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 student determined Young's Modulus of elasticity using the formula $$Y = \frac{Mgl^3}{4bd^3\delta}$$. The value of $$g$$ is taken to be 9.8 m s$$^{-2}$$ without any significant error, his observations are as following.
Then the fractional error in the measurement of $$Y$$ is:
Login to view the detailed solution.
An object of mass $$m$$ is being moved with a constant velocity under the action of an applied force of 2 N along a frictionless surface with following surface profile.
The correct applied force vs distance graph will be:
Login to view the detailed solution.
The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are $$R_1$$, $$R_2$$ and $$H_1$$, $$H_2$$ respectively. Choose the correct option:
Login to view the detailed solution.
.webp)
A block of mass $$m$$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is:
Given $$m = 8$$ kg, $$M = 16$$ kg
Assume all the surfaces shown in the figure to be frictionless.
Login to view the detailed solution.
A body of mass $$m$$ dropped from a height $$h$$ reaches the ground with a speed of $$0.8\sqrt{gh}$$. The value of work done by the air-friction is:
Login to view the detailed solution.
Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by $$E = 20\cos(2 \times 10^{10}t - 200x)$$ V m$$^{-1}$$. The dielectric constant of the medium is equal to: (Take $$\mu_r = 1$$)
Login to view the detailed solution.
Four particles each of mass $$M$$, move along a circle of radius $$R$$ under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:
Login to view the detailed solution.
A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($$\mu = \frac{4}{3}$$) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?
Login to view the detailed solution.
Due to cold weather, a 1 m water pipe of cross-sectional area 1 cm$$^2$$ is filled with ice at -10°C. Resistive heating is used to melt the ice. Current of 0.5 A is passed through 4 k$$\Omega$$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?
(Given latent heat of fusion for water/ice = $$3.33 \times 10^5$$ J kg$$^{-1}$$, specific heat of ice = $$2 \times 10^3$$ J kg$$^{-1}$$ °C$$^{-1}$$ and density of ice = $$10^3$$ kg m$$^{-3}$$)
Login to view the detailed solution.
A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?
Login to view the detailed solution.
A cube is placed inside an electric field, $$\vec{E} = 150y^2\hat{j}$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is:
Login to view the detailed solution.
A capacitor is connected to a 20 V battery through a resistance of 10$$\Omega$$. It is found that the potential difference across the capacitor rises to 2 V in 1 $$\mu$$s. The capacitance of the capacitor is _________ $$\mu$$F.
Given $$\ln\frac{10}{9} = 0.105$$
Login to view the detailed solution.
Two resistors $$R_1 = (4 \pm 0.8)$$ $$\Omega$$ and $$R_2 = (4 \pm 0.4)$$ $$\Omega$$ are connected in parallel. The equivalent resistance of their parallel combination will be:
Login to view the detailed solution.
Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility ($$\chi$$) vs Temperature (T) graph:
Which of the following combination will be represented by a diamagnetic material?
Login to view the detailed solution.
For the given circuit the current $$i$$ through the battery when the key is closed and the steady state has been reached is:
Login to view the detailed solution.
A square loop of side 20 cm and resistance 1 $$\Omega$$ is moved towards right with a constant speed $$v_0$$. The right arm of the loop is in a uniform magnetic field of 5 T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4$$\Omega$$. What should be the value of $$v_0$$ so that a steady current of 2 mA flows in the loop?
Login to view the detailed solution.
There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is 1:1. The magnetic field at point P is:
Login to view the detailed solution.
The temperature of an ideal gas in three dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K is:
$$m_e$$ = mass of electron = $$9 \times 10^{-31}$$ kg, $$h$$ = Planck constant = $$6.6 \times 10^{-34}$$ J s, $$k_B$$ = Boltzmann constant = $$1.38 \times 10^{-23}$$ J K$$^{-1}$$
Login to view the detailed solution.
The half life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$. Initially they have the same number of atoms. Then:
Login to view the detailed solution.
In the given figure, each diode has a forward bias resistance of 30 $$\Omega$$ and infinite resistance in reverse bias. The current $$I_1$$ will be:
Login to view the detailed solution.
The average translational kinetic energy of $$N_2$$ gas molecules at _________ °C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt.
