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.
The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1.5% and 1%, respectively, the maximum error in determining the density is:
Login to view the detailed solution.
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Two masses $$m_1 = 5$$ kg and $$m_2 = 10$$ kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of $$m_2$$ to stop the motion is:
.webp)
A particle is moving in a circular path of radius a under the action of an attractive potential $$U = -\frac{k}{2r^2}$$. Its total energy is:
Login to view the detailed solution.
In a collinear collision, a particle with an initial speed $$v_0$$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is:
Login to view the detailed solution.
It is found that if a neutron suffers an elastic collinear collision with a deuterium at rest, the fractional loss of its energy is $$P_d$$, while for its similar collision with a carbon nucleus at rest, the fractional loss of energy is $$P_c$$. The values of $$P_d$$ and $$P_c$$ are respectively:
Login to view the detailed solution.
The mass of a hydrogen molecule is $$3.32 \times 10^{-27}$$ kg. If $$10^{23}$$ hydrogen molecules strike, per second, a fixed wall of the area 2 cm$$^2$$ at an angle of 45$$^\circ$$ to the normal, and rebound elastically with a speed of $$10^3$$ m s$$^{-1}$$, then the pressure on the wall is nearly:
Login to view the detailed solution.
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:
From a uniform circular disc of radius R and mass 9 M, a small disc of radius $$\frac{R}{3}$$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $$n^{th}$$ power of R. If the period of rotation of the particle is T, then:
Login to view the detailed solution.
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $$\left(\frac{dr}{r}\right)$$, is:
Login to view the detailed solution.
Two moles of an ideal monoatomic gas occupies a volume V at 27$$^\circ$$C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.
Login to view the detailed solution.
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $$10^{12}$$ s$$^{-1}$$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 g mol$$^{-1}$$ and Avogadro number = $$6.02 \times 10^{23}$$)
Login to view the detailed solution.
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $$2.7 \times 10^3$$ kg m$$^{-3}$$ and its Young's modulus is $$9.27 \times 10^{10}$$ Pa. What will be the fundamental frequency of the longitudinal vibrations?
Login to view the detailed solution.
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$+\sigma$$, $$-\sigma$$ and $$+\sigma$$ respectively. The potential of shell B is:
Login to view the detailed solution.
A parallel plate capacitor of capacitance 90 pF is connected to a battery of EMF 20 V. If a dielectric material of dielectric constant $$K = \frac{5}{3}$$ is inserted between the plates, the magnitude of the induced charge will be:
Login to view the detailed solution.
Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10 $$\Omega$$. The internal resistance of the two batteries are 1 $$\Omega$$ and 2 $$\Omega$$ respectively. The voltage across the load lies between,
Login to view the detailed solution.
On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega$$. How much was the resistance on the left slot before interchanging the resistances?
Login to view the detailed solution.
In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 $$\Omega$$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.
Login to view the detailed solution.
The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $$B_1$$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $$B_2$$. The ratio $$\frac{B_1}{B_2}$$ is:
Login to view the detailed solution.
An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $$r_e$$, $$r_p$$, $$r_\alpha$$ respectively in a uniform magnetic field B. The relation between $$r_e$$, $$r_p$$, $$r_\alpha$$ is:
Login to view the detailed solution.
For an RLC circuit driven with voltage of amplitude $$v_m$$ and frequency $$\omega_0 = \frac{1}{\sqrt{LC}}$$, the current exhibits resonance. The quality factor, Q is given by:
Login to view the detailed solution.
In an A.C. circuit, the instantaneous e.m.f. and current are given by, $$E = 100 \sin 30t$$, $$I = 20 \sin\left(30t - \frac{\pi}{4}\right)$$. In one cycle of A.C., the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively:
Login to view the detailed solution.
An EM wave from air enters a medium. The electric fields are $$\vec{E_1} = E_{01}\hat{x}\cos\left[2\pi\nu\left(\frac{z}{c} - t\right)\right]$$ in air and $$\vec{E_2} = E_{02}\hat{x}\cos[k(2z - ct)]$$ in medium, where the wave number k and frequency $$\nu$$ refer to their values in the air. The medium is non-magnetic. If $$\epsilon_{r_1}$$ and $$\epsilon_{r_2}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct?
Login to view the detailed solution.
