AP EAPCET 2021 20TH AUGUST MORNING SHIFT

A glass flask weighting 390 g, having internal volume 500 cc just floats when half of it is filled with water. Specific gravity of the glass is

The number of protons, neutrons and electrons in $$_6^{13}$$C respectively are

Using Kjeldahl’s method over 1g of a soil sample, the ammonia evolved could neutralise 25 mL of 1 M H$$_2$$SO$$_4$$. Then, the percentage of nitrogen present in the sample is

If $$f(x)=2x^3+mx^2-13x+n$$ and 2, 3 are the roots of the equation $$f(x)=0$$, then the values of m and n are

The displacement of a particle starting from rest at $$t=0$$ is given by $$s=9 t^2-2 t^3$$. The time in seconds at which the particle will attain zero velocity is

Two cars A and B are moving with a velocity of 30 km/h in the same direction. They are separated by 10 km. The speed of another car C moving in the opposite direction, if it meets these two cars at an interval of eight minutes is

A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 $$\times$$ 10$$^7$$ Nm$$^{-2}$$. The area of cross-section from the wire is 10$$^{-6}$$ m$$^{2}$$. The maximum angular velocity with which it can be rotated in a horizontal circle is

A book is lying on a table. What is the angle between the normal reaction acting on the book on the table and the weight of the book?

The range of a projectile is 100 m. Its kinetic energy will be maximum after covering a distance of

A uniform chain has a mass m and length $$l$$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is

A rifle bullet loses $$\left(\frac{1}{25}\right)$$th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

When a force F = 17 $$-$$ 2x + 6x$$^2$$N acts on a body of mass 2 kg and displaces it from x = 0 m to x = 8 m, the work done is

A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30$$^\circ$$, then the angle of inclination of plane B must be (approximately)

Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a square of side $$b$$. Moment of inertia of the system about an axis along one of the sides of the square is

If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of inertia.

Water does not wet an oily glass because

Boiling water is changing into steam. The specific heat of boiling water is

If the volume of a block of metal changes by $$0.12 \%$$ when heated through $$20^{\circ} \mathrm{C}$$, then find its coefficient of linear expansion.

The pressure of a gas is proportional to

Isothermal process is the graph between

A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy when its displacement from mean position equals

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out the time period of oscillation would

The gravitational potential energy is maximum at

A geostationary satellite is taken to a new orbit, such that its distance from centre of the earth is doubled. Then, find the time period of this satellite in the new orbit.

Two charges 8 $$\mu$$C each are placed at the corners A and B of an equilateral triangle of side 0.2 m in air. The electric potential at the third corner C is

The induced emf cannot be produced by

Assertion (A) When plane of coil is perpendicular to magnetic field, magnetic flux linked with the coil is minimum, but induced emf is zero.

Reason (R) $$\phi=n A B \cos \theta$$ and $$e=\frac{d \phi}{d t}$$

A wire of length $$L$$ metre carrying a current $$I$$ ampere is bent in the form of a circle. Magnitude of its magnetic moment is

A paramagnetic sample showing a net magnetisation of $$0.8 \mathrm{~A} \mathrm{~m}^{-1}$$, when placed in an external magnetic field of strength $$0.8 \mathrm{~T}$$, at a temperature $$5 \mathrm{~K}$$. If the temperature is raised to $$20 \mathrm{~K}$$, then the magnetisation becomes

The electric and the magnetic fields associated with an electromagnetic wave propagating along the $$z$$-axis, can be represented by

A 60 $$\mu$$F parallel plate capacitor whose plates are separated by 6 mm is charged to 250 V, and then the charging source is removed. When a slab of dielectric constant 5 and thickness 3 mm is placed between the plates, find the change in the potential difference across the capacitor.

A 20 V AC is applied to a circuit consisting of a resistor and a coil with negligible resistance. If the voltage across the resistor is 12 V, the voltage across the coil is

The angular momentum of the orbital electron is integral multiple of

Which of the following values is the correct order of nuclear density?

The graph between the maximum speed $$(v_{max})$$ of a photoelectron and frequency $$(\nu)$$ of the incident radiation, in photoelectric effect is correctly represented by

An alloy of metals X and Y weighs 12 g and contains atoms X and Y in the ratio of 2 : 5. The percentage of metal X in the alloy is 20 by mass. If the atomic mass of X is 40 amu what is the atomic mass of metal Y ?

The masses of an electron, a proton and a neutron respectively will be n the ratio

Match the following species with the correct number of electrons present in them.

Which among the following statements is/are incorrect regarding real gases?

(i) Their compressibility factor is never equal to unity (Z $$\ne$$ 1).

(ii) The deviations from ideal behaviour are less at low pressures and high temperatures.

(iii) Intermolecular forces among gas molecules are equal to zero.

