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.
An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:
Login to view the detailed solution.
The position of a projectile launched from the origin at t = 0 is given by $$\vec{r} = (40\hat{i} + 50\hat{j})$$ m at t = 2s. If the projectile was launched at an angle $$\theta$$ from the horizontal, then $$\theta$$ is (take g = 10 ms$$^{-2}$$).
Login to view the detailed solution.
Water is flowing at a speed of 1.5 m s$$^{-1}$$ through a horizontal tube of cross-sectional area $$10^{-2}$$ m$$^2$$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = $$10^3$$ kg m$$^{-3}$$)
Login to view the detailed solution.
.webp)
A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:
Login to view the detailed solution.
A cylinder of mass M$$_C$$ and sphere of mass M$$_S$$ are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $$\frac{\sin\theta_C}{\sin\theta_S}$$ is:
Login to view the detailed solution.
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is $$a_e = 1.5 \times 10^{11}$$ m, that of Mar's orbit $$a_m = 2.28 \times 10^{11}$$ m, taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.
Login to view the detailed solution.
In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is:
Login to view the detailed solution.
A capillary tube is immersed vertically in water and the height of the water column is $$x$$. When this arrangement is taken into a mine of depth d, the height of the water column is $$y$$. If R is the radius of earth, the ratio $$\frac{x}{y}$$ is:
Login to view the detailed solution.
Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27°C to 77°C? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).
Login to view the detailed solution.
The equation of state for a gas is given by $$PV = nRT + \alpha V$$, where n is the number of moles and $$\alpha$$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T$$_0$$ and P$$_0$$ respectively. The work done by the gas when its temperature doubles isobarically will be:
Login to view the detailed solution.
Modern vacuum pumps can evacuate a vessel down to a pressure of $$4.0 \times 10^{-15}$$ atm. at room temperature (300 K). Taking R = 8.3 JK$$^{-1}$$ mole$$^{-1}$$, 1 atm = $$10^5$$ Pa and $$N_{Avogadro} = 6 \times 10^{23}$$ mole$$^{-1}$$, the mean distance between molecules of gas in an evacuated vessel will be of the order of:
Login to view the detailed solution.
Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s$$^{-1}$$, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take $$g = 10$$ m s$$^{-2}$$).
Login to view the detailed solution.
The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).
Login to view the detailed solution.
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $$x = a_1 \cos \omega t$$ and $$y = a_2 \cos 2\omega t$$ traces a curve given by:
Login to view the detailed solution.
A transverse wave is represented by: $$y = \frac{10}{\pi} \sin\left(\frac{2\pi}{T}t - \frac{2\pi}{\lambda}x\right)$$. For what value of the wavelength the wave velocity is twice the maximum particle velocity?
Login to view the detailed solution.
The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be: [Given: $$\epsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$/N-m$$^2$$, $$R_E = 6.37 \times 10^6$$ m]
Login to view the detailed solution.
Three capacitances, each of 3 $$\mu$$F, are provided. These cannot be combined to provide the resultant capacitance of:
Login to view the detailed solution.
A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of 1 $$\Omega$$. The battery terminals are connected to external resistance $$R$$. The minimum value of $$R$$, so that a current passes through the battery to charge it is:
Login to view the detailed solution.
The mid points of two small magnetic dipoles of length $$d$$ in end-on positions, are separated by a distance $$x$$ ($$x \gg d$$). The magnitude of force between them is proportional to $$x^{-n}$$ where n is:
Login to view the detailed solution.
The magnetic field of earth at the equator is approximately $$4 \times 10^{-5}$$ T. The radius of earth is $$6.4 \times 10^6$$ m. Then the dipole moment of the earth will be nearly of the order of:
Login to view the detailed solution.
When the rms voltages $$V_L$$, $$V_C$$ and $$V_R$$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $$V_L : V_C : V_R = 1 : 2 : 3$$. If the rms voltage of the AC source is 100 V, then $$V_R$$ is close to:
Login to view the detailed solution.
Match List I (Wavelength range of electromagnetic spectrum) with List II (Method of production of these waves) and select the correct option from the options given below the lists.
