KCET 2019

In the reaction of gold with aquaregia, oxidation state of nitrogen changes from

The number of $$\pi$$-bonds and $$\sigma$$-bonds present in naphthalene are respectively

The first ionisation enthalpy of the following elements are in the order :

A wire is stretched such that its volume remains constant. The poission's ratio of the material of the wire is

The trajectory of a projectile projected from origin is given by the equation $$y=x-\frac{2 x^2}{5}$$. The initial velocity of the projectile is

The given graph shows the variation of velocity $$v$$ with position $$x$$ for a particle moving along a straight line

Which of the following graph shows the variation of acceleration a with position x?

If $$P, Q$$ and $$R$$ are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?

$$\int_\limits{-3}^3 \cot ^{-1} x d x=$$

An object with mass $$5 \mathrm{~kg}$$ is acted upon by a force, $$\mathbf{F}=(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \mathrm{N}$$. If its initial velocity at $$t=0$$ is $$\mathbf{v}=(3 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$$, the time at which it will just have a velocity along $$y$$-axis is -

An aluminium sphere is dipped into water. Which of the following is true?

A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from $$A$$ to $$B$$, the angular momentum of the particle about $$O$$

A satellite is orbiting close to the earth and has a kinetic energy $$K$$. The minimum extra kinetic energy required by it just overcome the gravitation pull of the earth is

During inelastic collision between two objects, which of the following quantity always remains conserved?

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are $$v$$ and $$2 v$$ at any instant, then the speed of centre of mass of the system is

A cylindrical container containing water has a small hole at height of $$H=8 \mathrm{~cm}$$ from the bottom and at a depth of $$2 \mathrm{~cm}$$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $$x$$ is

A piston is performing S.H.M. in the vertical direction with a frequency of $$0.5 \mathrm{~Hz}$$. A block of $$10 \mathrm{~kg}$$ is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is

A thermodynamic system undergoes a cyclic process $$A B C$$ as shown in the diagram. The work done by the system per cycle is

The equation of a stationary wave is $$y=2 \sin \left(\frac{\pi x}{15}\right) \cos (48 \pi t)$$. The distance between a node and its next antinode is

If Young's double slit experiment, using monochromatic light of wavelength $$\lambda$$, the intensity of light at a point on the screen where path difference is $$\lambda$$ is $$K$$ units. The intensity of light at a point where path difference is $$\frac{\lambda}{3}$$ is

One mole of $$\mathrm{O}_2$$ gas is heated at constant pressure starting at $$27^{\circ} \mathrm{C}$$. How much energy must be added to the gas as to double its volume?

A transparent medium shows relation between $$i$$ and $$r$$ as shown. If the speed of light in vacuum is $$c$$, the Brewster angle for the medium is

A point object is moving uniformly towards the pole of a concave mirror of focal length $$25 \mathrm{~cm}$$ along its axis as shown below. The speed of the object is $$1 \mathrm{~ms}^{-1}$$. At $$t=0$$, the distance of the object from the mirror is $$50 \mathrm{~cm}$$. The average velocity of the image formed by the mirror between time $$t=0$$ and $$t=0.25 \mathrm{~s}$$ is

A certain prism is found to produce a minimum deviation of $$38^{\circ}$$. It produce a deviation of $$44^{\circ}$$ when the angle of incidence is either $$42^{\circ}$$ or $$62^{\circ}$$. What is the angle of incidence when it is undergoing minimum deviation?

An electromagnetic wave is travelling in $$x$$-direction with electric field vector given by, $$\mathbf{E}_y=E_0 \sin (k x-\omega t) \hat{\mathbf{j}}$$. The correct expression for magnetic field vector is

Due to Doppler's effect the shift in wavelength observed is $$0.1 \mathop A\limits^o$$ for a star producing wavelength $$6000 \mathop A\limits^o$$. Velocity of recession of the star will be

The phenomenon involved in the reflection of radio-waves by ionosphere is similar to

A toroid has 500 turns per meter length. If it carries a current of $$2 \mathrm{A}$$, the magnetic energy density inside the toroid is

An antenna uses electromagnetic waves of frequency $$5 \mathrm{~MHz}$$. For proper working, the size of the antenna should be

Coersivity of a magnet where the ferromagnet gets completely demagnetized is $$3 \times 10^3 \mathrm{~Am}^{-1}$$. The minimum current required to be passes in a solenoid having 1000 turns per metre, so that the magnet gets completely demagnetized when placed inside the solenoid is

A magnetic needle has a magnetic moment of $$5 \times 10^{-2} \mathrm{~Am}^2$$ and moment of inertia $$8 \times 10^{-6} \mathrm{~kgm}^2$$. It has a period of oscillation of $$2 \mathrm{~s}$$ in a magnetic field $$\mathbf{B}$$. The magnitude of magnetic field is approximately?