(Given $$k_B = 1.38 \times 10^{-23}$$ J K$$^{-1}$$) (Fill the nearest integer).
Login to view the detailed solution.
An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 km h$$^{-1}$$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is _________ $$\times 10^5$$ N m$$^{-1}$$.
Login to view the detailed solution.
When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time $$T$$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha T$$, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $$\frac{1}{\sqrt{x}} \cdot \frac{\alpha^2-1}{\alpha^2}$$ where $$x$$ = _________.
Login to view the detailed solution.
A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in the vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of the rod when it passes through its lowest position is _________ m s$$^{-1}$$.
(Take $$g = 10$$ m s$$^{-2}$$)
Login to view the detailed solution.
The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is $$x : 4$$ where $$x$$ is _________.
Login to view the detailed solution.
A uniform heating wire of resistance 36 $$\Omega$$ is connected across a potential difference of 240 V. The wire is then cut into half and a potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : $$x$$, where $$x$$ is _________.
Login to view the detailed solution.
A steel rod with $$y = 2.0 \times 10^{11}$$ N m$$^{-2}$$ and $$\alpha = 10^{-5}$$ °C$$^{-1}$$ of length 4 m and area of cross-section 10 cm$$^2$$ is heated from 0°C to 400°C without being allowed to extend. The tension produced in the rod is $$x \times 10^5$$ N where the value of $$x$$ is _________.
Login to view the detailed solution.
The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0°C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $$\frac{x}{10}$$. Then the value of $$x$$ (round off to the nearest integer) is _________.
(Given R = 8.31 J $$mol^{-1}$$ $$K^{-1}$$)
Login to view the detailed solution.
Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is $$2 \times 10^3$$ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $$\frac{\pi}{x}$$ rad h$$^{-1}$$, where $$x$$ is _________.
Login to view the detailed solution.
A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150 V. The ratio of minimum amplitude to maximum amplitude for the amplitude modulated wave is 50 : $$x$$, then value of $$x$$, is _________.
Login to view the detailed solution.
Number of paramagnetic oxides among the following given oxides is _________.
Li$$_2$$O, CaO, Na$$_2$$O$$_2$$, KO$$_2$$, MgO and K$$_2$$O
Login to view the detailed solution.
Hydrogen peroxide reacts with iodine in basic medium to give:
Login to view the detailed solution.
The potassium ferrocyanide solution gives a Prussian blue colour, when added to:
Login to view the detailed solution.
Which one of the following compounds is aromatic in nature?
The stereoisomers that are formed by electrophilic addition of bromine to trans-but-2-ene is/are:
Login to view the detailed solution.
In the following sequence of reactions, C$$_3$$H$$_6$$ $$\xrightarrow{H^+/H_2O}$$ A $$\xrightarrow[dil KOH]{KIO}$$ B + C. The compounds B and C respectively are:
Login to view the detailed solution.
Water sample is called cleanest on the basis of which one of the BOD values given below:
Login to view the detailed solution.
Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic reaction?
Login to view the detailed solution.
Match List - I with List - II.
List-I (Colloid Preparation Method) List-II (Chemical Reaction)
(a) Hydrolysis (i) 2AuCl$$_3$$ + 3HCHO + 3H$$_2$$O $$\rightarrow$$ 2Au(sol) + 3HCOOH + 6HCl
(b) Reduction (ii) As$$_2$$O$$_3$$ + 3H$$_2$$S $$\rightarrow$$ As$$_2$$S$$_3$$(sol) + 3H$$_2$$O
(c) Oxidation (iii) SO$$_2$$ + 2H$$_2$$S $$\rightarrow$$ 3S(sol) + 2H$$_2$$O
(d) Double Decomposition (iv) FeCl$$_3$$ + 3H$$_2$$O $$\rightarrow$$ Fe(OH)$$_3$$(sol) + 3HCl
Choose the most appropriate answer from the options given below:
Login to view the detailed solution.
Calamine and Malachite, respectively, are the ores of:
Login to view the detailed solution.
The oxide without nitrogen-nitrogen bond is:
Login to view the detailed solution.
In the given chemical reaction, colors of the Fe$$^{2+}$$ and Fe$$^{3+}$$ ions, are respectively:
$$5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}$$
Login to view the detailed solution.
