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.
Which of the following equations is dimensionally incorrect?
Where $$t$$ = time, $$h$$ = height, $$s$$ = surface tension, $$\theta$$ = angle, $$\rho$$ = density, $$a, r$$ = radius, $$g$$ = the acceleration due to gravity, $$V$$ = volume, $$p$$ = pressure, $$W$$ = work done, $$\tau$$ = torque, $$\epsilon$$ = permittivity, $$E$$ = electric field, $$J$$ = current density, $$L$$ = length.
Login to view the detailed solution.
Match List - I with List - II.
List - I List - II
(a) Torque (i) MLT$$^{-1}$$
(b) Impulse (ii) MT$$^{-2}$$
(c) Tension (iii) ML$$^2$$ T$$^{-2}$$
(d) Surface Tension (iv) MLT$$^{-2}$$
Choose the most appropriate answer from the option given below:
Login to view the detailed solution.
A helicopter is flying horizontally with a speed $$v$$ at an altitude $$h$$ has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?
Login to view the detailed solution.
.webp)
A body of mass $$M$$ moving at speed $$V_0$$ collides elastically with a mass $$m$$ at rest. After the collision, the two masses move at angles $$\theta_1$$ and $$\theta_2$$ with respect to the initial direction of motion of the body of mass $$M$$. The largest possible value of the ratio $$\frac{M}{m}$$, for which the angles $$\theta_1$$ and $$\theta_2$$ will be equal, is:
Login to view the detailed solution.
Angular momentum of a single particle moving with constant speed along circular path:
Login to view the detailed solution.
The masses and radii of the earth and moon are $$(M_1, R_1)$$ and $$(M_2, R_2)$$ respectively. Their centres are at a distance $$r$$ apart. Find the minimum escape velocity for a particle of mass $$m$$ to be projected from the middle of these two masses:
Login to view the detailed solution.
A uniform heavy rod of weight 10 kg m s$$^{-2}$$, cross-sectional area 100 cm$$^2$$ and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is $$2 \times 10^{11}$$ N m$$^{-2}$$. Neglecting the lateral contraction, find the elongation of rod due to its own weight:
Login to view the detailed solution.
A reversible engine has an efficiency of $$\frac{1}{4}$$. If the temperature of the sink is reduced by 58°C, its efficiency becomes double. Calculate the temperature of the sink:
Login to view the detailed solution.
For an ideal gas the instantaneous change in pressure $$P$$ with volume $$V$$ is given by the equation $$\frac{dP}{dV} = -aP$$. If $$P = P_0$$ at $$V = 0$$ is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here $$\mathcal{R}$$ is the gas constant)
Login to view the detailed solution.
Two particles $$A$$ and $$B$$ having charges 20 $$\mu$$C and $$-5$$ $$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?
Login to view the detailed solution.
Consider a galvanometer shunted with 5 $$\Omega$$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer?
Login to view the detailed solution.
A coil having $$N$$ turns is wound tightly in the form of a spiral with inner and outer radii $$a$$ and $$b$$ respectively. Find the magnetic field at centre, when a current $$I$$ passes through coil:
Login to view the detailed solution.
A small square loop of side $$a$$ and one turn is placed inside a larger square loop of side $$b$$ and one turn $$(b \gg a)$$. The two loops are coplanar with their centres coinciding. If a current $$I$$ is passed in the square loop of side $$b$$, then the coefficient of mutual inductance between the two loops is:
Login to view the detailed solution.
In an ac circuit, an inductor, a capacitor and a resistor are connected in series with $$X_L = R = X_C$$. Impedance of this circuit is:
Login to view the detailed solution.
An object is placed at the focus of concave lens having focal length $$f$$. What is the magnification and distance of the image from the optical centre of the lens?
Login to view the detailed solution.
Two plane mirrors $$M_1$$ and $$M_2$$ are at right angle to each other as shown. A point source $$P$$ is placed at $$a$$ and $$2a$$ meter away from $$M_1$$ and $$M_2$$ respectively. The shortest distance between the images thus formed is: (Take $$\sqrt{5} = 2.3$$)
Login to view the detailed solution.
A moving proton and electron have the same de-Broglie wavelength. If $$K$$ and $$P$$ denote the K.E. and momentum respectively. Then choose the correct option:
Login to view the detailed solution.
A sample of a radioactive nucleus $$A$$ disintegrates to another radioactive nucleus $$B$$, which in turn disintegrates to some other stable nucleus $$C$$. Plot of a graph showing the variation of number of atoms of nucleus $$B$$ versus time is: (Assume that at $$t = 0$$, there are no $$B$$ atoms in the sample)
Choose the correct waveform that can represent the voltage across $$R$$ of the following circuit, assuming the diode is ideal one:
Login to view the detailed solution.