In a permanent magnet at room temperature

In a cyclotron a charged particle

The magnetic fields at the centre O in the given figure is

The number of turns in a coil of galvanometer is tripled, then

A circular current loop of magnetic moment $$M$$ is in a arbitrary orientation in an external uniform magnetic field $$\mathbf{B}$$. The work done to rotate the loop by $$30^{\circ}$$ about an axis perpendicular to its plane is

Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ be the nuclear force and the electrostatic force between them

Two metal plates are separated by $$2 \mathrm{~cm}$$. The potentials of the plates are $$-10 \mathrm{~V}$$ and $$+30 \mathrm{~V}$$. The electric field between the two plates is

A particle of mass $$m$$ and charge $$q$$ is placed at rest in uniform electric field $$E$$ and then released. The kinetic energy attained by the particle after moving a distance $$y$$ is

Consider the situation given in figure. The wire $$A B$$ is slid on the fixed rails with a constant velocity. If the wire $$A B$$ is replaced by a semicircular wire, the magnitude of the induced current will

An electric dipole is kept in non-uniform electric field. It generally experiences

In the given circuit, the current through 2$$\Omega$$ resistor is

The readings of ammeter and voltmeter in the following circuit are respectively

A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance between them is increased, the potential energy of the system

A certain charge $$2 Q$$ is divided at first into two parts $$q_1$$ and $$q_2$$. Later the charges are placed at a certain distance. If the force of interaction between two chagrges is maximum then $$\frac{Q}{q_1}$$ is

The figure gives the electric potential $$V$$ as a function of distance through four regions on $$x$$-axis. Which of the following is true for the magnitude of the electric field $$E$$ in these regions?

Though the electron drift velocity is small and electron charge is very small, a conductor can carry an appreciably large current because

The variation of terminal potential difference $$V$$ with current flowing through a cell is as shown. The emf and internal resistance of the cell are

The frequency of an alternating current is $$50 \mathrm{~Hz}$$. What is the minimum time taken by current to reach its peak value from rms value?

Kirchhoff 's junction rule is a reflection of

A capacitor of capacitance $$C$$ charged by an amount $$Q$$ is connected in parallel with an uncharged capacitor of capacitance $$2 C$$. The final charges on the capacitors are

The equivalent capacitance between A and B is

In a potentiometer experiment, the balancing point with a cell is at a length $$240 \mathrm{~cm}$$. On shunting the cell with a resistance of $$2 \Omega$$, the balancing length becomes $$120 \mathrm{~cm}$$. The internal resistance of the cell is

An inductor of inductance $$L$$ and resistor $$R$$ are joined together in series and connected by a source of frequency $$\omega$$. The power dissipated in the circuit is

The end product of decay of $${ }_{90} \mathrm{Th}^{232}$$ is $${ }_{82} \mathrm{~Pb}^{208}$$. The number of $$\alpha$$ and $$\beta$$ particles emitted are respectively

A hydrogen atom is ground state absorbs $$10.2 \mathrm{~eV}$$ of energy. The orbital angular momentum of the electron is increased by

Frequency of revolution of an electron revolving in $$n$$th orbit of $$\mathrm{H}$$-atom is proportional to

In Rutherford experiment, for head-on collision of $$\alpha$$-particles with a gold nucleus, the impact parameter is

Which one of the following nuclei has shorter mean life?

The mass of $$\mathrm{AgCl}$$ precipitated when a solution containing $$11.70 \mathrm{~g}$$ of $$\mathrm{NaCl}$$ is added to a solution containing $$3.4 \mathrm{~g}$$ of $$\mathrm{AgNO}_3$$ is [Atomic mass of $$\mathrm{Ag}=108$$, Atomic mass of $$\mathrm{Na}=23$$]

The conductivity of semiconductor increases with increase in temperature because

In the following circuit, what are P and Q?

Light of certain frequency and intensity incident on a photosensitive material causes photoelectric effect. If both the frequency and intensity are doubled, the photoelectric saturation current becomes

An electron is moving with an initial velocity $$\mathbf{v}=v_0 \hat{\mathbf{i}}$$ and is in a uniform magnetic field $$\mathbf{B}=B_0 \hat{\mathbf{j}}$$. Then its de-Broglie wavelength

For a transistor amplifier, the voltage gain

In the reaction

$$\mathrm{B}(\mathrm{OH})_3+2 \mathrm{H}_2 \mathrm{O} \rightarrow\left[B(\mathrm{OH})_4\right]^{-}+\mathrm{H}_2 \stackrel{+}{\mathrm{O}}, \mathrm{B}(\mathrm{OH})_3$$

functions as

Solubility of AgCl is least in

The reaction in which $$\Delta H=\Delta U$$ is

Which of the following equations does not represent Charles's law for a given mass of gas at constant pressure?