Identify the element for which electronic configuration in +3 oxidation state is [Ar]3d$$^5$$:
Login to view the detailed solution.
The Crystal Field Stabilization Energy (CFSE) and magnetic moment (spin-only) of an octahedral aqua complex of a metal ion M$$^{Z+}$$ are $$-0.8\Delta_0$$ and 3.87 BM, respectively. Identify M$$^{Z+}$$:
Login to view the detailed solution.
Experimentally reducing a functional group cannot be done by which one of the following reagents?
Login to view the detailed solution.
Given below are two statements:
Statement I : The nucleophilic addition of sodium hydrogen sulphite to an aldehyde or a ketone involves proton transfer to form a stable ion.
Statement II : The nucleophilic addition of hydrogen cyanide to an aldehyde or a ketone yields amine as final product.
In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
In the following sequence of reactions a compound A, (molecular formula C$$_6$$H$$_{12}$$O$$_2$$) with a straight chain structure gives a C$$_4$$ carboxylic acid. A is:
$$A \xrightarrow[\mathrm{H_3O^+}]{\mathrm{LiAlH_4}} B \xrightarrow{\text{Oxidation}} \text{C}_4\text{-carboxylic acid}$$
Login to view the detailed solution.
Which one of the following gives the most stable Diazonium salt?
Login to view the detailed solution.
Identify A in the following reaction.
Login to view the detailed solution.
Monomer units of Dacron polymer are:
Login to view the detailed solution.
The number of atoms in 8 g of sodium is $$x \times 10^{23}$$. The value of x is _________. (Nearest integer)
Given: N$$_A$$ = $$6.02 \times 10^{23}$$ mol$$^{-1}$$, Atomic mass of Na = 23.0 u
Login to view the detailed solution.
A 50 watt bulb emits monochromatic red light of wavelength of 795 nm. The number of photons emitted per second by the bulb is $$x \times 10^{20}$$. The value of x is _________. (Nearest integer)
[Given: h = $$6.63 \times 10^{-34}$$ Js and c = $$3.0 \times 10^8$$ ms$$^{-1}$$]
Login to view the detailed solution.
The spin-only magnetic moment value of B$$_2^+$$ species is _________ $$\times 10^{-2}$$ BM (Nearest integer)
[Given: $$\sqrt{3}$$ = 1.73]
Login to view the detailed solution.
An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm. In the course of use at ambient temperature, the mass of the cylinder is reduced to 23.0 kg. The final pressure inside the cylinder is _________ atm. (Nearest integer)
(Assume LPG to be an ideal gas)
Login to view the detailed solution.
For the reaction 2NO$$_2$$(g) $$\rightleftharpoons$$ N$$_2$$O$$_4$$(g), when $$\Delta S = -176.0$$ J K$$^{-1}$$ and $$\Delta H = -57.8$$ kJ mol$$^{-1}$$ the magnitude of $$\Delta G$$ at 298 K for the reaction is _________ kJ mol$$^{-1}$$. (Nearest integer)
Login to view the detailed solution.
The molar solubility of Zn(OH)$$_2$$ in 0.1M NaOH solution is $$x \times 10^{-18}$$ M. The value of x is _________. (Nearest integer)
Given: The solubility product of Zn(OH)$$_2$$ is $$2 \times 10^{-20}$$
Login to view the detailed solution.
If 80 g of copper sulphate CuSO$$_4$$.5H$$_2$$O is dissolved in deionised water to make 5 L of solution. The concentration of the copper sulphate solution is $$x \times 10^{-3}$$ mol $$L^{-1}$$. The value of x is _________.
[Atomic masses Cu : 63.54u, S : 32u, O : 16u, H : 1u]
Login to view the detailed solution.
If the conductivity of mercury at 0°C is $$1.07 \times 10^6$$ S m$$^{-1}$$ and the resistance of a cell containing mercury is 0.243$$\Omega$$, then the cell constant of the cell is $$x \times 10^4$$ m$$^{-1}$$. The value of x is _________. (Nearest integer)
Login to view the detailed solution.
The sum of oxidation states of two silver ions in[Ag(NH₃)₂]⁺ and [Ag(CN)₂]⁻ complex is _________.
Login to view the detailed solution.
A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have _________ peptide linkages.
Login to view the detailed solution.