Unpolarized light of intensity I passes through an ideal polariser A. Another identical polariser B is placed behind A. The intensity of light beyond B is found to be $$\frac{I}{2}$$. Now another identical polariser C is placed between A and B. The intensity beyond B is now found to be $$\frac{I}{8}$$. The angle between polariser A and C is:
Login to view the detailed solution.
The angular width of the central maximum in a single slit diffraction pattern is 60$$^\circ$$. The width of the slit is 1 $$\mu$$m. The slit is illuminated by monochromatic plane waves. If another slit of the same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e., the distance between the centres of each slit.)
Login to view the detailed solution.
An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $$\lambda_n$$, $$\lambda_g$$ be the de Broglie wavelength of the electron in the $$n^{th}$$ state and the ground state respectively. Let $$\Lambda_n$$ be the wavelength of the emitted photon in the transition from the $$n^{th}$$ state to the ground state. For large n, (A, B are constants)
Login to view the detailed solution.
If the series limit frequency of the Lyman series is $$V_L$$, then the series limit frequency of the Pfund series is:
Login to view the detailed solution.
The reading of the ammeter for a silicon diode in the given circuit is:
A telephonic communication service is working at a carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?
Login to view the detailed solution.
The ratio of mass percent of C and H of an organic compound ($$C_XH_YO_Z$$) is 6 : 1. If one molecule of the above compound ($$C_XH_YO_Z$$) contains half as much oxygen as required to burn one molecule of compound $$C_XH_Y$$ completely to $$CO_2$$ and $$H_2O$$. The empirical formula of the compound $$C_XH_YO_Z$$ is:
Login to view the detailed solution.
According to molecular orbital theory, which of the following molecule will not be available?
Login to view the detailed solution.
Which of the following compounds contain(s) no covalent bond(s)?
KCl, PH$$_3$$, O$$_2$$, B$$_2$$H$$_6$$, H$$_2$$SO$$_4$$
Login to view the detailed solution.
Total number of lone pair of electrons in I$$_3^-$$ ion is:
Login to view the detailed solution.
The combustion of benzene (l) gives CO$$_2$$(g) and H$$_2$$O(l). Given that heat of combustion of benzene at constant volume is $$-3263.9$$ kJ mol$$^{-1}$$ at 25$$^\circ$$C; the heat of combustion (in kJ mol$$^{-1}$$) of benzene at constant pressure will be:
(R = 8.314 JK$$^{-1}$$ mol$$^{-1}$$)
Login to view the detailed solution.
Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction?
An aqueous solution contains 0.10 M H$$_2$$S and 0.20 M HCl. If the equilibrium constant for the formation of HS$$^-$$ from H$$_2$$S is $$1.0 \times 10^{-7}$$ and that of S$$^{2-}$$ from HS$$^-$$ ions is $$1.2 \times 10^{-13}$$, then the concentration of S$$^{2-}$$ ions in the aqueous solution is:
Login to view the detailed solution.
An aqueous solution contains an unknown concentration of Ba$$^{2+}$$. When 50 mL of a 1 M solution of Na$$_2$$SO$$_4$$ is added, BaSO$$_4$$ just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO$$_4$$ is $$1 \times 10^{-10}$$. What is the original concentration of Ba$$^{2+}$$?
Login to view the detailed solution.
Which of the following are Lewis acids?
Login to view the detailed solution.
Which of the following salts is the most basic in aqueous solution?
Login to view the detailed solution.
An alkali is titrated against acid with methyl orange as an indicator, which of the following is a correct combination?
Login to view the detailed solution.
Hydrogen peroxide oxidises [Fe(CN)$$_6$$]$$^{4-}$$ to [Fe(CN)$$_6$$]$$^{3-}$$ in acidic medium, but reduces [Fe(CN)$$_6$$]$$^{3-}$$ to [Fe(CN)$$_6$$]$$^{4-}$$ in alkaline medium. The other products formed are, respectively:
Login to view the detailed solution.
When metal M is treated with NaOH, a white gelatinous precipitate X is obtained, which is soluble in excess of NaOH. Compound X when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal M is:
Login to view the detailed solution.
Which of the following compounds will be suitable for Kjeldahl's method for nitrogen estimation?
The trans-alkenes are formed by the reduction of alkynes with:
Login to view the detailed solution.
The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting [3Ca$$_3$$(PO$$_4$$)$$_2$$.Ca(OH)$$_2$$] to:
Login to view the detailed solution.