Solution '$$A$$' contains acetone dissolved in chloroform and solution '$$B$$' contains acetone dissolved in carbon disulphide. The type of deviations from Raoult's law shown by solutions $$A$$ and $$B$$, respectively are

Two particle $$A$$ and $$B$$ are in motion. If the wavelength associated with '$$A$$' is $$33.33 \mathrm{~nm}$$, the wavelength associated with '$$B$$' whose momentum is $$\frac{1}{3} \mathrm{rd}$$ of '$$A$$' is

Which of the following statement is correct?

Critical Micelle concentration for a soap solution is $$1.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$$. Micelle formation is possible only when the concentration of soap solution in $$\mathrm{mol} \mathrm{~L}^{-1}$$ is

A non-volatile solute, '$$A$$' tetramerises in water to the extent of $$80 \%.$$ $$2 .5 \mathrm{~g}$$ of '$$A$$' in $$100 \mathrm{~g}$$ of water, lower the freezing point by $$0.3^{\circ} \mathrm{C}$$. The molar mass of '$$A$$' in $$\mathrm{g}$$ is $$\left(K_f\right.$$ for water $$=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1})$$

The number of moles of electron required to reduce 0.2 mole of $$\mathrm{Cr}_2 \mathrm{O}_7^{-2}$$ to $$\mathrm{Cr}^{+3}$$ is

Relative lowering of vapour pressure of a dilute solution of glucose dissolved in $$1 \mathrm{~kg}$$ of water is 0.002 . The molality of the solution is

Which of the following is an example of homogeneous catalysis?

The number of atoms in $$2.4 \mathrm{~g}$$ of body centred cubic crystal with edge length $$200 \mathrm{pm}$$ is (density $$=10 \mathrm{~g} \mathrm{~cm}^{-3}, \mathrm{~N}_A=6 \times 10^{23}$$ atoms$$/ \mathrm{mol}$$)

Give $$E_{\mathrm{Mn}^{+7} \mid \mathrm{Mn}^{+2}}^0=1.5 \mathrm{~V}$$ and $$E_{\mathrm{Mn}^{+4}\mid \mathrm{Mn}^{+2}}^0=1.2 \mathrm{~V}$$, then $$E_{\mathrm{Mn}^{+7} \mid \mathrm{Mn}^{+4}}^0$$ is

An aqueous solution of $$\mathrm{CuSO}_4$$ is subjected to electrolysis using inert electrodes. The $$\mathrm{pH}$$ of the solution will

1 mole of $$\mathrm{NaCl}$$ is doped with $$10^{-5}$$ mole of $$\mathrm{SrCl}_2$$. The number of cationic vacancies in the crystal lattice will be

Which of the following is a network crystalline solid?

One litre solution of $$\mathrm{MgCl}_2$$ is electrolysed completely by passing a current of $$1 \mathrm{~A}$$ for $$16 \mathrm{~min} 5 \mathrm{~sec}$$. The original concentration of $$\mathrm{MgCl}_2$$ solution was (Atomic mass of $$\mathrm{Mg}=24$$ )

Which of the following possess net dipole moment?

Addition of excess of $$\mathrm{AgNO}_3$$ to an aqueous solution of 1 mole of $$\mathrm{PdCl}_2 \cdot 4 \mathrm{NH}_3$$ gives 2 moles of $$\mathrm{AgCl}$$. The conductivity of this solution corresponds to

The plot of $$t_{1 / 2} \mathrm{~v} / \mathrm{s}~[R]_0$$ for a reaction is a straight-line parallel to $$X$$-axis. The unit for the rate constant of this reaction is

1L of $$2 \mathrm{M~CH}_3 \mathrm{COOH}$$ is mixed with 1L of $$3 \mathrm{M} \mathrm{~C}_2 \mathrm{H}_5 \mathrm{OH}$$ to form an ester. The rate of the reaction with respect to the initial rate when each solution is diluted with an equal volume of water will be

Which of the following pair contains 2 lone pair of electrons on the central atom?

Which is a wrong statement?

