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.
Login to view the detailed solution.
Motion of a particle in $$x-y$$ plane is described by a set of following equations $$x = 4\sin\left(\frac{\pi}{2} - \omega t\right)$$ m and $$y = 4\sin(\omega t)$$ m. The path of the particle will be
Login to view the detailed solution.
A particle of mass $$m$$ is moving in a circular path of constant radius $$r$$ such that its centripetal acceleration $$a_c$$ is varying with time $$t$$ as $$a_c = k^2rt^2$$, where $$k$$ is a constant. The power delivered to the particle by the force acting on it is
Login to view the detailed solution.
.webp)
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) M.I. of solid sphere of radius R about any tangent. | (I) $$\frac{5}{3}MR^2$$ |
| (B) M.I. of hollow sphere of radius R about any tangent. | (II) $$\frac{7}{5}MR^2$$ |
| (C) M.I. of circular ring of radius R about its diameter. | (III) $$\frac{1}{4}MR^2$$ |
| (D) M.I. of circular disc of radius R about any diameter. | (IV) $$\frac{1}{2}MR^2$$ |
Login to view the detailed solution.
Two planets $$A$$ and $$B$$ of equal mass are having their period of revolutions $$T_A$$ and $$T_B$$ such that $$T_A = 2T_B$$. These planets are revolving in the circular orbits of radii $$r_A$$ and $$r_B$$ respectively. Which out of the following would be the correct relationship of their orbits?
Login to view the detailed solution.
A water drop of diameter $$2$$ cm is broken into $$64$$ equal droplets. The surface tension of water is $$0.075$$ N m$$^{-1}$$. In this process the gain in surface energy will be
Login to view the detailed solution.
Login to view the detailed solution.
A radar sends an electromagnetic signal of electric field $$(E_0) = 2.25$$ V m$$^{-1}$$ and magnetic field $$(B_0) = 1.5 \times 10^{-8}$$ T which strikes a target on line of sight at a distance of $$3$$ km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time $$t = 0$$ from radar, then after how much time echo will reach to the radar?
Login to view the detailed solution.
The velocity of sound in a gas, in which two wavelengths $$4.08$$ m and $$4.16$$ m produce $$40$$ beats in $$12$$ s, will be
Login to view the detailed solution.
Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero.
Login to view the detailed solution.
The three charges $$\frac{q}{2}, q$$ and $$\frac{q}{2}$$ are placed at the corners $$A, D$$ and $$C$$ of a square of side $$a$$ as shown in figure. The magnitude of electric field ($$E$$) at the corner $$B$$ of the square, is
Login to view the detailed solution.
An infinitely long hollow conducting cylinder with radius $$R$$ carries a uniform current along its surface. Choose the correct representation of magnetic field $$(B)$$ as a function of radial distance $$(r)$$ from the axis of cylinder.
Login to view the detailed solution.
The refracting angle of a prism is $$A$$ and refractive index of the material of the prism is $$\cot\left(\frac{A}{2}\right)$$. Then the angle of minimum deviation will be
The aperture of the objective is $$24.4$$ cm. The resolving power of this telescope, if a light of wavelength $$2440$$ Å is used to see the object will be
Login to view the detailed solution.
The de Broglie wavelengths for an electron and a photon are $$\lambda_e$$ and $$\lambda_p$$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?
Login to view the detailed solution.
The $$Q$$-value of a nuclear reaction and kinetic energy of the projectile particle, $$K_p$$ are related as
Login to view the detailed solution.
In the following circuit, the correct relation between output ($$Y$$) and inputs $$A$$ and $$B$$ will be
Login to view the detailed solution.
For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode
Login to view the detailed solution.
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : $$n - p - n$$ transistor permits more current than a $$p - n - p$$ transistor.
Reason R : Electrons have greater mobility as a charge carrier.
Login to view the detailed solution.
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) Television signal | (I) 03 KHz |
| (B) Radio signal | (II) 20 KHz |
| (C) High Quality Music | (III) 02 MHz |
| (D) Human speech | (IV) 06 MHz |
Login to view the detailed solution.
A hanging mass $$M$$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $$2Mg$$ force. In this situation, tension in the string is $$\frac{x}{5}Mg$$ for $$x =$$ ______. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
Login to view the detailed solution.
A pendulum is suspended by a string of length $$250$$ cm. The mass of the bob of the pendulum is $$200$$ g. The bob is pulled aside until the string is at $$60°$$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ______ m s$$^{-1}$$. (if $$g = 10$$ m s$$^{-2}$$)
Login to view the detailed solution.
