A silver wire has a mass $$(0.6 \pm 0.006)$$ g, radius $$(0.5 \pm 0.005)$$ mm and length $$(4 \pm 0.04)$$ cm. The maximum percentage error in the measurement of its density will be
JEE WhatsApp Group
Sign in
Please select an account to continue using cracku.in
↓ →
JEE WhatsApp Group
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
A silver wire has a mass $$(0.6 \pm 0.006)$$ g, radius $$(0.5 \pm 0.005)$$ mm and length $$(4 \pm 0.04)$$ cm. The maximum percentage error in the measurement of its density will be
Login to view the detailed solution.
A projectile is launched at an angle $$\alpha$$ with the horizontal with a velocity $$20$$ m s$$^{-1}$$. After $$10$$ s, its inclination with horizontal is $$\beta$$. The value of $$\tan\beta$$ will be : $$(g = 10$$ m s$$^{-2})$$.
Login to view the detailed solution.
A girl standing on road holds her umbrella at $$45°$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $$15\sqrt{2}$$ km h$$^{-1}$$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is
Login to view the detailed solution.
.webp)
A system of two blocks of masses $$m = 2$$ kg and $$M = 8$$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $$0.5$$. The maximum horizontal force $$F$$ that can be applied to the block of mass $$M$$ so that the blocks move together will be $$(g = 9.8$$ m s$$^{-2})$$
Login to view the detailed solution.
Two blocks of masses $$10$$ kg and $$30$$ kg are placed on the same straight line with coordinates $$(0, 0)$$ cm and $$(x, 0)$$ cm respectively. The block of $$10$$ kg is moved on the same line through a distance of $$6$$ cm towards the other block. The distance through which the block of $$30$$ kg must be moved to keep the position of centre of mass of the system unchanged is
Login to view the detailed solution.
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $$5$$ times its mass?
(Assume the collision to be head-on elastic collision)
Login to view the detailed solution.
Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.
Login to view the detailed solution.
The velocity of a small ball of mass $$m$$ and density $$d_1$$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $$d_2$$, then the viscous force acting on the ball will be
Login to view the detailed solution.
A mixture of hydrogen and oxygen has volume $$2000$$ cm$$^3$$, temperature $$300$$ K, pressure $$100$$ kPa and mass $$0.76$$ g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$]
Login to view the detailed solution.
The displacement of simple harmonic oscillator after $$3$$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is
Login to view the detailed solution.
An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is
Login to view the detailed solution.
A force of $$10$$ N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.
Login to view the detailed solution.
A $$72$$ $$\Omega$$ galvanometer is shunted by a resistance of $$8$$ $$\Omega$$. The percentage of the total current which passes through the galvanometer is
Login to view the detailed solution.
The susceptibility of a paramagnetic material is $$99$$. The permeability of the material in Wb/A - m, is
[Permeability of free space $$\mu_0 = 4\pi \times 10^{-7}$$ Wb/A - m]
Login to view the detailed solution.
The current flowing through an ac circuit is given by $$I = 5\sin(120\pi t)$$ A. How long will the current take to reach the peak value starting from zero?
Login to view the detailed solution.
Match List - I with List - II
| List-I | List-II |
|---|---|
| (a) Ultraviolet rays | (i) Study crystal structure |
| (b) Microwaves | (ii) Greenhouse effect |
| (c) Infrared waves | (iii) Sterilizing surgical instrument |
| (d) X-rays | (iv) Radar system |
Login to view the detailed solution.
Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be
Login to view the detailed solution.
An $$\alpha$$ particle and a carbon 12 atom has same kinetic energy $$K$$. The ratio of their de-Broglie wavelengths $$(\lambda_\alpha : \lambda_{C12})$$ is
Login to view the detailed solution.
A hydrogen atom in its ground state absorbs $$10.2$$ eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of (Given, Planck's constant $$= 6.6 \times 10^{-34}$$ Js).
Login to view the detailed solution.
Identify the correct Logic Gate for the following output ($$Y$$) of two inputs $$A$$ and $$B$$.
Login to view the detailed solution.
A pendulum of length $$2$$ m consists of a wooden bob of mass $$50$$ g. A bullet of mass $$75$$ g is fired towards the stationary bob with a speed $$v$$. The bullet emerges out of the bob with a speed $$\frac{v}{3}$$ and the bob just completes the vertical circle. The value of $$v$$ is ______ m s$$^{-1}$$
(if $$g = 10$$ m s$$^{-2}$$).
