each are connected in the form of a square. The equivalent resistance between the diagonally opposite corners of the square is

• (A) \(12\ \Omega\)
• (B) \(3/4\ \Omega\)
• (C) \(6\ \Omega\)
• (D) \(3\ \Omega\)

The number of free electrons per cm of copper wire is \(2\times10^{21}\). The average drift speed of the electrons is \(0.25\ \text{mm/s}\). The current flowing is

• (A) \(0.8\ \text{A}\)
• (B) \(8\ \text{A}\)
• (C) \(80\ \text{A}\)
• (D) \(800\ \text{A}\)

The sensitivity of a potentiometer can be increased by

• (A) Increasing the emf of the cell
• (B) Decreasing the emf of the cell
• (C) Increasing the length of the potentiometer wire
• (D) Decreasing the length of the potentiometer wire

  is the rule used to know the direction of the induced current in the circuit.

• (A) Fleming’s left hand rule
• (B) Fleming’s right hand rule
• (C) Right hand thumb rule
• (D) Ampere’s rule

As the earth rotates, the magnetic poles:

• (A) stay the same
• (B) change a little
• (C) switch completely
• (D) disappear

Induced EMF’s are always in such a direction as to   the change that generated them

• (A) oppose
• (B) against
• (C) favor
• (D) unfavour

An electric circuit consists of a charged capacitor \(C\), a resistor \(R\) and a switch \(S\). Initially, the switch is open and all devices are connected in series. A circular loop of wire is placed in the same plane as the circuit. Which one of the following is true about the induced current in the loop after the switch is closed?

• (A) it is clockwise and increases
• (B) it is counter clockwise and increases
• (C) it is clockwise and decreases
• (D) it is counter clockwise and decreases

Two identical coaxial coils \(P\) and \(Q\) carrying equal amount of current in the same direction are brought nearer. The current in

• (A) \(P\) increases while in \(Q\) decreases
• (B) \(Q\) increases while in \(P\) decreases
• (C) both \(P\) and \(Q\) increases
• (D) both \(P\) and \(Q\) decreases

Alternating voltage \((V)\) is represented by the equation

• (A) \(V(t)=V_m e^t\)
• (B) \(V(t)=V_m\sin \omega t\)
• (C) \(V(t)=V_m\cot \omega t\)
• (D) \(V(t)=V_m\tan \omega t\)

Power factor of the following circuit will be zero

• (A) Resistance
• (B) Inductance
• (C) Capacitance
• (D) Both (b) and (c)

The speed of electromagnetic waves in vacuum is

• (A) \(30\times10^8\ \text{ms}^{-1}\)
• (B) \(4\times10^8\ \text{ms}^{-1}\)
• (C) \(3.0\times10^8\ \text{ms}^{-1}\)
• (D) \(3.0\times10^9\ \text{ms}^{-1}\)

Rays that are used in taking photos during conditions of smoke, darkness is

• (A) X-rays
• (B) Gamma rays
• (C) Ultraviolet rays
• (D) Infrared rays

Angle which is formed between normal ray and ray entering a medium is known as

• (A) critical angle
• (B) angle of incidence
• (C) angle of reflection
• (D) angle of refraction

In projectors   lenses are used

• (A) Convex
• (B) Concave
• (C) Bipolar
• (D) Convex lens and Concave

Dispersion can be noticed by passing a white light through

• (A) glass
• (B) mirror
• (C) water
• (D) prism

Red light is used for signals because it has

• (A) long wavelength
• (B) high intensity
• (C) high frequency
• (D) low refraction in the medium

Kinetic energy of photo electron \(E_K\) changes with frequency \((f)\) of light. Which of the following graph represents this emission?

• (A) Graph A
• (B) Graph B
• (C) Graph C
• (D) Graph D

If the kinetic energy of a free electron doubles, its de Broglie wavelength changes by the factor

• (A) \(2\)
• (B) \(1/2\)
• (C) \(\sqrt{2}\)
• (D) \(1/\sqrt{2}\)

Light of two different frequencies whose photons have energies \(1\ \text{eV}\) and \(2.5\ \text{eV}\) respectively, successively illuminate a metallic surface whose work function is \(0.5\ \text{eV}\). Ratio of maximum speeds of emitted electrons will be

• (A) \(1:2\)
• (B) \(1:5\)
• (C) \(1:1\)
• (D) \(1:4\)

If the energy of a particle is reduced to half then the percentage increase in the de-Broglie wavelength is about

• (A) \(100\%\)
• (B) \(61\%\)
• (C) \(34\%\)
• (D) \(41\%\)

Which of the following particles has a lepton number of \(+1\)?