Among the following, the main reactions occurring in blast furnace during extraction of iron from haematite are

(i) $$\mathrm{Fe}_2 \mathrm{O}_3+3 \mathrm{CO} \rightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_2$$

(ii) $$\mathrm{FeO}+\mathrm{SiO}_2 \rightarrow \mathrm{FeSiO}_3$$

(iii) $$\mathrm{Fe}_2 \mathrm{O}_3+3 \mathrm{C} \rightarrow 2 \mathrm{Fe}+3 \mathrm{CO}$$

(iv) $$\mathrm{CaO}+\mathrm{SiO}_2 \rightarrow \mathrm{CaSiO}_3$$

Which cleansing agent gets precipitated in hard water?

Which of the following is not true regarding the usage of hydrogen as a fuel?

The metal nitrate that liberates $$\mathrm{NO}_2$$ on heating

The elements in which electrons are progressively filled in $$4 f$$-orbital are called

0.1 mole of $$\mathrm{XeF}_6$$ is treated with $$1.8 \mathrm{~g}$$ of water. The product obtained is

Which among the following is the strongest ligand?

Oxidation state of copper is +1 in

A mixture of $$\mathrm{NaCl}$$ and $$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$$ is heated with conc. $$\mathrm{H}_2 \mathrm{SO}_4$$, deep red vapours are formed. Which of the following statements is false?

Incorrect statement with reference to $$\mathrm{Ce}(Z=58)$$ is

Which of the following statements is wrong?

The formula of pentaaquanitratochromium (III) nitrate is,

Which of the following halide undergoes hydrolysis on warming with water/aqueous $$\mathrm{NaOH}$$ ?

The compound having longest C$$-$$Cl bond is

The alkyl halides required to prepare by Wurtz reaction are

2-butyne is reduced to trans-but-2-ene using

Resonance effect is not observed in

Eutrophication causes

Match the following acids with their $$pKa$$ values :

Which is the most suitable reagent for the following conversion?

Which of the following can be used to test the acidic nature of ethanol?

The reagents $$A, B$$ and $$C$$ respectively are

Propanoic acid undergoes HVZ reaction to give chloropropanoic acid. The product obtained is

$$P \xrightarrow{\mathrm{H}_2 / \text { Pd- } \mathrm{BaSO}_4} Q \xrightarrow[\text { (ii)Dil. } \mathrm{HCl}]{\text { (i) Con. } \mathrm{NaOH}}$$

$$R$$ and $$S$$ form benzyl benzoate when treated with each other. Hence $$P$$ is

Cis-1, 4-polyisoprene is called

The polymer containing five methylene groups in it s repeating unit is

Which of the following is least soluble in water at $$298 \mathrm{~K}$$ ?

In nucleic acids, the nucleotides are joined together by

If aniline is treated with $$1: 1$$ mixture of conc. $$\mathrm{HNO}_3$$ and conc. $$\mathrm{H}_2 \mathrm{SO}_4$$, p-nitroaniline and $$m$$-nitroaniline are formed nearly in equal amounts. This is due to

The vitamin that helps in clotting of blood is

If $$P(n): 2^n< n !$$ Then the smallest positive integer for which $$P(n)$$ is true, is

If $$\alpha$$ and $$\beta$$ are roots of the equation $$x^2=x+1=0$$, then $$\alpha^2+\beta^2$$ is

The number of 4 digit numbers without repetition that can be formed using the digits $$1,2,3,4,5,6,7$$ in which each number has two odd digits and two even digits is

Anti-histamine among the following is

Which of the following is generally water insoluble?

The third term of a GP is 9. The product of its first five terms is

On the set of positive rational, a binary operation * is defined by $$a * b=\frac{2 a b}{5}$$. If $$2 * x=3^{-1}$$, then $$x=$$

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

If $$A$$ and $$B$$ are two events of a sample space $$S$$ such that $$P(A)=0.2, P(B)=0.6$$ and $$P(A \mid B)=0.5$$ then $$P\left(A^{\prime} \mid B\right)=$$

A random variable '$$X$$' has the following probability distribution

Then the value of $$k$$ is

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $$S=\{1,2,3,4,5,6,7\}$$ and reports that it is even. The probability that is actually even is

If '$$X$$' has a binomial distribution with parameters $$n=6, p$$ and $$P(X=2)=12$$, $$P(X=3)=5$$ then $$P=$$

If $$|\mathbf{a}|=16,|\mathbf{b}|=4$$, then $$\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=$$

The number of terms in the expansion of $$\left(x^2+y^2\right)^{25}-\left(x^2-y^2\right)^{25}$$ after simplification is

A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is

If $$A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}$$, then the number of onto functions from $$A$$ to $$B$$ is