Login to view the detailed solution.
The area of cross-section of a large tank is $$0.5$$ m$$^2$$. It has a narrow opening near the bottom having area of cross-section $$1$$ cm$$^2$$. A load of $$25$$ kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $$40$$ cm above the bottom, will be ______ cm s$$^{-1}$$.
[Take $$g = 10$$ m s$$^{-2}$$]
Login to view the detailed solution.
In a carnot engine, the temperature of reservoir is $$527°$$C and that of sink is $$200$$ K. If the work done by the engine when it transfers heat from reservoir to sink is $$12000$$ kJ, the quantity of heat absorbed by the engine from reservoir is ______ $$\times 10^6$$ J.
Login to view the detailed solution.
A capacitor of capacitance $$50$$ pF is charged by $$100$$ V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.
Login to view the detailed solution.
A $$220$$ V, $$50$$ Hz AC source is connected to a $$25$$ V, $$5$$ W lamp and an additional resistance $$R$$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $$R$$ (in ohm) will be
Login to view the detailed solution.
A cell, shunted by a $$8$$ $$\Omega$$ resistance, is balanced across a potentiometer wire of length $$3$$ m. The balancing length is $$2$$ m when the cell is shunted by $$4$$ $$\Omega$$ resistance. The value of internal resistance of the cell will be ______ $$\Omega$$.
Login to view the detailed solution.
The current density in a cylindrical wire of radius $$4$$ mm is $$4 \times 10^6$$ A m$$^{-2}$$. The current through the outer portion of the wire between radial distances $$\frac{R}{2}$$ and $$R$$ is ______ $$\pi$$ A.
Login to view the detailed solution.
In Young's double slit experiment the two slits are $$0.6$$ mm distance apart. Interference pattern is observed on a screen at a distance $$80$$ cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ______ nm.
Login to view the detailed solution.
A beam of monochromatic light is used to excite the electron in $$Li^{++}$$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $$x \times 10^{-10}$$ m. The value of $$x$$ is ______.
[Given $$hc = 1242$$ eV nm]
Login to view the detailed solution.
The height of a transmitting antenna at the top of a tower is $$25$$ m and that of receiving antenna is, $$49$$ m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $$K\sqrt{5} \times 10^2$$ m. The value of $$K$$ is ______.
(Assume radius of Earth is $$64 \times 10^5$$ m) [Calculate upto nearest integer value]
Login to view the detailed solution.
Given below are two statements : one is labelled as Assertion and the other is labelled as Reason.
Assertion: The ionic radii of $$O^{2-}$$ and $$Mg^{2+}$$ are same.
Reason: Both $$O^{2-}$$ and $$Mg^{2+}$$ are isoelectronic species.
Login to view the detailed solution.
Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II
| List-I (Shape) | List-II (Molecules) |
|---|---|
| A T-shaped | I. $$XeF_4$$ |
| B Trigonal planar | II. $$SF_4$$ |
| C Square planar | III. $$ClF_3$$ |
| D See-saw | IV. $$BF_3$$ |
Login to view the detailed solution.
Match List - I with List - II.
| List-I | List-II |
|---|---|
| (A) Spontaneous process | (I) $$\Delta H < 0$$ |
| (B) Process with $$\Delta P = 0, \Delta T = 0$$ | (II) $$\Delta G_{T,P} < 0$$ |
| (C) $$\Delta H_{reaction}$$ | (III) Isothermal and isobaric process |
| (D) Exothermic Process | (IV) [Bond energies in reactants] - [Bond energies in products] |
Choose the correct answer from the options given below
Login to view the detailed solution.
Addition of $$H_2SO_4$$ to $$BaO_2$$ produces
Login to view the detailed solution.
$$BeCl_2$$ reacts with $$LiAlH_4$$ to give
Match List - I with List - II.
| List-I (Si-Compounds) | List-II (Si-Polymeric/Other Products) |
|---|---|
| A $$(CH_3)_4Si$$ | I Chain Silicone |
| B $$(CH_3)Si(OH)_3$$ | II Dimeric Silicone |
| C $$(CH_3)_2Si(OH)_2$$ | III Silane |
| D $$(CH_3)_3Si(OH)$$ | IV 2D-Silicone |
Choose the correct answer from the options given below
Login to view the detailed solution.