• (A) \(H^+\)
• (B) \(\mu^-\)
• (C) \(e^+\)
• (D) \(p\)

\(\alpha\)-particles of energy \(400\ \text{keV}\) are bombarded on nucleus of \({}^{82}\text{Pb}\). In scattering of \(\alpha\)-particles, its minimum distance from nucleus will be

• (A) \(0.59\ \text{nm}\)
• (B) \(0.59\ \text{Å}\)
• (C) \(5.9\ \text{pm}\)
• (D) \(0.59\ \text{pm}\)

Two protons are kept at a distance of \(40\times10^{-10}\text{ m}\). \(F_n\) is the nuclear force and \(F_e\) is the electrostatic force between them. Then

• (A) \(F_n \gg F_e\)
• (B) \(F_n = F_e\)
• (C) \(F_n \ll F_e\)
• (D) \(F_n \ne F_e\)

The inputs of a NAND gate are connected together. The resulting circuit is  

• (A) OR gate
• (B) AND gate
• (C) NOT gate
• (D) None of the above

The current in a semiconductor is produced by

• (A) electrons only
• (B) holes only
• (C) negative ions
• (D) both electrons and holes

The V-I curve for a diode shows

• (A) the voltage across the diode for a given current
• (B) the amount of current for a given bias voltage
• (C) the power dissipation
• (D) voltage amplification

The molecular mass of acetic acid dissolved in water is \(60\) and when dissolved in benzene it is \(120\). This difference in behaviour of \(CH_3COOH\) is because

• (A) Water prevents association of acetic acid
• (B) Acetic acid does not fully dissolve in water
• (C) Acetic acid fully dissolves in benzene
• (D) Acetic acid does not ionize in benzene

One mole of component \(X\) and two moles of component \(Y\) are mixed at room temperature to form an ideal binary solution. The \(\Delta H_{mix}\) is

• (A) \(0\)
• (B) \(2\)
• (C) \(3\)
• (D) \(1\)

An increase in equivalent conductance of a strong electrolyte with dilution is mainly due to

• (A) Increase in both i.e. number of ions and ionic mobility of ions.
• (B) Increase in number of ions
• (C) Increase in ionic mobility of ions
• (D) 100% ionization of electrolyte at normal dilution

Saturated solution of \(KNO_3\) is used to make salt bridge because

• (A) Velocity of \(K^+\) is greater than that of \(NO_3^-\)
• (B) Velocity of \(NO_3^-\) is greater than that of \(K^+\)
• (C) Velocity of both \(K^+\) and \(NO_3^-\) are nearly the same
• (D) \(KNO_3\) is highly soluble in water

The half-cell reaction for the SHE is given by

• (A) \(2H^+(aq)+2e^- \rightleftharpoons 2H_2(g)\)
• (B) \(2H^+(aq)+2e^- \rightleftharpoons H_2(g)\)
• (C) \(H^+(aq)+e^- \rightleftharpoons H_2(g)\)
• (D) \(Hg_2^{2+}(aq)+2e^- \rightleftharpoons 2Hg(l)\)

What will be the order of the reaction when the initial concentration is doubled the time of half reaction is doubled?

• (A) Third
• (B) Second
• (C) Zero
• (D) First

Surface tension of lyophilic sol is

• (A) greater than \(H_2O\)
• (B) equal to \(H_2O\)
• (C) less than \(H_2O\)
• (D) none of these

Name the method used for separation of sulphide ores?

• (A) Hydraulic washing
• (B) Magnetic separation
• (C) Froth floatation
• (D) Leaching

\(P_4\) reacts with \(X\) selectively to give \(P_4O_6\). The \(X\) is

• (A) A mixture of \(O_2\) and \(N_2\)
• (B) \(KMnO_4\)
• (C) Jones reagent
• (D) \(K_2Cr_2O_7\)

\(ICl_2^-\) is isostructural with

• (A) \(XeF_2\)
• (B) \(SbCl_3\)
• (C) \(BaCl_2\)
• (D) \(TeF_2\)

Helium is preferred to be used in balloons instead of hydrogen because it is

• (A) Incombustible
• (B) Lighter than hydrogen
• (C) More abundant than hydrogen
• (D) Non-polarizable

Which of the following transition metal ion has magnetic moment \(3.87\) BM?