The number of pairs $$a, b$$ of real numbers, such that whenever $$\alpha$$ is a root of the equation $$x^2 + ax + b = 0$$, $$\alpha^2 - 2$$ is also a root of this equation, is:
Login to view the detailed solution.
Let $$P_1, P_2, \ldots, P_{15}$$ be 15 points on a circle. The number of distinct triangles formed by points $$P_i, P_j, P_k$$ such that $$i + j + k \neq 15$$, is:
Login to view the detailed solution.
Let $$S_n = 1 \cdot (n-1) + 2 \cdot (n-2) + 3 \cdot (n-3) + \ldots + (n-1) \cdot 1$$, $$n \geq 4$$.
The sum $$\sum_{n=4}^{\infty} \frac{2 S_n}{n!} - \frac{1}{(n-2)!}$$ is equal to:
Login to view the detailed solution.
Let $$a_1, a_2, \ldots, a_{21}$$ be an A.P. such that $$\sum_{n=1}^{20} \frac{1}{a_n a_{n+1}} = \frac{4}{9}$$. If the sum of this A.P. is 189, then $$a_6 a_{16}$$ is equal to:
Login to view the detailed solution.
If $$n$$ is the number of solutions of the equation $$2\cos x \cdot 4\sin\frac{\pi}{4} + x\sin\frac{\pi}{4} - x - 1 = 1$$, $$x \in [0, \pi]$$ and $$S$$ is the sum of all these solutions, then the ordered pair $$(n, S)$$ is:
Login to view the detailed solution.
Consider the parabola with vertex $$\left(\frac{1}{2}, \frac{3}{4}\right)$$ and the directrix $$y = \frac{1}{2}$$. Let P be the point where the parabola meets the line $$x = -\frac{1}{2}$$. If the normal to the parabola at P intersects the parabola again at the point Q, then $$(PQ)^2$$ is equal to:
Login to view the detailed solution.
Let $$\theta$$ be the acute angle between the tangents to the ellipse $$\frac{x^2}{9} + \frac{y^2}{1} = 1$$ and the circle $$x^2 + y^2 = 3$$ at their point of intersection in the first quadrant. Then $$\tan\theta$$ is equal to:
Login to view the detailed solution.
Which of the following is equivalent to the Boolean expression $$p \wedge \sim q$$?
Login to view the detailed solution.
Consider the system of linear equations
$$-x + y + 2z = 0$$
$$3x - ay + 5z = 1$$
$$2x - 2y - az = 7$$
Let $$S_1$$ be the set of all $$a \in R$$ for which the system is inconsistent and $$S_2$$ be the set of all $$a \in R$$ for which the system has infinitely many solutions. If $$nS_1$$ and $$nS_2$$ denote the number of elements in $$S_1$$ and $$S_2$$ respectively, then
Login to view the detailed solution.
$$\cos^{-1}(\cos(-5)) + \sin^{-1}(\sin(6)) - \tan^{-1}(\tan(12))$$ is equal to:
(The inverse trigonometric functions take the principal values)
Login to view the detailed solution.
Find the range of
$$f(x)=\log_{\sqrt5}\left(3+\cos\left(\frac{3\pi}{4}+x\right)+\cos\left(\frac{\pi}{4}+x\right)-\cos\left(\frac{\pi}{4}-x\right)-\cos\left(\frac{3\pi}{4}-x\right)\right).$$
Login to view the detailed solution.
The function $$f(x) = x^3 - 6x^2 + ax + b$$ is such that $$f(2) = f(4) = 0$$. Consider two statements:
$$S_1$$: there exists $$x_1, x_2 \in (2, 4)$$, $$x_1 \lt x_2$$, such that $$f'(x_1) = -1$$ and $$f'(x_2) = 0$$.
$$S_2$$: there exists $$x_3, x_4 \in (2, 4)$$, $$x_3 \lt x_4$$, such that $$f$$ is decreasing in $$(2, x_4)$$, increasing in $$(x_4, 4)$$ and $$2f'(x_3) = \sqrt{3}f(x_4)$$. Then
Login to view the detailed solution.
Let $$f : R \rightarrow R$$ be a continuous function. Then $$\lim_{x \to \pi/4} \frac{\frac{\pi}{4}\int_2^{\sec^2 x} f(x) dx}{x^2 - \frac{\pi^2}{16}}$$ is equal to:
Login to view the detailed solution.