Which type of 'defect' has the presence of cations in the interstitial sites?
Login to view the detailed solution.
For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?
Login to view the detailed solution.
How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B = 10.8 u)
Login to view the detailed solution.
At 518$$^\circ$$C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr was 1.00 Torr s$$^{-1}$$ when 5% had reacted and 0.50 Torr s$$^{-1}$$ when 33% had reacted. The order of the reaction is:
Login to view the detailed solution.
The compound that does not produce nitrogen gas by thermal decomposition is:
Login to view the detailed solution.
Consider the following reaction and statements:
$$[Co(NH_3)_4Br_2]^+ + Br^- \rightarrow [Co(NH_3)_3Br_3] + NH_3$$
(i) Two isomers are produced if the reactant complex ion is a cis-isomer.
(ii) Two isomers are produced if the reactant complex ion is a trans-isomer.
(iii) Only one isomer is produced if the reactant complex ion is a trans-isomer.
(iv) Only one isomer is produced if the reactant complex ion is a cis-isomer.
The correct statements are:
Login to view the detailed solution.
The oxidation states of Cr in [Cr(H$$_2$$O)$$_6$$]Cl$$_3$$, [Cr(C$$_6$$H$$_6$$)$$_2$$] and K$$_2$$[Cr(CN)$$_2$$(O)$$_2$$(O$$_2$$)(NH$$_3$$)], respectively, are:
Login to view the detailed solution.
The major product of the following reaction is:
Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br$$_2$$ to form product B. A and B are respectively:
The major product formed in the following reaction is:
Phenol on treatment with $$CO_2$$ in the presence of NaOH followed by acidification produces compound X as the major product. X on treatment with $$(CH_3CO)_2O$$ in the presence of catalytic amount of $$H_2SO_4$$ produces:
The increasing order of basicity of the following compounds is:
Glucose on prolonged heating with HI gives:
Login to view the detailed solution.
The predominant form of histamine present in human blood is (pK$$_a$$, Histidine = 6.0):
Let $$S = \{x \in R : x \geq 0$$ & $$2|\sqrt{x} - 3| + \sqrt{x}(\sqrt{x} - 6) + 6 = 0\}$$. Then S:
Login to view the detailed solution.
If $$\alpha, \beta \in C$$ are the distinct roots of the equation $$x^2 - x + 1 = 0$$, then $$\alpha^{101} + \beta^{107}$$ is equal to:
Login to view the detailed solution.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
Login to view the detailed solution.
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series $$1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \ldots$$ If $$B - 2A = 100\lambda$$, then $$\lambda$$ is equal to:
Login to view the detailed solution.
Let $$a_1, a_2, a_3, \ldots, a_{49}$$ be in A.P. such that $$\sum_{k=0}^{12} a_{4k+1} = 416$$ and $$a_9 + a_{43} = 66$$. If $$a_1^2 + a_2^2 + \ldots + a_{17}^2 = 140m$$, then m is equal to:
Login to view the detailed solution.
The sum of the co-efficient of all odd degree terms in the expansion of $$\left(x + \sqrt{x^3 - 1}\right)^5 + \left(x - \sqrt{x^3 - 1}\right)^5$$, $$(x > 1)$$ is:
Login to view the detailed solution.
If sum of all the solutions of the equation $$8\cos x \cdot \left(\cos\left(\frac{\pi}{6} + x\right) \cdot \cos\left(\frac{\pi}{6} - x\right) - \frac{1}{2}\right) = 1$$ in $$[0, \pi]$$ is $$k\pi$$, then k is equal to:
Login to view the detailed solution.
A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is:
Login to view the detailed solution.
If the tangent at (1, 7) to the curve $$x^2 = y - 6$$ touches the circle $$x^2 + y^2 + 16x + 12y + c = 0$$ then the value of c is:
Login to view the detailed solution.
Tangent and normal are drawn at P(16, 16) on the parabola $$y^2 = 16x$$, which intersect the axis of the parabola at A & B, respectively. If C is the center of the circle through the points P, A & B and $$\angle CPB = \theta$$, then a value of $$\tan \theta$$ is:
Login to view the detailed solution.
Two sets A and B are as under: $$A = \{(a, b) \in R \times R : |a - 5| < 1$$ and $$|b - 5| < 1\}$$; $$B = \{(a, b) \in R \times R : 4(a - 6)^2 + 9(b - 5)^2 \leq 36\}$$. Then:
Login to view the detailed solution.