• (A) \(Mn^{2+}\)
• (B) \(Co^{3+}\)
• (C) \(Fe^{2+}\)
• (D) \(Co^{2+}\)

Lanthanoids are difficult to purify due to their

• (A) large size
• (B) similar chemical and physical properties
• (C) paramagnetic nature
• (D) radioactivity

Correct order of ionic radius of the following \(Ln^{3+}\) ions is

• (A) \(Ho > Lu > Ce > Sm\)
• (B) \(Lu > Ce > Ho > Sm\)
• (C) \(Ce > Sm > Ho > Lu\)
• (D) \(Lu > Ho > Sm > Ce\)

  ion forms colored aqua complexes.

• (A) \(Cu^{2+}\)
• (B) \(Zn^{2+}\)
• (C) \(Ti^{4+}\)
• (D) \(Mn^{7+}\)

A ligand can also be regarded as

• (A) Lewis acid
• (B) Bronsted base
• (C) Lewis base
• (D) Bronsted acid

Monomer which is used to make Poly Vinyl Chloride (PVC) is called

• (A) chloroethene
• (B) chloromethane
• (C) chloropropane
• (D) chlorobutane

Which carbon-halogen bond has the lowest bond enthalpy?

• (A) C-Br
• (B) C-Cl
• (C) C-F
• (D) C-I

What is the correct IUPAC name of the given compound?

• (A) 1-Bromo-2-ethylpropane
• (B) 1-Bromo-2-ethyl-2-methyl ethane
• (C) 1-Bromo-2-methylbutane
• (D) 2-Methyl-1-bromobutane

Molecules whose mirror image is non-superimposable over them are known as chiral. Which of the following molecules is chiral in nature?

• (A) 2-Bromobutane
• (B) 1-Bromobutane
• (C) 2-Bromopropane
• (D) 2-Bromopropan-2-ol

In the given reaction, \(X\) is  .

• (A) Benzene
• (B) Chlorobenzene
• (C) 1,2-Dichlorobenzene
• (D) 1,3,5-Trichlorobenzene

Benzoyl chloride can be prepared from benzoic acid by

• (A) \(SO_2Cl_2\)
• (B) \(Cl_2/\text{Light}\)
• (C) \(SOCl_2\)
• (D) \(Cl_2+H_2O\)

Phenol can be converted to \(o\)-hydroxybenzaldehyde by

• (A) Riemer-Tiemann reaction
• (B) Tischenko reaction
• (C) Sandmeyer reaction
• (D) Wurtz reaction

What happens when glycol reacts with lead tetraacetate?

• (A) No reaction
• (B) Ketones will be formed
• (C) Aldehyde will not be formed
• (D) Monohydric alcohols will be formed

Which of the following acids is manufactured using sawdust?

• (A) Option A structure
• (B) Option B structure
• (C) Option C structure
• (D) Option D structure

Hydrolysis of \(CH_3CH_2NO_2\) with \(85\%\ H_2SO_4\) gives which of the following compound

• (A) \(CH_3CH_2OH\)
• (B) \(C_2H_6\)
• (C) \(CH_3CHNO\)
• (D) \(CH_3COOH\)

The hydrolysis of an ester \((A)\) gives an Acid \((B)\) and an Alcohol \((C)\). The acid \((B)\) reduces Fehling solution. Oxidation of the alcohol \((C)\) gives the acid \((B)\). The ester \((A)\) is

• (A) Methyl formate
• (B) Ethyl formate
• (C) Methyl acetate
• (D) Ethyl acetate

Which of the following statement about primary amines is false?