List I: List II:
(a) 700 nm to 1 mm (i) Vibration of atoms and molecules
(b) 1 nm to 400 nm (ii) Inner shell electrons in atoms moving from one energy level to a lower level
(c) < 10$$^{-3}$$ nm (iii) Radioactive decay of the nucleus
(d) 1 mm to 0.1 m (iv) Magnetron valve
Login to view the detailed solution.
A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $$\frac{4}{3}$$, and the diver's eyes are 15 cm below the surface of the water. Then the radius of the circle is:
Login to view the detailed solution.
The focal lengths of objective lens and eye lens of a Galilean Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition the Magnifying Power of the Galilean Telescope should be:
Login to view the detailed solution.
Using monochromatic light of wavelength $$\lambda$$, an experimentalist sets up the Young's double slit experiment in three ways as shown. If she observes that $$y = \beta'$$, the wavelength of light used is:
Login to view the detailed solution.
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
Login to view the detailed solution.
If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of Li$$^{++}$$ is:
Login to view the detailed solution.
An n-p-n transistor has three leads A, B and C. Connecting B and C by moist fingers, A to the positive lead of an ammeter, and C to the negative lead of the ammeter, one finds large deflection. Then, A, B and C refer respectively to:
Login to view the detailed solution.
Identify the gate and match A, B, Y in the bracket to check.
Login to view the detailed solution.
A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?
Login to view the detailed solution.
Dissolving 120 g of a compound of (mol. wt. 60) in 1000 g of water gave a solution of density 1.12 g/mL. The molarity of the solution is:
Login to view the detailed solution.
The amount of oxygen in 3.6 moles of water is:
Login to view the detailed solution.
The energy of an electron in first Bohr's orbit of H atom is $$-13.6$$ eV. The energy value of electron in the first excited state of Li$$^{2+}$$ is:
Login to view the detailed solution.
In the following sets of reactants which two sets best exhibit the amphoteric character of Al$$_2$$O$$_3$$ · xH$$_2$$O?
Set I: Al$$_2$$O$$_3$$ · xH$$_2$$O$$_{(s)}$$ + OH$$^-_{(aq)}$$
Set II: Al$$_2$$O$$_3$$x · H$$_2$$O$$_{(s)}$$ + H$$_2$$O$$_{(l)}$$
Set III: Al$$_2$$O$$_3$$x · H$$_2$$O$$_{(s)}$$ + H$$^+_{(aq)}$$
Set IV: Al$$_2$$O$$_3$$ · xH$$_2$$O$$_{(s)}$$ + NH$$_{3(aq)}$$
Login to view the detailed solution.
The number and type of bonds in C$$_2^{2-}$$ ion in CaC$$_2$$ are:
Login to view the detailed solution.
Which of the following has unpaired electron(s)?
Login to view the detailed solution.
The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is: (Atomic masses: He = 4 u, O = 16 u)
Login to view the detailed solution.
Van der Waal's equation for a gas is stated as, $$P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2$$. This equation reduces to the perfect gas equation, $$P = \frac{nRT}{V}$$ When,
Login to view the detailed solution.
The standard enthalpy of formation of NH$$_3$$ is $$-46.0$$ kJ/mol. If bond enthalpy of H$$_2$$ is $$-436$$ kJ/mol and that of N$$_2$$ is $$-712$$ kJ/mol, the average bond enthalpy of N$$-$$H bond in NH$$_3$$ is:
Login to view the detailed solution.
At a certain temperature, only 50% HI is dissociated into H$$_2$$ and I$$_2$$ at equilibrium. The equilibrium constant is:
Login to view the detailed solution.
In which of the following pairs is A more stable than B?
Login to view the detailed solution.
In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is:
Login to view the detailed solution.
A current of 10.0 A flows for 2.00 h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250 mol of metal X at the cathode. The oxidation state of X in the molten salt is: (F = 96,500 C)
Login to view the detailed solution.
The standard electrode potentials ($$E^\circ_{M^{+}/M}$$) of four metals A, B, C and D are $$-1.2$$ V, 0.6 V, 0.85 V and $$-0.76$$ V, respectively. The sequence of deposition of metals on applying potential is:
Login to view the detailed solution.
The half-life period of a first-order reaction is 15 minutes. The amount of substance left after one hour will be:
Login to view the detailed solution.
The form of iron obtained from blast furnace is:
Login to view the detailed solution.