(iv) They obey van der Waals’ equation, $$pV = nRT$$

For the reaction, $$\mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})$$ at $$T=100^{\circ} \mathrm{C}$$ and $$p=1 \mathrm{~atm}$$, choose the correct option.

At $$60^{\circ} \mathrm{C}$$, dinitrogen tetroxide is dissociated. Find it's standard free energy change at this temperature and one atmosphere. [Given $$\log 1.33=0.1239$$]

Le-Chatelier's principle is not applicable to

The solubility of $$\operatorname{AgBr}(s)$$, having solubility product $$5 \times 10^{-10}$$ in $$0.2 \mathrm{~M} \mathrm{~NaBr}$$ solution equals

If the $$K_{\mathrm{H}}$$ values for $$\operatorname{Ar}(g), \mathrm{CO}_2(g), \mathrm{HCHO}(g)$$ and $$\mathrm{CH}_4(\mathrm{~g})$$ respectively are $$40.39,1.67, 1.83 \times 10^{-5}$$ and $$0.413$$ , then identify the correct increasing order of their solubilities.

If 500 mL of CaCl$$_2$$ solution contains 3.01 $$\times$$ 10$$^{22}$$ chloride ions, molarity of the solution will be

Which of the following statement is incorrect?

Which among the following species does not show disproportionation reaction?

In an adsorption experiment, a graph between $$\log (x / m)$$ versus $$\log p$$ was found to be linear with a slope of $$45^{\circ}$$. The intercept on $$\log (x / m)$$ axis was found to be 0.3010. The amount of gas adsorbed per gram of charcoal under a pressure of $$0.5 \mathrm{~atm}$$ is

If hydrogen electrons dipped in two solutions of pH = 3 and pH = 6 are connected by a salt bridge, the emf of the resulting cell is

Which statement among the following is incorrect?

For zero order reaction, a plot of $$t_{1 / 2}$$ versus $$[A]_0$$ will be

Bond order is an inverse measure of

Which of the following molecule has the maximum dipole moment?

The correct order of electronegativity of carbon in various hybridisation states is

The correct order of sulphur-oxygen bond in $$\mathrm{SO}_3, \mathrm{~S}_2 \mathrm{O}_3^{2-}$$ and $$\mathrm{SO}_4^{2-}$$ is

Which of the following does not form double salts?

What would be the product of following reaction?

$$\mathrm{SiCl}_4 \stackrel{\text { Excess of } \mathrm{H}_2 \mathrm{O}}{\longrightarrow} \text { ? (Major product) }$$

Which of the following is not arranged in the correct sequence?

Which among the following is coloured?

Potassium cyanide is made alkaline with NaOH and boiled with thiosulphate ions. The solution is cooled and acidified with HCl and this solution with iron (III) chloride produces

$$\mathrm{AlF}_3$$ is soluble in HF only in the presence of KF due to formation of

Which of the following complexes formed by nickel is tetrahedral and paramagnetic?

Which among the following is not a greenhouse gas?

Which of the following is not explained by hyperconjugation?

Which compound among the following is most reactive towards electrophilic reagents?

An organic compound of molecular formula $$\mathrm{C_6H_6Br_2}$$ has six carbon atoms in a ring system, two non-conjugate double bonds and two bromo groups at 1, 4-positions. Then the compound is

Identify (Z) in the following reaction.

$$\mathrm{C{H_3}COOH\buildrel {LiAl{H_4}} \over \longrightarrow (X)\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{573\,K}^{Cu}} (Y)\buildrel {dil.\,NaOH} \over \longrightarrow (Z)}$$

Vitamin-B$$_1$$ is

The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is

The value of $${ }^6 P_4+4 \cdot{ }^6 P_3$$ is

Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white and 6 black balls is

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum value of the AM of $$\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$$ and $$\cos \left(\gamma+\frac{\pi}{2}\right)$$ is equal to

What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ?

If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}$$ is equal to

If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third quadrant, then the value of $$\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}$$ is equal to

If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$, then

$$\frac{d}{d x}\left\{\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\right\}$$ is equal to

If $$y=\tan ^{-1}\left\{\frac{a x-b}{b x+a}\right\}$$, then $$y^{\prime}$$ is equal to

In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is

In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B E=\frac{\pi}{3}$$, then the area of $$\triangle A B C$$ is

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.

If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are

Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are the points of maximum and minimum, respectively, of the function $$f(x)=2 x^3-9 a x^2+12 a^2 x+1$$.

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively. If its diameter is increasing at a rate of 2 cm/s, then at what rate must its altitude change, in order to keep its volume constant?