• (A) Alkyl amines are stronger bases than aryl amines
• (B) Alkyl amines react with nitrous acid to produce alcohols
• (C) Aryl amines react with nitrous acid to produce phenols
• (D) Alkyl amines are stronger bases than ammonia

Nucleic acid is a polymer of

• (A) Nucleosides
• (B) Amino acids
• (C) Nucleotides
• (D) Glucose

Which is not a macromolecule

• (A) DNA
• (B) Starch
• (C) Palmitate
• (D) Insulin

Sugars are

• (A) Optically active polyhydroxy aldehydes
• (B) Optically active polyhydroxy ketones
• (C) Optically active polyhydroxy aldehydes or ketones
• (D) Polyhydroxy aldehydes or ketones which may or may not be optically active

Rayon yarns are obtained from

• (A) Polymethylene
• (B) Polyesters
• (C) Cellulose
• (D) Styrene

Terylene is the polymer of

• (A) Melamine and formaldehyde
• (B) Ethylene glycol and terephthalic acid
• (C) Vinyl chloride and formaldehyde
• (D) Hexamethylene diamine and adipic acid

Condensation product of caprolactam is

• (A) Nylon-6
• (B) Nylon-66
• (C) Nylon-60
• (D) Nylon-6,10

An azo dye is fixed on fabrics by the process applicable in

• (A) Vat dyes
• (B) Mordant dyes
• (C) Developed dyes
• (D) Substantive dyes

The domain of the function \(f(x)=\sqrt{x-1}+\sqrt{6-x}\) is

• (A) \([0,\infty)\)
• (B) \((-\infty,6)\)
• (C) \([1,6]\)
• (D) None of these

Let \(R\) be a relation in \(N\) defined by \(R=\{(x,y): x+2y=8\}\). The range of \(R\) is

• (A) \(\{2,4,6\}\)
• (B) \(\{1,2,3\}\)
• (C) \(\{1,2,3,4,6\}\)
• (D) None of these

Two finite sets have \(m\) and \(n\) elements. Then total number of subsets of the first set is \(56\) more than that of the total number of subsets of the second. The value of \(m\) and \(n\) are

• (A) \(7,6\)
• (B) \(6,3\)
• (C) \(5,1\)
• (D) \(8,7\)

If \(aN=\{ax:x\in N\}\) and \(bN\cap cN=dN\) where \(b,c\in N\) are relatively prime then

• (A) \(d=bc\)
• (B) \(c=bd\)
• (C) \(b=cd\)
• (D) \(a=bd\)

If \(a,b\) are the roots of \(x^2+px+1=0\) and \(c,d\) are the roots of \(x^2+qx+1=0\), the value of \(E=(a-c)(b-c)(a+d)(b+d)\) is

• (A) \(p^2-q^2\)
• (B) \(q^2-p^2\)
• (C) \(q^2+p^2\)
• (D) \((p+q)^2\)

If \(\alpha,\beta\) are the roots of \(ax^2+bx+c=0\) and \(\alpha+h,\beta+h\) are the roots of \(px^2+qx+r=0\), then \(h=\)

• (A) \(\left[\frac{b}{a}-\frac{q}{p}\right]\)
• (B) \(\frac{1}{2}\left[\frac{b}{a}-\frac{q}{p}\right]\)
• (C) \(-\frac{1}{2}\left[\frac{a}{b}-\frac{p}{q}\right]\)
• (D) \(\frac{1}{2}\left[\frac{a}{b}-\frac{p}{q}\right]\)

The common roots of the equations \(x^3+2x^2+2x+1=0\) and \(1+x^{2002}+x^{2003}=0\) are (where \(\omega\) is a complex cube root of unity)

• (A) \(\omega,\omega^2\)
• (B) \(1,\omega^2\)
• (C) \(-1,-\omega\)
• (D) \(\omega,-\omega^2\)

The area of the triangle whose vertices are \((3,8)\), \((-4,2)\) and \((5,1)\) is

• (A) \(63/2\)
• (B) \(61/2\)
• (C) \(59/2\)
• (D) \(57/2\)

The largest value of the third determinant whose elements are equal to 1 or 0 is

• (A) \(0\)
• (B) \(2\)
• (C) \(4\)
• (D) \(6\)

If \(A=(a_{ij})\) is a \(3\times 3\) diagonal matrix such that \(a_{11}=1\), \(a_{22}=2\) and \(a_{33}=3\), then \(|A|\)

• (A) \(6\)
• (B) \(7\)
• (C) \(-6\)
• (D) \(-7\)