In the following logic circuit the sequence of the inputs $$A$$, $$B$$ are $$(0, 0), (0, 1), (1, 0)$$ and $$(1, 1)$$. The output $$Y$$ for this sequence will be:
Login to view the detailed solution.
A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10 m s$$^{-2}$$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is _________. (Take $$g = 10$$ m s$$^{-2}$$)
Login to view the detailed solution.
A block moving horizontally on a smooth surface with a speed of 40 m s$$^{-1}$$ splits into two equal parts. If one of the parts moves at 60 m s$$^{-1}$$ in the same direction, then the fractional change in the kinetic energy will be $$x : 4$$ where $$x$$ = _________.
Login to view the detailed solution.
When a rubber ball is taken to a depth of _________ m in deep sea, its volume decreases by 0.5%.
(The bulk modulus of rubber = $$9.8 \times 10^8$$ N m$$^{-2}$$, Density of sea water = $$10^3$$ kg m$$^{-3}$$, g = 9.8 m s$$^{-2}$$)
Login to view the detailed solution.
A particle of mass 1 kg is hanging from a spring of force constant 100 N m$$^{-1}$$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $$T$$. The time when the kinetic energy and potential energy of the system will become equal, is $$\frac{T}{n}$$. The value of $$n$$ is _________.
Login to view the detailed solution.
A wire having a linear mass density $$9.0 \times 10^{-4}$$ kg m$$^{-1}$$ is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is _________ m.
Login to view the detailed solution.
A capacitor of 50$$\mu$$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is _________ $$\mu$$C.
Login to view the detailed solution.
The voltage drop across 15 $$\Omega$$ resistance in the given figure will be _________ V.
Login to view the detailed solution.
A square-shaped wire with a resistance of each side 3 $$\Omega$$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in a unit of $$\Omega$$ will is _________.
Login to view the detailed solution.
The electric field in an electromagnetic wave is given by
$$E = (50 \text{ N C}^{-1})\sin\omega\left(t - \frac{z}{c}\right)$$
The energy contained in a cylinder of volume $$V$$ is $$5.5 \times 10^{-12}$$ J. The value of $$V$$ is _________ cm$$^3$$.
(given $$\epsilon_0 = 8.8 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)
Login to view the detailed solution.
If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is _________ km (Take radius of Earth = 6400 km)
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) : Metallic character decreases and non-metallic character increases on moving from left to right in a period.
Reason (R): It is due to increase in ionisation enthalpy and decrease in electron gain enthalpy, when one moves from left to right in a period.
In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas? (P and V stand for pressure and volume of the gas respectively)
Login to view the detailed solution.
Monomer of Novolac is:
Login to view the detailed solution.
The major component/ingredient of Portland Cement is:
Login to view the detailed solution.
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason.
Assertion (A): A simple distillation can be used to separate a mixture of propanol and propanone.
Reason (R): Two liquids with a difference of more than 20°C in their boiling points can be separated by simple distillations.
In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
Choose the correct name for compound given below:
Login to view the detailed solution.
BOD values (in ppm) for clean water (A) and polluted water (B) are expected respectively as:
Login to view the detailed solution.
Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression?
Login to view the detailed solution.
Select the graph that correctly describes the adsorption isotherms at two temperatures $$T_1$$ and $$T_2$$ ($$T_1 > T_2$$) for a gas:
($$x$$ - mass of the gas adsorbed, $$m$$ - mass of adsorbent, $$P$$ - pressure)
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): Treatment of bromine water with propene yields 1-bromopropan-2-ol.
Reason (R): Attack of water on bromonium ion follows Markovnikov rule and results in 1-bromopropan-2-ol.
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 structure of the dichromate ion, there is a:
Login to view the detailed solution.
Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature? (Given Z for Nd = 60, Yb = 70, La = 57, Ce = 58)
Login to view the detailed solution.
The denticity of an organic ligand, biuret is:
Login to view the detailed solution.
The structure of product C, formed by the following sequence of reactions is:
CH$$_3$$COOH + SOCl$$_2$$ $$\rightarrow$$ A $$\xrightarrow[AlCl_{3}]{Benzene}$$ B $$\xrightarrow[OH]{KCN}$$ C
The correct order of reactivity of the given chlorides with acetate in acetic acid is:
Login to view the detailed solution.
Given below are two statements:
Statement I : The process of producing syn-gas is called gasification of coal.
Statement II : The composition of syn-gas is CO + CO$$_2$$ + H$$_2$$ (1 : 1 : 1).
In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
The major products A and B in the following set of reactions are:
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) : Aluminium is extracted from bauxite by the electrolysis of molten mixture of Al$$_2$$O$$_3$$ with cryolite.
Reason (R) : The oxidation state of Al in cryolite is +3.
In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
The major product formed in the following reaction is:
Login to view the detailed solution.