Tangents are drawn to the hyperbola $$4x^2 - y^2 = 36$$ at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\triangle PTQ$$ is:
Login to view the detailed solution.
For each $$t \in R$$, let $$[t]$$ be the greatest integer less than or equal to t. Then $$\lim_{x \to 0^+} x\left(\left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] + \ldots + \left[\frac{15}{x}\right]\right)$$
Login to view the detailed solution.
The Boolean expression $$\sim(p \vee q) \vee (\sim p \wedge q)$$ is equivalent to:
Login to view the detailed solution.
If $$\sum_{i=1}^{9}(x_i - 5) = 9$$ and $$\sum_{i=1}^{9}(x_i - 5)^2 = 45$$, then the standard deviation of the 9 items $$x_1, x_2, \ldots, x_9$$ is:
Login to view the detailed solution.
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45$$^\circ$$, 30$$^\circ$$ and 30$$^\circ$$, then the height of the tower (in m) is:
Login to view the detailed solution.
Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is:
Login to view the detailed solution.
If the system of linear equations
$$x + ky + 3z = 0$$
$$3x + ky - 2z = 0$$
$$2x + 4y - 3z = 0$$
has a non-zero solution (x, y, z), then $$\frac{xz}{y^2}$$ is equal to:
Login to view the detailed solution.
If $$\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix} = (A + Bx)(x - A)^2$$, then the ordered pair (A, B) is equal to:
Login to view the detailed solution.
Let $$S = \{t \in R : f(x) = |x - \pi| \cdot (e^{|x|} - 1)\sin|x|$$ is not differentiable at $$t\}$$. Then the set S is equal to:
Login to view the detailed solution.
If the curves $$y^2 = 6x$$, $$9x^2 + by^2 = 16$$ intersect each other at right angles, then the value of b is:
Login to view the detailed solution.
Let $$f(x) = x^2 + \frac{1}{x^2}$$ and $$g(x) = x - \frac{1}{x}$$, $$x \in R - \{-1, 0, 1\}$$. If $$h(x) = \frac{f(x)}{g(x)}$$, then the local minimum value of h(x) is:
Login to view the detailed solution.
The integral $$\int \frac{\sin^2 x \cos^2 x}{(\sin^5 x + \cos^3 x \sin^2 x + \sin^3 x \cos^2 x + \cos^5 x)^2} dx$$ is equal to
(where C is the constant of integration).
Login to view the detailed solution.
The value of $$\int_{-\pi/2}^{\pi/2} \frac{\sin^2 x}{1+2^x} dx$$ is:
Login to view the detailed solution.
Let $$g(x) = \cos x^2$$, $$f(x) = \sqrt{x}$$, and $$\alpha, \beta (\alpha < \beta)$$ be the roots of the quadratic equation $$18x^2 - 9\pi x + \pi^2 = 0$$. Then the area (in sq. units) bounded by the curve $$y = (gof)(x)$$ and the lines $$x = \alpha$$, $$x = \beta$$ and $$y = 0$$, is:
Login to view the detailed solution.
Let $$y = y(x)$$ be the solution of the differential equation $$\sin x \frac{dy}{dx} + y \cos x = 4x$$, $$x \in (0, \pi)$$. If $$y\left(\frac{\pi}{2}\right) = 0$$, then $$y\left(\frac{\pi}{6}\right)$$ is equal to:
Login to view the detailed solution.
Let $$\vec{u}$$ be a vector coplanar with the vectors $$\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$$ and $$\vec{b} = \hat{j} + \hat{k}$$. If $$\vec{u}$$ is perpendicular to $$\vec{a}$$ and $$\vec{u} \cdot \vec{b} = 24$$, then $$|\vec{u}|^2$$ is equal to:
Login to view the detailed solution.
If $$L_1$$ is the line of intersection of the planes $$2x - 2y + 3z - 2 = 0$$, $$x - y + z + 1 = 0$$ and $$L_2$$ is the line of intersection of the planes $$x + 2y - z - 3 = 0$$, $$3x - y + 2z - 1 = 0$$, then the distance of the origin from the plane, containing the lines $$L_1$$ and $$L_2$$ is:
Login to view the detailed solution.
The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, $$x + y + z = 7$$ is:
Login to view the detailed solution.
A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:
Login to view the detailed solution.
Educational materials for JEE preparation
Share