A man of $$60$$ kg is running on the road and suddenly jumps into a stationary trolly car of mass $$120$$ kg. Then the trolly car starts moving with velocity $$2$$ m s$$^{-1}$$. The velocity of the running man was ______ m s$$^{-1}$$, when he jumps into the car.
Login to view the detailed solution.
The position vector of $$1$$ kg object is $$\vec{r} = (3\hat{i} - \hat{j})$$ m and its velocity $$\vec{v} = (3\hat{j} + \hat{k})$$ m s$$^{-1}$$. The magnitude of its angular momentum is $$\sqrt{x}$$ N m s, where $$x$$ is ______
Login to view the detailed solution.
The total internal energy of two mole monoatomic ideal gas at temperature $$T = 300$$ K will be ______ J. (Given $$R = 8.31$$ J mol$$^{-1}$$ K$$^{-1}$$)
Login to view the detailed solution.
A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $$R$$ using a given resistor of $$15$$ $$\Omega$$. The galvanometer $$(G)$$ shows null deflection when tapping key is at $$43$$ cm mark from end $$A$$. If the end correction for end $$A$$ is $$2$$ cm, then the determined value of $$R$$ will be ______ $$\Omega$$.
Login to view the detailed solution.
Current measured by the ammeter $$(A)$$ in the reported circuit when no current flows through $$10\Omega$$ resistance, will be ______ A.
Login to view the detailed solution.
A singly ionized magnesium atom $$(A = 24)$$ ion is accelerated to kinetic energy $$5$$ keV, and is projected perpendicularly into a magnetic field $$B$$ of the magnitude $$0.5$$ T. The radius of path formed will be ______ cm.
Login to view the detailed solution.
An AC source is connected to an inductance of $$100$$ mH, a capacitance of $$100$$ $$\mu$$F and a resistance of $$120$$ $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity $$2$$ J °C$$^{-1}$$ will get heated by $$16°$$C is ______ s.
Login to view the detailed solution.
A telegraph line of length $$100$$ km has a capacity of $$0.01$$ $$\mu$$F km$$^{-1}$$ and it carries an alternating current at $$0.5$$ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ______ mH. (If $$\pi = \sqrt{10}$$)
Login to view the detailed solution.
Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above "E" in the group is
Login to view the detailed solution.
Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?
Login to view the detailed solution.
Which of the following structures are aromatic in nature?
Login to view the detailed solution.
The formula of the purple colour formed in Lassaigne's test for sulphur using sodium nitroprusside is
Login to view the detailed solution.
Which amongst the following is not a pesticide?
Login to view the detailed solution.
The incorrect statement about the imperfections in solids is
Login to view the detailed solution.
The Zeta potential is related to which property of colloids?
Login to view the detailed solution.
Given are two statements one is labelled as Assertion and other is labelled as Reason.
Assertion: Magnesium can reduce $$Al_2O_3$$ at a temperature below $$1350°$$C, while above $$1350°$$C aluminium can reduce MgO.
Reason: The melting and boiling points of magnesium are lower than those of aluminium.
Login to view the detailed solution.
Nitrogen gas is obtained by thermal decomposition of:
Login to view the detailed solution.
Given below are two statements :
Statement I: The pentavalent oxide of group-15 element, $$E_2O_5$$, is less acidic than trivalent oxide, $$E_2O_3$$, of the same element.
Statement II : The acidic character of trivalent oxide of group 15 elements, $$E_2O_3$$, decreases down the group.
Login to view the detailed solution.
Dihydrogen reacts with CuO to give
Login to view the detailed solution.
Which one of the lanthanoids given below is the most stable in divalent form?
Login to view the detailed solution.
Given below are two statements :
Statement I: $$[Ni(CN)_4]^{2-}$$ is square planar and diamagnetic complex, with $$dsp^2$$ hybridization for Ni but $$[Ni(CO)_4]$$ is tetrahedral, paramagnetic and with $$sp^3$$ hybridication for Ni.
Statement II : $$[NiCl_4]^{2-}$$ and $$[Ni(CO)_4]$$ both have same d-electron configuration, have same geometry and are paramagnetic.
In light the above statements, choose the correct answer form the options given below
Login to view the detailed solution.
The major product (P) in the reaction
Login to view the detailed solution.
Which one of the following compounds is inactive towards $$S_N1$$ reaction?