If the determinant of the matrix \[ \begin{vmatrix} 1 & 3 & 2\\ 0 & 5 & -6\\ 2 & 7 & 8 \end{vmatrix} \] is \(26\), then the determinant of the matrix \[ \begin{vmatrix} 2 & 7 & 8\\ 0 & 5 & -6\\ 1 & 3 & 2 \end{vmatrix} \] is

• (A) \(-26\)
• (B) \(26\)
• (C) \(0\)
• (D) \(52\)

The lines \(px+qy+r=0\), \(qx+ry+p=0\) and \(rx+py+q=0\) are concurrent if

• (A) \(pq+qr+rp=0\)
• (B) \(p^2+q^2+r^2=2pqr\)
• (C) \(p^3+q^3+r^3=3pqr\)
• (D) \(p^4+q^4+r^4=4pqr\)

If \(A\) and \(B\) are two square matrices of order \(3\) such that \(|A|=-2,\ |B|=5\), then \(|4AB|=\)

• (A) \(-40\)
• (B) \(-256\)
• (C) \(-640\)
• (D) \(-90\)

If \(A\) and \(B\) are two skew symmetric matrices of the same order then \(AB\) is skew symmetric if and only if

• (A) \(AB+BA=0\)
• (B) \(AB-BA=0\)
• (C) \(AB+BA=1\)
• (D) \(AB-BA=1\)

In a class tournament when the participants were to play one game with another, two class players fell ill, having played three games each. If the total number of games played is \(84\), the number of participants at the beginning was

• (A) \(15\)
• (B) \(30\)
• (C) \(78\)
• (D) \(48\)

Rajdhani express going from Bombay to Delhi stops at five intermediate stations ten passengers enter the train during the journey with ten different tickets of two classes. The number of different sets of tickets they may have is

• (A) \({}^{15}C_{10}\)
• (B) \({}^{20}C_{10}\)
• (C) \({}^{30}C_{10}\)
• (D) \({}^{40}C_{10}\)

\(N\) different objects can be arranged taken all at a time in

• (A) \((N-1)!\) ways
• (B) \((N+1)!\) ways
• (C) \(N!\) ways
• (D) \((2N)!\) ways

A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed by Mahesh to try all the combinations?

• (A) \(90\) minutes
• (B) \(120\) minutes
• (C) \(60\) minutes
• (D) \(100\) minutes

If \(C_r={}^{10}C_r\), then \[ 2C_0+\frac{2^2}{2}C_1+\frac{2^3}{3}C_2+\cdots+\frac{2^{11}}{11}C_{10} \] is equal to:

• (A) \(\dfrac{3^{11}-1}{11}\)
• (B) \(\dfrac{2^{11}-1}{11}\)
• (C) \(\dfrac{3^{11}-1}{12}\)
• (D) \(\dfrac{2^{11}-1}{12}\)

If \(\alpha,\beta\) are the roots of \(x^2-3x+a=0\), and \(\gamma,\delta\) are the roots of \(x^2-12x+b=0\), and the numbers \(\alpha,\beta,\gamma,\delta\) in order form an increasing G.P., then:

• (A) \(a=3,b=12\)
• (B) \(a=12,b=3\)
• (C) \(a=2,b=32\)
• (D) \(a=4,b=16\)

If the product of three positive real numbers say \(a,b,c\) be \(27\), then the minimum value of \(ab+bc+ca\) is equal to

• (A) \(27^{4/3}\)
• (B) \(27^{1/3}\)
• (C) \(27^{2/3}\)
• (D) \(27\)

If \(x^2+y^2=t-\frac{1}{t}\) and \(x^4+y^4=t^2+\frac{1}{t^2}\), then \(\frac{x}{y}\frac{dy}{dx}\) is equal to

• (A) \(1\)
• (B) \(t\)
• (C) \(-1\)
• (D) \(-t\)

The value of \(c\) satisfied by Rolle’s theorem for the function \(f(x)=\log\left(\frac{x^2+6}{5x}\right)\) in the interval \([2,3]\) is

• (A) \(\sqrt{6}\)
• (B) \(-\sqrt{6}\)
• (C) \(5\sqrt{6}\)
• (D) \(-5\sqrt{6}\)

Find the solution of \((x^2-3y^2)dx+2xydy=0\)