The gas evolved on heating CaF$$_2$$ and SiO$$_2$$ with concentrated H$$_2$$SO$$_4$$, on hydrolysis gives a white gelatinous precipitate. The precipitate is:
Login to view the detailed solution.
Which of the following is not formed when H$$_2$$S reacts with acidic K$$_2$$Cr$$_2$$O$$_7$$ solution?
Login to view the detailed solution.
The correct statement about the magnetic properties of [Fe(CN)$$_6$$]$$^{3-}$$ and [FeF$$_6$$]$$^{3-}$$ is: (Z = 26).
Login to view the detailed solution.
A compound of vanadium chloride has spin only magnetic moment of 1.73 BM. Its formula is:
Login to view the detailed solution.
An octahedral complex of Co$$^{3+}$$ is diamagnetic. The hybridisation involved in the formation of the complex is:
Login to view the detailed solution.
Allyl phenyl ether can be prepared by heating:
Login to view the detailed solution.
For the compounds CH$$_3$$Cl, CH$$_3$$Br, CH$$_3$$I and CH$$_3$$F, the correct order of increasing C-halogen bond length is:
Login to view the detailed solution.
In a nucleophilic substitution reaction: R $$-$$ Br + Cl$$^-$$ $$\xrightarrow{DMF}$$ R $$-$$ Cl + Br$$^-$$, which one of the following undergoes complete inversion of configuration?
Login to view the detailed solution.
In the hydroboration-oxidation reaction of propene with diborane, H$$_2$$O$$_2$$ and NaOH, the organic compound formed is:
Login to view the detailed solution.
Which is the major product formed when acetone is heated with iodine and potassium hydroxide?
Login to view the detailed solution.
Which one of the following reactions will not result in the formation of carbon-carbon bond?
Login to view the detailed solution.
The major product of the reaction is:
Login to view the detailed solution.
Structure of some important polymers are given. Which one represents Buna-S?
Login to view the detailed solution.
Which one of the following class of compounds is obtained by polymerization of acetylene?
Login to view the detailed solution.
If $$\frac{1}{\sqrt{\alpha}}$$, $$\frac{1}{\sqrt{\beta}}$$ are the roots of the equation $$ax^2 + bx + 1 = 0$$, $$(a \neq 0, a, b \in R)$$, then the equation $$x(x + b^3) + (a^3 - 3abx) = 0$$ has roots:
Login to view the detailed solution.
If equations $$ax^2 + bx + c = 0$$, $$(a, b, c \in R, a \neq 0)$$ and $$2x^2 + 3x + 4 = 0$$ have a common root, then $$a : b : c$$ equals:
Login to view the detailed solution.
Let $$w(Im\ w \neq 0)$$ be a complex number. Then, the set of all complex numbers $$z$$ satisfying the equation $$w - \bar{w}z = k(1 - z)$$, for some real number $$k$$, is:
Login to view the detailed solution.
The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is:
Login to view the detailed solution.
Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4$$^{th}$$ term is:
Login to view the detailed solution.
If the sum $$\frac{3}{1^2} + \frac{5}{1^2+2^2} + \frac{7}{1^2+2^2+3^2} + \ldots$$ + up to 20 terms is equal to $$\frac{k}{21}$$, then $$k$$ is equal to:
Login to view the detailed solution.
The number of terms in the expansion of $$(1+x)^{101}(1-x+x^2)^{100}$$ in powers of $$x$$ is:
Login to view the detailed solution.
If $$\operatorname{cosec} \theta = \frac{p+q}{p-q}$$ ($$p \neq q, p \neq 0$$), then $$\left|\cot\left(\frac{\pi}{4} + \frac{\theta}{2}\right)\right|$$ is equals to:
Login to view the detailed solution.
The number of values of $$\alpha$$ in $$[0, 2\pi]$$ for which $$2\sin^3\alpha - 7\sin^2\alpha + 7\sin\alpha = 2$$, is:
Login to view the detailed solution.
Given three points $$P$$, $$Q$$, $$R$$ with $$P(5, 3)$$ and $$R$$ lies on the $$x$$-axis. If the equation of $$RQ$$ is $$x - 2y = 2$$ and $$PQ$$ is parallel to the $$x$$-axis, then the centroid of $$\Delta PQR$$ lies on the line:
Login to view the detailed solution.