Let $$I_{n,m} = \int_0^{1/2} \frac{x^n}{x^m-1} dx$$, $$\forall n > m$$ and $$n, m \in N$$. Consider a matrix $$A = a_{ij_{3 \times 3}}$$ where $$a_{ij} = \begin{cases} I_{6+i,3} - I_{i+3,3}, & i \leq j \\ 0, & i > j \end{cases}$$. Then adj $$A^{-1}$$ is:
Login to view the detailed solution.
The function $$f(x)$$, that satisfies the condition $$f(x) = x + \int_0^{\pi/2} \sin x \cos y f(y) dy$$, is:
Login to view the detailed solution.
The area, enclosed by the curves $$y = \sin x + \cos x$$ and $$y = |\cos x - \sin x|$$ and the lines $$x = 0$$, $$x = \frac{\pi}{2}$$, is:
Login to view the detailed solution.
If $$y = y(x)$$ is the solution curve of the differential equation $$x^2 dy + (y - \frac{1}{x}) dx = 0$$; $$x > 0$$ and $$y(1) = 1$$, then $$y\left(\frac{1}{2}\right)$$ is equal to:
Login to view the detailed solution.
The distance of line $$3y - 2z - 1 = 0 = 3x - z + 4$$ from the point $$(2, -1, 6)$$ is:
Login to view the detailed solution.
Let the acute angle bisector of the two planes $$x - 2y - 2z + 1 = 0$$ and $$2x - 3y - 6z + 1 = 0$$ be the plane P. Then which of the following points lies on P?
Login to view the detailed solution.
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is:
Login to view the detailed solution.
If for the complex numbers $$z$$ satisfying $$|z - 2 - 2i| \leq 1$$, the maximum value of $$|3iz + 6|$$ is attained at $$a + ib$$, then $$a + b$$ is equal to _________.
Login to view the detailed solution.
All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is _________.
Login to view the detailed solution.
If the sum of the coefficients in the expansion of $$(x + y)^n$$ is 4096, then the greatest coefficient in the expansion is _________.
Login to view the detailed solution.
Let the points of intersections of the lines $$x - y + 1 = 0$$, $$x - 2y + 3 = 0$$ and $$2x - 5y + 11 = 0$$ are the mid points of the sides of a triangle ABC. Then the area of the triangle ABC is _________.
Login to view the detailed solution.
A man starts walking from the point $$P(-3, 4)$$, touches the x-axis at $$R$$, and then turns to reach at the point $$Q(0, 2)$$. The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $$50[(PR)^2 + (RQ)^2]$$ is equal to _________.
Login to view the detailed solution.
Let $$f(x) = x^6 + 2x^4 + x^3 + 2x + 3$$, $$x \in R$$. Then the natural number $$n$$ for which $$\lim_{x \to 1} \frac{x^n f(1) - f(x)}{x - 1} = 44$$ is _________.
Login to view the detailed solution.
Let $$f(x)$$ be a polynomial of degree 3 such that $$f(k) = -\frac{2}{k}$$ for $$k = 2, 3, 4, 5$$. Then the value of $$52 - 10 f(10)$$ is equal to _________.
Login to view the detailed solution.
Let $$[t]$$ denote the greatest integer $$\leq t$$. The number of points where the function $$f(x) = [x]|x^2 - 1| + \sin\frac{\pi}{[x]+3} - [x+1]$$, $$x \in (-2, 2)$$ is not continuous is _________.
Login to view the detailed solution.
Let $$\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k}$$ and $$\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$$. Let a vector $$\vec{v}$$ be in the plane containing $$\vec{a}$$ and $$\vec{b}$$. If $$\vec{v}$$ is perpendicular to the vector $$3\hat{i} + 2\hat{j} - \hat{k}$$ and its projection on $$\vec{a}$$ is 19 units, then $$|2\vec{v}|^2$$ is equal to _________.
Login to view the detailed solution.
Let $$X$$ be a random variable with distribution.
If the mean of $$X$$ is 2.3 and variance of $$X$$ is $$\sigma^2$$, then $$100\sigma^2$$ is equal to _________.
Login to view the detailed solution.
Educational materials for JEE preparation
Share