The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of

If $$\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C$$, then $$k$$ is equal to

$$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to

If $$\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.$$ then $$f(x) \cdot g(x)$$ is equal to

Given, $$\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}$$, then $$4 A+2 B+4 C$$ is equal to

If $$\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R$$, then $$\frac{P}{Q}$$ is equal to

Let $$f(x)=x^3$$ and $$g(x)=3^x$$, then the quadratic equation whose roots are solutions of the equation $$(f \circ g)(x)=(g \circ f)(x)$$ (for $$x \neq 0$$) is

$$f(x)=\sin x+\cos x \cdot g(x)=x^2-1$$, then $$g(f(x))$$ is invertible if

If $$f: z \rightarrow z$$ is defined by $$f(x)=x^9-11 x^8-2 x^7+22 x^6+x^4 -12 x^3+11 x^2+x-3, \forall x \in z$$, then $$f(11)$$ is equal to

$$\mathop {\lim }\limits_{n \to \infty } {{n{{(2n + 1)}^2}} \over {(n + 2)({n^2} + 3n - 1)}}$$ is equal to

If the function $$f(x)$$, defined below, is continuous on the interval $$[0,8]$$, then $$f(x)=\left\{\begin{array}{cc}x^2+a x+b & , \quad 0 \leq x < 2 \\ 3 x+2, & 2 \leq x \leq 4 \\ 2 a x+5 b & , 4 < x \leq 8\end{array}\right.$$

If $$f(x)$$, defined below, is continuous at $$x=4$$, then

$$f(x) = \left\{ {\matrix{ {{{x - 4} \over {|x - 4|}} + a} & , & {x < 4} \cr {a + b} & , & {x = 4} \cr {{{x - 4} \over {|x - 4|}} + b} & , & {x > 4} \cr } } \right.$$

If $$\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}} $$, then the value of a is equal to

$$\int_1^2 {{{{x^3} - 1} \over {{x^2}}}} $$ is equal to

If $$y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)$$ and $$x \neq 0$$. When $$x=-1, \frac{d y}{d x}$$ is equal to

If $$f(x)=2x^2+3x-5$$, then the value of $$f'(0)+3f'(-1)$$ is equal to

Find the equation of the circle which passes through origin and cuts off the intercepts $$-$$2 and 3 over the $$X$$ and $$Y$$-axes respectively.

The locus of a point, which is at a distance of 4 units from $$(3,-2)$$ in $$x y$$-plane is

The length of the common chord of the circles $$x^2+y^2+3x+5y+4=0$$ and $$x^2+y^2+5x+3y+4=0$$ is __________ units.

If the circle $$x^2+y^2-4 x-8 y-5=0$$ intersects the line $$3 x-4 y-m=0$$ in two distinct points, then the number of integral values of '$$m$$' is

Let $$C$$ be the circle center $$(0,0)$$ and radius 3 units. The equation of the locus of the mid-points of the chords of the circle $$c$$ that subtends an angle of $$\frac{2 \pi}{3}$$ at its centre is

The angle between the pair of tangents drawn from $$(1,1)$$ to the circle $$x^2+y^2+4 x+4 y-1=0$$ is

Find the equation of the circle which passes through the point $$(1,2)$$ and the points of intersection of the circles $$x^2+y^2-8 x-6 y+21=0$$ and $$x^2+y^2-2 x-15=0$$

If one focus of a hyperbola is $$(3,0)$$, the equation of its directrix is $$4 x-3 y-3=0$$ and its eccentricity $$e=5 / 4$$, then the coordinates of its vertex is

The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a parameter) are

When the axes are rotated through an angle 45$$^\circ$$, the new coordinates of a point P are (1, $$-$$1). The coordinates of P in the original system are

If the bisectors of the pair of lines $$x^2-2 m x y-y^2=0$$ is represented by $$x^2-2 n x y-y^2=0$$, then

If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ will subtend a right angle at

The correct order of acidic strength among the following is

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\alpha^{2021}, \beta^{2021}$$ is given by

If $$2, 1$$ and $$1$$ are roots of the equation $$x^3-4 x^2+5 x-2=0$$, then the roots of $$\left(x+\frac{1}{3}\right)^3-4\left(x+\frac{1}{3}\right)^2+5\left(x+\frac{1}{3}\right)-2=0$$

In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?

The probabilities that $$A$$ and $$B$$ speak truth are $$\frac{4}{5}$$ and $$\frac{3}{4}$$ respectively. The probability that they contradict each other when asked to speak on a fact is

One card is selected at random from 27 cards numbered form 1 to 27. What is the probability that the number on the card is even or divisible by 5.

The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 is

Let $$\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}$$ and $$\mathbf{w}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}$$. Then which of the following statement is true?