Login to view the detailed solution.
The correct structure of product 'A' formed in the following reaction,
Login to view the detailed solution.
Identify the major product formed in the following sequence of reactions :
Login to view the detailed solution.
A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives a/an
Login to view the detailed solution.
Which one of the following is NOT a copolymer?
Login to view the detailed solution.
Stability of $$\alpha$$-Helix structure of proteins depends upon
Login to view the detailed solution.
If the work function of a metal is $$6.63 \times 10^{-19}$$ J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ______ nm. Nearest integer
[Given : $$h = 6.63 \times 10^{-34}$$ J s, and $$c = 3 \times 10^{8}$$ m s$$^{-1}$$]
Login to view the detailed solution.
The hybridization of P exhibited in $$PF_5$$ is $$sp^x d^y$$. The value of $$y$$ is ______
Login to view the detailed solution.
$$4.0$$ L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is $$20$$ L. The amount of heat absorbed in this expansion is ______ L atm.
Login to view the detailed solution.
A $$2.0$$ g sample containing $$MnO_2$$ is treated with HCl liberating $$Cl_2$$. The $$Cl_2$$ gas is passed into a solution of KI and $$60.0$$ mL of $$0.1$$ M $$Na_2S_2O_3$$ is required to titrate the liberated iodine. The percentage of $$MnO_2$$ in the sample is ______ Nearest integer
[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]
Login to view the detailed solution.
In the estimation of bromine, $$0.5$$ g of an organic compound gave $$0.40$$ g of silver bromide. The percentage of bromine in the given compound is ______ % (nearest integer)
(Relative atomic masses of Ag and Br are 108u and 80u, respectively).
Login to view the detailed solution.
The vapour pressures of two volatile liquids A and B at $$25°$$C are $$50$$ Torr and $$100$$ Torr, respectively. If the liquid mixture contains $$0.3$$ mole fraction of A, then the mole fraction of liquid B in the vapour phase is $$\frac{x}{17}$$. The value of $$x$$ is ______
Login to view the detailed solution.
The solubility product of a sparingly soluble salt $$A_2X_3$$ is $$1.1 \times 10^{-23}$$. If specific conductance of the solution is $$x \times 10^{-3}$$ S m$$^2$$ mol$$^{-1}$$. The value of $$x$$ is ______
Login to view the detailed solution.
The quantity of electricity in Faraday needed to reduce $$1$$ mol of $$Cr_2O_7^{2-}$$ to $$Cr^{3+}$$ is ______
Login to view the detailed solution.
For a first order reaction A $$\to$$ B, the rate constant, $$k = 5.5 \times 10^{-14}$$ s$$^{-1}$$. The time required for $$67\%$$ completion of reaction is $$x \times 10^{-1}$$ times the half life of reaction. The value of $$x$$ is ______ Nearest integer) (Given : $$\log 3 = 0.4771$$)
Login to view the detailed solution.
Number of complexes which will exhibit synergic bonding amongst, $$[Cr(CO)_6], [Mn(CO)_5]$$ and $$[Mn_2(CO)_{10}]$$ is ______
Login to view the detailed solution.
The total number of 5-digit numbers, formed by using the digits $$1, 2, 3, 5, 6, 7$$ without repetition, which are multiple of $$6$$, is
Login to view the detailed solution.
Let $$A_1, A_2, A_3, \ldots$$ be an increasing geometric progression of positive real numbers. If $$A_1 A_3 A_5 A_7 = \frac{1}{1296}$$ and $$A_2 + A_4 = \frac{7}{36}$$, then the value of $$A_6 + A_8 + A_{10}$$ is equal to
Login to view the detailed solution.
If $$\sum_{k=1}^{31} \left(^{31}C_{k}\right) \left(^{31}C_{k-1} \right) - \sum_{k=1}^{30} \left(^{30}C_{k}\right) \left(^{30}C_{k-1} \right)= \frac{\alpha(60!)}{(30!)(31!)}$$, where $$\alpha \in R$$, then the value of $$16\alpha$$ is equal to
Login to view the detailed solution.
If the tangents drawn at the point $$O(0,0)$$ and $$P(1+\sqrt{5}, 2)$$ on the circle $$x^2 + y^2 - 2x - 4y = 0$$ intersect at the point $$Q$$, then the area of the triangle $$OPQ$$ is equal to
Login to view the detailed solution.