• (A) \(x^2-y^2=kx^2\)
• (B) \(y^2-x^2=kx^3\)
• (C) \(y^2-x^2=-kx^3\)
• (D) \(x^2-y^2=-kx^2\)

If \(I=\displaystyle\int_0^1 \frac{x^2}{1+x^6}\,dx\), then \(I=\)

• (A) \(\frac{\pi}{8}\)
• (B) \(\frac{\pi}{4}\)
• (C) \(\frac{\pi}{12}\)
• (D) \(\frac{\pi}{2}\)

The distance between the circumcenter and orthocenter of the triangle whose vertices are \((0,0)\), \((6,8)\) and \((-4,3)\) is

• (A) \(\frac{125}{8}\) units
• (B) \(\frac{\sqrt5}{2}\) units
• (C) \(\frac{5\sqrt5}{2}\) units
• (D) \(5\sqrt5\) units

The lines \(2x-3y=5\) and \(3x-4y=7\) are the diameters of a circle of area \(154\) sq.unit. The equation of this circle is

• (A) \(x^2+y^2+2x-2y=62\)
• (B) \(x^2+y^2+2x-2y=47\)
• (C) \(x^2+y^2-2x+2y=47\)
• (D) \(x^2+y^2-2x+2y=62\)

If \(\vec{a}=2\hat{i}+\hat{j}-8\hat{k}\) and \(\vec{b}=\hat{i}+3\hat{j}-4\hat{k}\), then the magnitude of \(\vec{a}+\vec{b}\) is

• (A) \(13\)
• (B) \(\frac{13}{3}\)
• (C) \(\frac{3}{13}\)
• (D) \(\frac{4}{13}\)

The point of intersection of the lines \[ \frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} \] and \[ \frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2} \] is

• (A) \((0,0,-4)\)
• (B) \((1,0,0)\)
• (C) \((0,2,0)\)
• (D) \((1,2,0)\)

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\), then

• (A) \(\vec{a}\) is parallel to \(\vec{b}\)
• (B) \(\vec{a}\) is perpendicular to \(\vec{b}\)
• (C) \(|\vec{a}|=|\vec{b}|\)
• (D) \(\vec{a}\) and \(\vec{b}\) are unit vectors

\(\left|\begin{matrix}x_1 & y_1\\ x_2 & y_2\end{matrix}\right|\) represents the area of

• (A) Circle
• (B) Ellipse
• (C) Triangle
• (D) Parallelogram

A random variable \(X\) has the following probability mass function as follows: \[ \begin{array}{c|ccc} X & -2 & 3 & 1 \\ \hline P(X=x) & \frac{a}{6} & \frac{a}{4} & \frac{a}{12} \end{array} \] Then the value of \(a\) is

• (A) \(1\)
• (B) \(2\)
• (C) \(3\)
• (D) \(4\)

The diameter of an electric cable \(X\) is a continuous random variable with probability density function \[ f(x)=kx(1-x),\quad 0\leq x\leq 1. \] Find \[ P\left(X<\frac{1}{2}\ \middle|\ \frac{1}{3}<X<\frac{2}{3}\right) \]

• (A) \(\frac{1}{4}\)
• (B) \(\frac{1}{2}\)
• (C) \(\frac{3}{2}\)
• (D) \(\frac{3}{4}\)

The mean of a binomial distribution is \(5\) and its standard deviation is \(2\). Then the value of \(n\) and \(p\) are

• (A) \(\left(\frac{4}{5},25\right)\)
• (B) \(\left(25,\frac{4}{5}\right)\)
• (C) \(\left(\frac{1}{5},25\right)\)
• (D) \(\left(25,\frac{1}{5}\right)\)

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed \(3\) times, what is the probability of getting \(2\) tails and \(1\) head.

• (A) \(2/9\)
• (B) \(1/9\)
• (C) \(2/27\)
• (D) \(4/27\)

If \(\triangle ABC\) and \(\triangle PQR\) are similar triangles in which \(\angle A=47^\circ\) and \(\angle Q=83^\circ\), then \(\angle C\) is

• (A) \(60^\circ\)
• (B) \(70^\circ\)
• (C) \(90^\circ\)
• (D) \(50^\circ\)

Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two

• (A) adjacent rays
• (B) linear rays
• (C) Multiple rays
• (D) opposite rays

If \(\sin\theta=\frac{24}{25}\) and \(0^\circ<\theta<90^\circ\), then what is the value of \(\cos\theta\)?