If $$U$$ is the universal set with 100 elements; $$A$$ and $$B$$ are two set such that $$n(A)=50, n(B)=60, n(A \cap B)=20$$ then $$n\left(A^{\prime} \cap B^{\prime}\right)=$$

If the angle between $$\mathbf{a}$$ & $$\mathbf{b}$$ is $$\frac{2 \pi}{3}$$ and the projection of $$\mathbf{a}$$ in the direction of $$\mathbf{b}$$ is $$-$$2 , the $$|\mathbf{a}|=$$

If $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]$$, Then $$\left|A B B^{\prime}\right|=$$

$$[\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=$$

$$X Y$$ plane divides the line joining the points $$A(2,3,-5)$$ and $$B(-1,-2,-3)$$ in the ratio

The distance of the point $$(1,2,1)$$ from the line $$\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2}$$ is.

Foot of the perpendicular drawn from the point $$(1,3,4)$$ to the plane $$2 x-y+z+3=0$$ is

Acute angel between the line $$\frac{(x-5)}{2}=\frac{y+1}{-1}=\frac{z+4}{1}$$ and the plane $$3 x-4 y-z+5=0$$ is

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

The constant term in the expansion of $$\left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1\end{array}\right|$$ is

If $$P$$ and $$Q$$ are symmetric matrices of the same order then $$P Q-Q P$$ is

If $$3 A+4 B^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]$$ and $$2 B+3 A^{\prime}\left[\begin{array}{cc}-1 & 18 \\ 4 & 0 \\ -5 & -7\end{array}\right]$$ then $$B=$$

The negative of the statement "All continuous functions are differentiable."

Mean and standard deviation of 100 items are 50 and 4 , respectively. The sum of all squares of the items is

If $$f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$$ then $$f^{\prime}(0)=$$

If $$\cos x=|\sin x|$$ then, the general solution is

The shaded region in the figure is the solution set of the inequations.

If $$a+\frac{\pi}{2}<2 \tan ^{-1} x+3 \cot ^{-1} x< b$$ then '$$a$$' and '$$b$$' are respectively.

$$\cos \left[2 \sin ^{-1} \frac{3}{4}+\cos ^{-1} \frac{3}{4}\right]=$$

$$\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=$$

If $$|3 x-5| \leq 2$$ then

The value of $$\sqrt{24.99}$$ is

The domain of the function $$f: R \rightarrow R$$ defined by $$f(x)=\sqrt{x^2-7 x+12}$$ is

The area of the region above $$X$$-axis included between the parabola $$y^2=x$$ and the circle $$x^2+y^2=2 x$$ in square units is

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ is defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one of the following is not true?

The area of the region bounded by $$Y$$-axis, $$y=\cos x$$ and $$y=\sin x, 0 \leq x \leq \frac{\pi}{2}$$ is

Rolle's theorem is not applicable in which one of the following cases?

$$\sum_\limits{r=1}^n(2 r-1)=x$$ then, $$ \lim _\limits{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac{3^3}{x^2}+\ldots+\frac{n^3}{x^2}\right]=$$

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then $$A, B, C$$ are respectively

$$\int x^3 \sin 3 x d x=$$

If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuous at $$x=0$$, then $$k=$$

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

The equation of the curve passing through the point $$(1,1)$$ such that the slope of the tangent at any point $$(x, y)$$ is equal to the product of its co-ordinates is

If $$[x]$$ represents the greatest integer function and $$f(x)=x-[x]-\cos x$$, then $$f^{\prime}\left(\frac{\pi}{2}\right)=$$

The integrating factor of the differential equation $$\left(2 x+3 y^2\right) d y=y d x(y>0)$$ is

The order of the differential equation $$y=C_1 e^{C_2+x}+C_3 e^{C_4+x}$$ is

If $$x=a \sec ^2 \theta$$ & $$y=a \tan ^2 \theta$$, then $$\frac{d^2 y}{d x^2}=$$

$$\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}$$, then $$\frac{d y}{d x}=$$

$$\int_\limits0^2\left[x^2\right] d x=$$

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of $$X$$-axis is

The sides of an equilateral triangle are increasing at the rate of $$4 \mathrm{~cm} / \mathrm{sec}$$. The rate at which its area is increasing, when the side is $$14 \mathrm{~cm}$$

$$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$

The interval in which the function $$f(x)=x^3-6 x^2+9 x+10$$ is increasing in

The eccentricity of the ellipse $$9 x^2+25 y^2=225$$ is

Masses of three wires of copper are in the ratio $$1: 3: 5$$ and their lengths are in the ratio $$5: 3: 1$$. The ratio of their electrical resistance are

The inverse of the matrix $$\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]$$ is