L-isomer of a compound 'A'($$C_4H_8O_4$$) gives a positive test with $$[Ag(NH_3)_2]^+$$. Treatment of 'A' with acetic anhydride yields triacetate derivative. Compound 'A' produces an optically active compound (B) and an optically inactive compound (C) on treatment with bromine water and $$HNO_3$$ respectively. Compound (A) is :
Login to view the detailed solution.
Given below are two Statements :
Statement I : Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide.
Statement II : Photochemical smog has components, ozone, nitric oxide, acrolein, formaldehyde, PAN etc.
In the light of the above statements, choose the most appropriate answer from the options given below.
Login to view the detailed solution.
Given below are two statements : one is labelled as Assertion and the other is labelled as Reason.
Assertion: At $$10°$$C, the density of a $$5$$ M solution of KCl [atomic masses of K & Cl are $$39$$ & $$35.5$$ g mol$$^{-1}$$ respectively], is 'x' g mL$$^{-1}$$. The solution is cooled to $$-21°$$C. The molality of the solution will remain unchanged.
Reason: The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the most appropriate answer from the options given below.
Login to view the detailed solution.
Match List - I with List - II.
| List-I | List-II |
|---|---|
| A Lyophilic colloid | I Liquid-liquid colloid |
| B Emulsion | II Protective colloid |
| C Positively charged colloid | III $$FeCl_3 + NaOH$$ |
| D Negatively charged colloid | IV $$FeCl_3$$ + hot water |
Choose the correct answer from the options given below
Login to view the detailed solution.
Match List - I with List - II.
| List-I | List-II |
|---|---|
| A Concentration of gold ore | I Aniline |
| B Leaching of alumina | II NaOH |
| C Froth stabiliser | III $$SO_2$$ |
| D Blister copper | IV NaCN |
Choose the correct answer from the options given below
Login to view the detailed solution.
Heating white phosphorus with conc. NaOH solution gives mainly
Login to view the detailed solution.
Which of the following will have maximum stabilization due to crystal field?
Login to view the detailed solution.
The major product of the following reaction is
Login to view the detailed solution.
Which of the following reactions will yield benzaldehyde as a product?
Login to view the detailed solution.
'A' and 'B' respectively are
A $$\xrightarrow[(2) Zn-H_2O]{(1) O_3 \atop}$$ Ethane-1,2-dicarbaldehyde + Glyoxal/Oxaldehyde
B $$\xrightarrow[(2) Zn-H_2O]{(1) O_3 \atop}$$ 5-oxohexanal
Login to view the detailed solution.
Given below are two statements :
Statement - I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom.
Statement - II : The group is migrated in Hofmann degradation reaction to electron deficient atom.
In the light of the above statements, choose the most appropriate answer from the options given below
Login to view the detailed solution.
Match List - I with List - II.
| List-I (Polymer) | List-II (Used in) |
|---|---|
| A Bakelite | I Radio and television cabinets |
| B Glyptal | II Electrical switches |
| C PVC | III Paints and Lacquers |
| D Polystyrene | IV Water pipes |
Login to view the detailed solution.
Match List - I with List - II.
Choose the correct answer from the options given below
Login to view the detailed solution.
Which of the following is structure of a separating funnel?
Login to view the detailed solution.
If the uncertainty in velocity and position of a minute particle in space are, $$2.4 \times 10^{-26}$$ (ms$$^{-1}$$) and $$10^{-7}$$ (m) respectively. The mass of the particle in g is ______ (Nearest integer)
(Given : $$h = 6.626 \times 10^{-34}$$ Js)
Login to view the detailed solution.
$$2NOCl(g) \rightleftharpoons 2NO(g) + Cl_2(g)$$
In an experiment, $$2.0$$ moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be $$0.4$$ mol/L. The equilibrium constant at $$30°$$C is ______ $$\times 10^{-4}$$.
Login to view the detailed solution.
Total number of possible stereoisomers of dimethyl cyclopentane is ______
Login to view the detailed solution.
Metal deficiency defect is shown by $$Fe_{0.93}O$$. In the crystal, some $$Fe^{2+}$$ cations are missing and loss of positive charge is compensated by the presence of $$Fe^{3+}$$ ions. The percentage of $$Fe^{2+}$$ ions in the $$Fe_{0.93}O$$ crystals is ______ (Nearest integer)
Login to view the detailed solution.
Two elements A and B which form $$0.15$$ moles of $$A_2B$$ and $$AB_3$$ type compounds. If both $$A_2B$$ and $$AB_3$$ weigh equally, then the atomic weight of A is ______ times of atomic weight of B.