Let the eccentricity of the hyperbola $$H : \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ be $$\sqrt{\frac{5}{2}}$$ and length of its latus rectum be $$6\sqrt{2}$$. If $$y = 2x + c$$ is a tangent to the hyperbola $$H$$, then the value of $$c^2$$ is equal to
Login to view the detailed solution.
Let $$p, q, r$$ be three logical statements. Consider the compound statements
$$S_1 : ((\sim p) \vee q) \vee ((\sim p) \vee r)$$ and $$S_2 : p \to (q \vee r)$$
Then, which of the following is NOT true?
Login to view the detailed solution.
Let $$AB$$ and $$PQ$$ be two vertical poles, $$160$$ m apart from each other. Let $$C$$ be the middle point of $$B$$ and $$Q$$, which are feet of these two poles. Let $$\frac{\pi}{8}$$ and $$\theta$$ be the angles of elevation from $$C$$ to $$P$$ and $$A$$, respectively. If the height of pole $$PQ$$ is twice the height of pole $$AB$$, then $$\tan^2\theta$$ is equal to
Login to view the detailed solution.
Let $$A$$ be a matrix of order $$3 \times 3$$ and $$\det(A) = 2$$. Then $$\det(\det(A) \text{ adj}(5 \text{ adj}(A^3)))$$ is equal to
Login to view the detailed solution.
If the system of linear equations
$$2x + 3y - z = -2$$
$$x + y + z = 4$$
$$x - y + |\lambda|z = 4\lambda - 4$$ where $$\lambda \in \mathbb{R}$$,
has no solution, then
Login to view the detailed solution.
Let a function $$f : \mathbb{N} \to \mathbb{N}$$ be defined by
$$f(n) = \begin{cases} 2n, & n = 2, 4, 6, 8, \ldots \\ n-1, & n = 3, 7, 11, 15, \ldots \\ \frac{n+1}{2}, & n = 1, 5, 9, 13, \ldots \end{cases}$$
then, $$f$$ is
Login to view the detailed solution.
Let $$f : \mathbb{R} \to \mathbb{R}$$ be defined as $$f(x) = \begin{cases} [e^x], & x < 0 \\ ae^x + [x-1], & 0 \leq x < 1 \\ b + [\sin(\pi x)], & 1 \leq x < 2 \\ [e^{-x}] - c, & x \geq 2 \end{cases}$$
where $$a, b, c \in \mathbb{R}$$ and $$[t]$$ denotes greatest integer less than or equal to $$t$$. Then, which of the following statements is true?
Login to view the detailed solution.
The number of real solutions of $$x^7 + 5x^3 + 3x + 1 = 0$$ is equal to ______
Login to view the detailed solution.
Let $$[t]$$ denote the greatest integer less than or equal to $$t$$. Then the value of the integral $$\int_0^1 [-8x^2 + 6x - 1] dx$$ is equal to
Login to view the detailed solution.
The area of the region $$S = \{(x,y) : y^2 \leq 8x, y \geq \sqrt{2}x, x \geq 1\}$$ is
Login to view the detailed solution.
Let the solution curve $$y = y(x)$$ of the differential equation, $$\left[\frac{x}{\sqrt{x^2-y^2}} + e^{y/x}\right]x\frac{dy}{dx} = x + \left[\frac{x}{\sqrt{x^2-y^2}} + e^{y/x}\right]y$$ pass through the points $$(1, 0)$$ and $$(2\alpha, \alpha), \alpha > 0$$. Then $$\alpha$$ is equal to
Login to view the detailed solution.
Let $$y = y(x)$$ be the solution of the differential equation $$x(1 - x^2)\frac{dy}{dx} + (3x^2y - y - 4x^3) = 0, x > 1$$ with $$y(2) = -2$$. Then $$y(3)$$ is equal to
Login to view the detailed solution.
If two distinct point $$Q$$, $$R$$ lie on the line of intersection of the planes $$-x + 2y - z = 0$$ and $$3x - 5y + 2z = 0$$ and $$PQ = PR = \sqrt{18}$$ where the point $$P$$ is $$(1, -2, 3)$$, then the area of the triangle $$PQR$$ is equal to
Login to view the detailed solution.
The acute angle between the planes $$P_1$$ and $$P_2$$, when $$P_1$$ and $$P_2$$ are the planes passing through the intersection of the planes $$5x + 8y + 13z - 29 = 0$$ and $$8x - 7y + z - 20 = 0$$ and the points $$(2, 1, 3)$$ and $$(0, 1, 2)$$, respectively, is
Login to view the detailed solution.