Which one of the following compounds contains $$\beta - C_1 - C_4$$ glycosidic linkage?
Login to view the detailed solution.
Ge (Z = 32) in its ground state electronic configuration has x completely filled orbitals with m$$_l$$ = 0. The value of x is _________.
Login to view the detailed solution.
According to the following figure, the magnitude of the enthalpy change of the reaction A + B $$\rightarrow$$ M + N in kJ mol$$^{-1}$$ is equal to _________. (Integer answer)
Login to view the detailed solution.
A$$_3$$B$$_2$$ is a sparingly soluble salt of molar mass M (g mol$$^{-1}$$) and solubility x g L$$^{-1}$$. The solubility product satisfies K$$_{sp}$$ = $$a\left(\frac{x}{M}\right)^5$$. The value of a is _________. (Integer answer)
Login to view the detailed solution.
The number of hydrogen bonded water molecule(s) associated with stoichiometry CuSO$$_4$$.5H$$_2$$O is _________.
Login to view the detailed solution.
The molarity of the solution prepared by dissolving 6.3 g of oxalic acid (H$$_2$$C$$_2$$O$$_4$$.2H$$_2$$O) in 250 mL of water in mol L$$^{-1}$$ is $$x \times 10^{-2}$$. The value of x is _________. (Nearest integer)
[Atomic mass : H : 1.0, C : 12.0, O : 16.0 J]
Login to view the detailed solution.
Consider the following cell reaction Cd$$(s)$$ + Hg$$_2$$SO$$_4$$(s) + $$\frac{9}{5}$$H$$_2$$O$$(l)$$ $$\rightleftharpoons$$ CdSO$$_4$$.$$\frac{9}{5}$$H$$_2$$O$$(s)$$ + 2Hg$$(l)$$.
The value of E$$^0_{cell}$$ is 4.315 V at 25°C. If $$\Delta H°$$ = -825.2 kJ mol$$^{-1}$$, the standard entropy change $$\Delta S°$$ in J K$$^{-1}$$ is _________. (Nearest integer)
[Given : Faraday constant = 96487 C mol$$^{-1}$$]
Login to view the detailed solution.
For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is _________. (Integer answer)
Login to view the detailed solution.
Consider the sulphides HgS, PbS, CuS, Sb$$_2$$S$$_3$$, As$$_2$$S$$_3$$ and CdS. Number of these sulphides soluble in 50% HNO$$_3$$ is _________.
Login to view the detailed solution.
The number of halogen/(s) forming halic (V) acid is _________.
Login to view the detailed solution.
The total number of reagents from those given below, that can convert nitrobenzene into aniline is _________. (Integer answer)
I. Sn - HCl
II. Sn - NH$$_4$$OH
III. Fe - HCl
IV. Zn - HCl
V. H$$_2$$ - Pd
VI. H$$_2$$ - Raney Nickel
Login to view the detailed solution.
The sum of 10 terms of the series $$\frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \ldots$$ is:
Login to view the detailed solution.
Three numbers are in an increasing geometric progression with common ratio $$r$$. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference $$d$$. If the fourth term of GP is $$3r^2$$, then $$r^2 - d$$ is equal to:
Login to view the detailed solution.
$$\text{cosec } 18°$$ is a root of the equation:
Login to view the detailed solution.
If $$p$$ and $$q$$ are the lengths of the perpendiculars from the origin on the lines, $$x\text{cosec}\alpha - y\sec\alpha = k\cot 2\alpha$$ and $$x\sin\alpha + y\cos\alpha = k\sin 2\alpha$$ respectively, then $$k^2$$ is equal to:
Login to view the detailed solution.
The length of the latus rectum of a parabola, whose vertex and focus are on the positive $$x$$-axis at a distance $$R$$ and $$S (> R)$$ respectively from the origin, is:
Login to view the detailed solution.
The line $$12x\cos\theta + 5y\sin\theta = 60$$ is tangent to which of the following curves?
Login to view the detailed solution.
$$\lim_{x \to 0} \frac{\sin^2(\pi\cos^4 x)}{x^4}$$ is equal to:
Login to view the detailed solution.
Let $$*, \square \in \{\wedge, \vee\}$$ be such that the Boolean expression $$(p * \sim q) \Rightarrow (p \square q)$$ is a tautology. Then:
Login to view the detailed solution.
A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is:
Login to view the detailed solution.
Which of the following is not correct for relation $$R$$ on the set of real numbers?
Login to view the detailed solution.
If $$a_r = \cos\frac{2r\pi}{9} + i\sin\frac{2r\pi}{9}$$, $$r = 1, 2, 3, \ldots$$, $$i = \sqrt{-1}$$, then the determinant $$\begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \end{vmatrix}$$ is equal to:
Login to view the detailed solution.