Login to view the detailed solution.
$$2$$ g of a non-volatile non-electrolyte solute is dissolved in $$200$$ g of two different solvents A and B whose ebullioscopic constants are in the ratio of $$1 : 8$$. The elevation in boiling points of A and B are in the ratio $$\frac{x}{y}$$ ($$x : y$$). The value of $$y$$ is ______ (Nearest Integer)
Login to view the detailed solution.
The limiting molar conductivities of NaI, $$NaNO_3$$ and $$AgNO_3$$ are $$12.7, 12.0$$ and $$13.3$$ mS m$$^2$$ mol$$^{-1}$$, respectively (all at $$25°$$C). The limiting molar conductivity of AgI at this temperature is ______ mS m$$^2$$ mol$$^{-1}$$.
Login to view the detailed solution.
The rate constant for a first order reaction is given by the following equation :
$$\ln k = 33.24 - \frac{2.0 \times 10^4 K}{T}$$
The Activation energy for the reaction is given by ______ kJ mol$$^{-1}$$. (In Nearest integer) (Given : $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)
Login to view the detailed solution.
The number of statement(s) correct from the following for Copper is/are
(A) Cu(II) complexes are always paramagnetic
(B) Cu(I) complexes are generally colourless
(C) Cu(I) is easily oxidized
(D) In Fehling solution, the active reagent has Cu(I)
Login to view the detailed solution.
Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the mangenese product formed from the above reaction is ______ B.M. (Nearest Integer)
Login to view the detailed solution.
The area of the polygon, whose vertices are the non-real roots of the equation $$\bar{z} = iz^2$$ is
Login to view the detailed solution.
If $$x = \sum_{n=0}^{\infty} a^n, y = \sum_{n=0}^{\infty} b^n, z = \sum_{n=0}^{\infty} c^n$$, where $$a, b, c$$ are in A.P. and $$|a| < 1, |b| < 1, |c| < 1, abc \neq 0$$, then
Login to view the detailed solution.
The value of $$\cos\left(\frac{2\pi}{7}\right) + \cos\left(\frac{4\pi}{7}\right) + \cos\left(\frac{6\pi}{7}\right)$$ is equal to
Login to view the detailed solution.
In an isosceles triangle $$ABC$$, the vertex $$A$$ is $$(6, 1)$$ and the equation of the base $$BC$$ is $$2x + y = 4$$. Let the point $$B$$ lie on the line $$x + 3y = 7$$. If $$(\alpha, \beta)$$ is the centroid of $$\triangle ABC$$, then $$15(\alpha + \beta)$$ is equal to
Login to view the detailed solution.
Let the eccentricity of an ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a > b$$, be $$\frac{1}{4}$$. If this ellipse passes through the point $$\left(-4\sqrt{\frac{2}{5}}, 3\right)$$, then $$a^2 + b^2$$ is equal to
Login to view the detailed solution.
Let $$a$$ be an integer such that $$\lim_{x \to 7} \frac{18 - [1-x]}{[x-3a]}$$ exists, where $$[t]$$ is greatest integer $$\leq t$$. Then $$a$$ is equal to
Login to view the detailed solution.
The boolean expression $$(\sim(p \wedge q)) \vee q$$ is equivalent to
Login to view the detailed solution.
Let the system of linear equations $$x + 2y + z = 2, \alpha x + 3y - z = \alpha, -\alpha x + y + 2z = -\alpha$$ be inconsistent. Then $$\alpha$$ is equal to
Login to view the detailed solution.
$$\sin^{-1}\left(\sin\frac{2\pi}{3}\right) + \cos^{-1}\left(\cos\frac{7\pi}{6}\right) + \tan^{-1}\left(\tan\frac{3\pi}{4}\right)$$ is equal to
Login to view the detailed solution.
If $$\cos^{-1}\left(\frac{y}{2}\right) = \log_e\left(\frac{x}{5}\right)^5, |y| < 2$$, then
Login to view the detailed solution.
The number of distinct real roots of $$x^4 - 4x + 1 = 0$$ is
Login to view the detailed solution.
The lengths of the sides of a triangle are $$10 + x^2, 10 + x^2$$ and $$20 - 2x^2$$. If for $$x = k$$, the area of the triangle is maximum, then $$3k^2$$ is equal to
Login to view the detailed solution.
$$\int \frac{(x^2+1)e^x}{(x+1)^2} dx = f(x)e^x + C$$, where $$C$$ is a constant, then $$\frac{d^3f}{dx^3}$$ at $$x = 1$$ is equal to
Login to view the detailed solution.