Let the plane $$P : \vec{r} \cdot \vec{a} = d$$ contain the line of intersection of two planes $$\vec{r} \cdot (\hat{i} + 3\hat{j} - \hat{k}) = 6$$ and $$\vec{r} \cdot (-6\hat{i} + 5\hat{j} - \hat{k}) = 7$$. If the plane $$P$$ passes through the point $$(2, 3, \frac{1}{2})$$, then the value of $$\frac{|13\vec{a}|^2}{d^2}$$ is equal to
Login to view the detailed solution.
The probability, that in a randomly selected 3-digit number at least two digits are odd, is
Login to view the detailed solution.
The number of real solutions of the equation $$e^{4x} + 4e^{3x} - 58e^{2x} + 4e^x + 1 = 0$$ is ______
Login to view the detailed solution.
The number of elements in the set $$\{z = a + ib \in C : a, b \in \mathbb{Z}$$ and $$1 < |z - 3 + 2i| < 4\}$$ is ______
Login to view the detailed solution.
The number of positive integers $$k$$ such that the constant term in the binomial expansion of $$\left(2x^3 + \frac{3}{x^k}\right)^{12}, x \neq 0$$ is $$2^8 \cdot l$$, where $$l$$ is an odd integer, is ______
Login to view the detailed solution.
A ray of light passing through the point $$P(2, 3)$$ reflects on the $$X$$-axis at point $$A$$ and the reflected ray passes through the point $$Q(5, 4)$$. Let $$R$$ be the point that divides the line segment $$AQ$$ internally into the ratio $$2 : 1$$. Let the co-ordinates of the foot of the perpendicular $$M$$ from $$R$$ on the bisector of the angle $$PAQ$$ be $$(\alpha, \beta)$$. Then, the value of $$7\alpha + 3\beta$$ is equal to ______
Login to view the detailed solution.
Let the lines $$y + 2x = \sqrt{11} + 7\sqrt{7}$$ and $$2y + x = 2\sqrt{11} + 6\sqrt{7}$$ be normal to a circle $$C : (x-h)^2 + (y-k)^2 = r^2$$. If the line $$\sqrt{11}y - 3x = \frac{5\sqrt{77}}{3} + 11$$ is tangent to the circle $$C$$, then the value of $$(5h - 8k)^2 + 5r^2$$ is equal to ______
Login to view the detailed solution.
The mean and standard deviation of 15 observations are found to be $$8$$ and $$3$$ respectively. On rechecking it was found that, in the observations, $$20$$ was misread as $$5$$. Then, the correct variance is equal to ______
Login to view the detailed solution.
Let $$R_1$$ and $$R_2$$ be relations on the set $$\{1, 2, \ldots, 50\}$$ such that $$R_1 = \{(p, p^n) : p$$ is a prime and $$n \geq 0$$ is an integer$$\}$$ and $$R_2 = \{(p, p^n) : p$$ is a prime and $$n = 0$$ or $$1\}$$. Then, the number of elements in $$R_1 - R_2$$ is ______
Login to view the detailed solution.
Let $$A = \{1, a_1, a_2, \ldots a_{18}, 77\}$$ be a set of integers with $$1 < a_1 < a_2 < \ldots < a_{18} < 77$$. Let the set $$A + A = \{x + y : x, y \in A\}$$ contain exactly $$39$$ elements. Then, the value of $$a_1 + a_2 + \ldots + a_{18}$$ is equal to ______
Login to view the detailed solution.
Let $$l$$ be a line which is normal to the curve $$y = 2x^2 + x + 2$$ at a point $$P$$ on the curve. If the point $$Q(6, 4)$$ lies on the line $$l$$ and $$O$$ is origin, then the area of the triangle $$OPQ$$ is equal to ______
Login to view the detailed solution.
If $$\vec{a} = 2\hat{i} + \hat{j} + 3\hat{k}, \vec{b} = 3\hat{i} + 3\hat{j} + \hat{k}$$ and $$\vec{c} = c_1\hat{i} + c_2\hat{j} + c_3\hat{k}$$ are coplanar vectors and $$\vec{a} \cdot \vec{c} = 5, \vec{b} \perp \vec{c}$$, then $$122(c_1 + c_2 + c_3)$$ is equal to ______
Login to view the detailed solution.
Educational materials for JEE preparation
Share