• (A) \(\frac{12}{15}\)
• (B) \(\frac{7}{25}\)
• (C) \(\frac{3}{5}\)
• (D) \(\frac{4}{5}\)

Rewrite the expression as single function of an angle, if \[ \frac{2\tan31^\circ}{1-\tan^2 31^\circ}=? \]

• (A) \(\tan62^\circ\)
• (B) \(\tan31^\circ\)
• (C) \(\tan15^\circ\)
• (D) \(\tan10^\circ\)

According to the passage, why does water travel through plants in unbroken columns?

• (A) Root pressure moves the water very rapidly.
• (B) The attraction between water molecules is strong.
• (C) The living cell of plants pushes the water molecules together.
• (D) Atmospheric pressure supports the columns.

All the following may be components of a virus EXCEPT

• (A) RNA
• (B) Plant cells
• (C) Carbohydrates
• (D) a coat of protein

The synonym of ’profusion’ is

• (A) abundance
• (B) bleed
• (C) blend
• (D) express

All the following sentences about Nicaraguan sign language are true EXCEPT

• (A) The language has been created since 1979.
• (B) The language is based on speech and lip reading.
• (C) The language incorporates signs which children used at home.
• (D) The language was perfected by younger children.

Which idea is presented in the final paragraph?

• (A) English was probably once a creole.
• (B) The English past tense system is inaccurate.
• (C) Linguists have proven that English was created by children.
• (D) Children say English past tenses differently from adults.

Enjoyment is the motto of the

• (A) youth who usher humanity into the third millennium
• (B) youth who rebel against the establishment
• (C) youth looking for an alternative mode of development
• (D) vast majority of the youth today

Summer vacation in old time means

• (A) Grand get together with friends
• (B) Recalling father’s tales
• (C) Playing modern Indian games
• (D) Enjoying with family members

What does "a good conversationalist" refer to?

• (A) sympathetic communicator
• (B) efficient communicator
• (C) who reads others emotion and talk accordingly
• (D) who can talk pleasantly to ameliorate the situation

In the given passage who considers Interviews to be immoral?

• (A) V.S. Naipaul
• (B) Rudyard Kipling
• (C) Mark Twain
• (D) Rudyard Kipling and Mark Twain

According to the author, what is the benefit of public reasoning or argumentation?

• (A) It produces a rich and dynamic democracy.
• (B) It creates chaos and public disagreements that make governing difficult.
• (C) It allowed the British to divide and rule Indians.
• (D) By promoting arguments and discord it hurts the cause of secularism.

The author is making a comparison between

• (A) Science-fiction and Epics
• (B) Science fiction and non-fiction
• (C) Science-Fiction and Romance
• (D) Pulp Fiction and Epics

Based on the given passage which of the following statements is true

• (A) Human beings are awfully close to their material possessions
• (B) Civilizations are built through great efforts.
• (C) One must always try to acquire better things.
• (D) Human existence is casual and haphazard.

The word ’cavalier’ as used in the passage means all of the following except

• (A) Haughty
• (B) Rash
• (C) Prudent
• (D) Frenetic

The expression \(x^2-x+1=0\) has

• (A) One proper linear factor
• (B) Two proper linear factors
• (C) No proper linear factor
• (D) Cannot be determined

If ’+’ means ’divided by’, ’-’ means ’add’, ’ ’ means ’minus’ and ’/’ means ’multiplied by’, what will be the value of the following expression?
\(\{(17\ 12) - (4/2)\} + (23 - 6)\)/0

• (A) infinite
• (B) \(0\)
• (C) \(118\)
• (D) \(219\)

Starting from a Point ’M’ Harish walked \(18\) m towards South. He turned to his left and walked \(5\)m. He then turned to his left and walked \(18\) m. He again turned to his left and walked \(35\) m and reached a point ’P’. How far is Harish from the point ’M’ and in which direction?

• (A) \(10\) m East
• (B) \(10\) m South
• (C) \(10\) m West
• (D) None of these

\((1+\tan A+\sec A)(1+\sec A-\tan A)-2\sec A=\)

• (A) \(0\)
• (B) \(-2\)
• (C) \(1\)
• (D) \(2\)