The value of the integral $$\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)} dx$$ is equal to
Login to view the detailed solution.
Let $$\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}$$, where $$a, b, c$$ are constants, represent a circle passing through the point $$(2, 5)$$. Then the shortest distance of the point $$(11, 6)$$ from this circle is
Login to view the detailed solution.
If $$\frac{dy}{dx} + \frac{2^{x-y}(2^y-1)}{2^x - 1} = 0, x, y > 0, y(1) = 1$$, then $$y(2)$$ is equal to
Login to view the detailed solution.
Let $$\vec{a} = \hat{i} + \hat{j} - \hat{k}$$ and $$\vec{c} = 2\hat{i} - 3\hat{j} + 2\hat{k}$$. Then the number of vectors $$\vec{b}$$ such that $$\vec{b} \times \vec{c} = \vec{a}$$ and $$|\vec{b}| \in \{1, 2, \ldots, 10\}$$ is
Login to view the detailed solution.
If two straight lines whose direction cosines are given by the relations $$l + m - n = 0, 3l^2 + m^2 + cnl = 0$$ are parallel, then the positive value of $$c$$ is
Login to view the detailed solution.
Five numbers $$x_1, x_2, x_3, x_4, x_5$$ are randomly selected from the numbers $$1, 2, 3, \ldots, 18$$ and are arranged in the increasing order $$(x_1 < x_2 < x_3 < x_4 < x_5)$$. The probability that $$x_2 = 7$$ and $$x_4 = 11$$ is
Login to view the detailed solution.
Let $$X$$ be a random variable having binomial distribution $$B(7, p)$$. If $$P(X = 3) = 5P(X = 4)$$, then the sum of the mean and the variance of $$X$$ is
Login to view the detailed solution.
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is ______
Login to view the detailed solution.
If the sum of the first ten terms of the series $$\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501} + \ldots$$ is $$\frac{m}{n}$$, where $$m$$ and $$n$$ are co-prime numbers, then $$m + n$$ is equal to ______
Login to view the detailed solution.
If the coefficient of $$x^{10}$$ in the binomial expansion of $$\left(\frac{\sqrt{x}}{5^{1/4}} + \frac{\sqrt{5}}{x^{1/3}}\right)^{60}$$ is $$5^k l$$, where $$l, k \in N$$ and $$l$$ is coprime to $$5$$, then $$k$$ is equal to ______
Login to view the detailed solution.
A rectangle $$R$$ with end points of the one of its sides as $$(1, 2)$$ and $$(3, 6)$$ is inscribed in a circle. If the equation of a diameter of the circle is $$2x - y + 4 = 0$$, then the area of $$R$$ is ______
Login to view the detailed solution.
A circle of radius $$2$$ unit passes through the vertex and the focus of the parabola $$y^2 = 2x$$ and touches the parabola $$y = \left(x - \frac{1}{4}\right)^2 + \alpha$$, where $$\alpha > 0$$. Then $$(4\alpha - 8)^2$$ is equal to ______
Login to view the detailed solution.
The positive value of the determinant of the matrix $$A$$, whose $$Adj(Adj(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}$$, is ______
Login to view the detailed solution.
Let $$f : R \to R$$ be a function defined $$f(x) = \frac{2e^{2x}}{e^{2x}+e}$$. Then $$f\left(\frac{1}{100}\right) + f\left(\frac{2}{100}\right) + f\left(\frac{3}{100}\right) + \ldots + f\left(\frac{99}{100}\right)$$ is equal to ______
Login to view the detailed solution.
If the sum of all the roots of the equation $$e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0$$ is $$\log_e P$$, then $$P$$ is equal to ______
Login to view the detailed solution.
Let $$A_1 = \{(x,y) : |x| \leq y^2, |x| + 2y \leq 8\}$$ and $$A_2 = \{(x,y) : |x| + |y| \leq k\}$$. If $$27$$ (Area $$A_1$$) $$= 5$$ (Area $$A_2$$), then $$k$$ is equal to ______
Login to view the detailed solution.
Let the mirror image of the point $$(a, b, c)$$ with respect to the plane $$3x - 4y + 12z + 19 = 0$$ be $$(a - 6, \beta, \gamma)$$. If $$a + b + c = 5$$, then $$7\beta - 9\gamma$$ is equal to ______
Login to view the detailed solution.
Educational materials for JEE preparation
Share