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

The position vectors of the points $$A$$ and $$B$$ with respect to $$O$$ are $$2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$$. The length of the internal bisector of $$\angle B O A$$ of $$\triangle A O B$$ is (take proportionality constant is 2)

Let $$\mathbf{a}=\hat{\mathbf{i}}$$ and $$\mathbf{b}=\hat{\mathbf{j}}$$, the point of intersection of the lines $$\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}$$ and $$\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}$$ is

If the lines, $$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$ and $$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$ are coplanar, then $$\sin ^{-1}(\sin \lambda)+\cos ^{-1}(\cos \lambda)$$ is equal to

If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthocentre, centroid, circumcentre and incentre, then H + G + S + I is equal to

A(2, 3, 4), B(4, 5, 7), C(2, $$-$$6, 3) and D(4, $$-$$4, k) are four points. If the line AB is parallel to CD, then k is equal to

The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ meets the line $$\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}$$ at $$A$$ and the plane $$2 x-y+2 z+7=0$$ at $$B$$. Then $$A B$$ is equal to

If the direction cosines of two lines are $$\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)$$ and $$\left( {{5 \over {13}},{{12} \over {13}},0} \right)$$, then identify the direction ratios of a line which is bisecting one o the angle between them.

If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z \cos A=0$$ and $$x \cos B+y \cos A-z=0$$

The trace of the matrix $$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$ is

If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]^{-1} =\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$$, then

What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ?

For the random variable X with probability distribution is given by the table

The mean of X is

Let an angle of a triangle is 60$$^\circ$$. If the variance of the angles of the triangle is 1014$$^\circ$$, then the other two angles are

The mean deviation from the mean of the set of observation $$-1,0,4$$ is

If $$z_1=2+3 i$$ and $$z_2=3+2 i$$, where $$i=\sqrt{-1}$$, then $$\left[\begin{array}{cc}z_1 & z_2 \\ -\bar{z}_2 & \bar{z}_1\end{array}\right]\left[\begin{array}{cc}\bar{z}_1 & -z_2 \\ \bar{z}_2 & z_1\end{array}\right]$$ is equal to

If $$a > 0$$ and $$z=x+i y$$, then $$\log _{\cos ^2 \theta}|z-a|>\log _{\cos ^2 \theta}|z-a i|,(\theta \in R)$$ implies

The radius of the circle represented by $$(1+i)(1+3i)(1+7i)=x+iy$$ is $$(i=\sqrt{-1})$$.

If one root of the equation $$i x^2-2(i+1) x+(2-i)=0$$ is $$(2-i)$$, then the other root is

If $$1, \alpha_1, \alpha_2, \alpha_3$$ and $$\alpha_4$$ are the roots of $$z^5-1=0$$ and $$\omega$$ is a cube root of units, then $$(\omega-1)\left(\omega-\alpha_1\right)\left(\omega-\alpha_2\right)\left(\omega-\alpha_3\right)\left(\omega-\alpha_4\right)+\omega$$ is equal to

If $$\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$$, then $$\theta$$ is equal to

Find the equation of a straight line passing through $$(-5,6)$$ and cutting off equal intercepts on the coordinate axes.

The equation of a straight line which passes through the point $$\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$$ and perpendicular to $$(x \sec \theta+y \operatorname{cosec} \theta)=a$$ is

Line has slope $$m$$ and $$y$$-intercept 4 . The distance between the origin and the line is equal to

The equation of the base of an equilateral triangle is $$x+y=2$$ and one vertex is $$(2,-1)$$, then the length of the side of the triangle is

If the lines, joining the origin to the points of intersection of the curve $$2 x^2-2 x y+3 y^2+2 x-y-1=0$$ and the line $$x+2 y=k$$, are at right angles, then $$k^2$$ equals

The acute angle between lines $$6 x^2+11 x y-10 y^2=0$$ is

The equation of bisector of the angle between the lines represented by $$3 x^2-5 x y+4 y^2=0$$ is

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $$(f_a )$$ cannot be ignored, the forces acting on the ball at the position X are represented by

For a monoatomic ideal gas is following the cyclic process ABCA shown in the U versus p plot, identify the incorrect option.

A string fixed at both ends vibrate in 5 loops as shown in the figure. The total number of nodes and anti-nodes respectively are

The position of the direct image obtained at O, when a monochromatic beam of light is passed through a plane transmission grating at normal incidence is shown in figure. The diffracted images A, B, and C correspond to the first, second and third order diffraction. When the source is replaced by another source of shorter wavelength,

What is the electric flux for Gaussian surface $$A$$ that encloses the charged particles in free space? [Given, $$q_1=-14 \mathrm{~nC}, q_2=78.85 \mathrm{~nC}, \left.q_3=-56 \mathrm{~nC}\right]$$

What is the net force on the square coil?

Five current carrying conductors meet at a point P. What is the magnitude and direction of the current in the fifth conductor?

The truth table given below corresponds to logic gate.

In the face centered unit cell, the lattice points are present at

Which compound among the following will have a permanent dipole moment?

Identify the product of the following reaction.

Identify the major product of the following reaction.