If the following system of linear equations
$$2x + y + z = 5$$
$$x - y + z = 3$$
$$x + y + az = b$$
has no solution, then:
Login to view the detailed solution.
The function $$f(x) = |x^2 - 2x - 3| \cdot e^{9x^2-12x+4}$$ is not differentiable at exactly:
Login to view the detailed solution.
If the function $$f(x) = \begin{cases} \frac{1}{x}\log_e\left(\frac{1+\frac{x}{b}}{1-\frac{x}{b}}\right), & x < 0 \\ k, & x = 0 \\ \frac{\cos^2 x - \sin^2 x - 1}{\sqrt{x^2+1}-1}, & x > 0 \end{cases}$$ is continuous at $$x = 0$$, then $$\frac{1}{a} + \frac{1}{b} + \frac{4}{k}$$ is equal to:
Login to view the detailed solution.
The number of real roots of the equation $$e^{4x} + 2e^{3x} - e^x - 6 = 0$$ is:
Login to view the detailed solution.
The integral $$\int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} dx$$ is equal to: (where $$C$$ is a constant of integration)
Login to view the detailed solution.
Let $$f$$ be a non-negative function in $$[0, 1]$$ and twice differentiable in $$(0, 1)$$. If
$$\int_0^x \sqrt{1 - (f'(t))^2} dt = \int_0^x f(t) dt$$, $$0 \leq x \leq 1$$ and $$f(0) = 0$$, then $$\lim_{x \to 0} \frac{1}{x^2} \int_0^x f(t) dt$$:
Login to view the detailed solution.
If $$\frac{dy}{dx} = \frac{2^{x+y} - 2^x}{2^y}$$, $$y(0) = 1$$, then $$y(1)$$ is equal to:
Login to view the detailed solution.
Let $$\vec{a}$$ and $$\vec{b}$$ be two vectors such that $$|2\vec{a} + 3\vec{b}| = |3\vec{a} + \vec{b}|$$ and the angle between $$\vec{a}$$ and $$\vec{b}$$ is 60°. If $$\frac{1}{8}\vec{a}$$ is a unit vector, then $$|\vec{b}|$$ is equal to:
Login to view the detailed solution.
Let the equation of the plane, that passes through the point $$(1, 4, -3)$$ and contains the line of intersection of the planes $$3x - 2y + 4z - 7 = 0$$ and $$x + 5y - 2z + 9 = 0$$, be $$\alpha x + \beta y + \gamma z + 3 = 0$$, then $$\alpha + \beta + \gamma$$ is equal to:
Login to view the detailed solution.
A point $$z$$ moves in the complex plane such that $$\arg\left(\frac{z-2}{z+2}\right) = \frac{\pi}{4}$$, then the minimum value of $$|z - 9\sqrt{2} - 2i|^2$$ is equal to _________.
Login to view the detailed solution.
The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is _________.
Login to view the detailed solution.
If $$\left(\frac{x^6}{4^4}\right) k$$ is the term, independent of $$x$$, in the binomial expansion of $$\left(\frac{x}{4} - \frac{12}{x^2}\right)^{12}$$, then $$k$$ is equal to _________.
Login to view the detailed solution.
If the variable line $$3x + 4y = \alpha$$ lies between the two circles $$(x-1)^2 + (y-1)^2 = 1$$ and $$(x-9)^2 + (y-1)^2 = 4$$, without intercepting a chord on either circle, then the sum of all the integral values of $$\alpha$$ is _________.
Login to view the detailed solution.
The mean of 10 numbers
$$7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \ldots$$ is _________.
Login to view the detailed solution.
If $$R$$ is the least value of $$a$$ such that the function $$f(x) = x^2 + ax + 1$$ is increasing on $$[1, 2]$$ and $$S$$ is the greatest value of $$a$$ such that the function $$f(x) = x^2 + ax + 1$$ is decreasing on $$[1, 2]$$, then the value of $$|R - S|$$ is _________.
Login to view the detailed solution.
Let $$[t]$$ denote the greatest integer $$\leq t$$. Then the value of $$8 \cdot \int_{-\frac{1}{2}}^{1} \left([2x] + |x|\right) dx$$ is _________.
Login to view the detailed solution.
If $$x\phi(x) = \int_5^x (3t^2 - 2\phi'(t)) dt$$, $$x > -2$$, $$\phi(0) = 4$$, then $$\phi(2)$$ is _________.
Login to view the detailed solution.
The square of the distance of the point of intersection of the line $$\frac{x-1}{2} = \frac{y-2}{3} = \frac{z+1}{6}$$ and the plane $$2x - y + z = 6$$ from the point $$(-1, -1, 2)$$ is _________.
Login to view the detailed solution.
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is $$p$$, then $$98p$$ is equal to _________.
Login to view the detailed solution.
Educational materials for JEE preparation
Share