Let $$a$$ and $$b$$ be any two numbers satisfying $$\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{4}$$. Then, the foot of perpendicular from the origin on the variable line $$\frac{x}{a} + \frac{y}{b} = 1$$ lies on:
Login to view the detailed solution.
If the point $$(1, 4)$$ lies inside the circle $$x^2 + y^2 - 6x + 10y + p = 0$$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $$p$$ is the interval:
Login to view the detailed solution.
If $$OB$$ is the semi-minor axis of an ellipse, $$F_1$$ and $$F_2$$ are its foci and the angle between $$F_1B$$ and $$F_2B$$ is a right angle, then the square of the eccentricity of the ellipse is:
Login to view the detailed solution.
If $$f(x)$$ is continuous and $$f\left(\frac{9}{2}\right) = \frac{2}{9}$$, then $$\lim_{x \to 0} f\left(\frac{1-\cos 3x}{x^2}\right)$$ equals to:
Login to view the detailed solution.
The contrapositive of the statement "I go to school if it does not rain" is:
In a set of $$2n$$ distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then, the mean of the new set of observations:
Login to view the detailed solution.
Let $$P$$ be the relation defined on the set of all real numbers such that $$P = \{(a, b) : \sec^2 a - \tan^2 b = 1\}$$. Then, $$P$$ is:
Login to view the detailed solution.
If $$B$$ is a $$3 \times 3$$ matrix such that $$B^2 = 0$$, then $$\det[(I + B)^{50} - 50B]$$ is equal to:
Login to view the detailed solution.
If $$a$$, $$b$$, $$c$$ are non-zero real numbers and if the system of equations
$$(a-1)x = y + z$$
$$(b-1)y = x + z$$
$$(c-1)z = x + y$$
has a non-trivial solution, then $$ab + bc + ca$$ equals:
Login to view the detailed solution.
If $$y = e^{nx}$$, then $$\frac{d^2y}{dx^2} \cdot \frac{d^2x}{dy^2}$$ is equal to:
Login to view the detailed solution.
If $$f(x) = \left(\frac{3}{5}\right)^x + \left(\frac{4}{5}\right)^x - 1$$, $$x \in R$$, then the equation $$f(x) = 0$$ has:
Login to view the detailed solution.
If the Rolle's theorem holds for the function $$f(x) = 2x^3 + ax^2 + bx$$ in the interval $$[-1, 1]$$ for the point $$c = \frac{1}{2}$$, then the value of $$2a + b$$ is:
Login to view the detailed solution.
$$\int \frac{\sin^8 x - \cos^8 x}{1 - 2\sin^2 x \cos^2 x} dx$$ is equal to:
Login to view the detailed solution.
The integral $$\int_0^{\frac{1}{2}} \frac{\ln(1+2x)}{1+4x^2} dx$$ equals:
Login to view the detailed solution.
Let $$A = \{(x, y) : y^2 \leq 4x, y - 2x \geq -4\}$$. The area of the region $$A$$ in square units is:
Login to view the detailed solution.
If the differential equation representing the family of all circles touching $$x$$-axis at the origin is $$(x^2 - y^2)\frac{dy}{dx} = g(x)y$$, then $$g(x)$$ equals:
Login to view the detailed solution.
If $$|\vec{a}| = 2$$, $$|\vec{b}| = 3$$ and $$|2\vec{a} - \vec{b}| = 5$$, then $$|2\vec{a} + \vec{b}|$$ equals:
Login to view the detailed solution.
Equation of the plane which passes through the point of intersection of lines $$\frac{x-1}{3} = \frac{y-2}{1} = \frac{z-3}{2}$$ and $$\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{3}$$ and has the largest distance from the origin is:
Login to view the detailed solution.
A line in the 3-dimensional space makes an angle $$\theta$$ ($$0 < \theta \leq \frac{\pi}{2}$$) with both the X and Y-axes. Then, the set of all values of $$\theta$$ is in the interval:
Login to view the detailed solution.
If $$A$$ and $$B$$ are two events such that $$P(A \cup B) = P(A \cap B)$$, then the incorrect statement amongst the following statements is:
Login to view the detailed solution.
Educational materials for JEE preparation
Share