In an expression $$a \times 10^b$$;
JEE WhatsApp Group
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.
In an expression $$a \times 10^b$$;
Login to view the detailed solution.
Young's modulus is determined by the equation given by $$Y = 49000 \frac{m}{l} \frac{dyn}{cm^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modulus $$(Y)$$ is estimated by taking data from $$M - l$$ plot in graph paper. The smallest scale divisions are $$5 \text{ g}$$ and $$0.02 \text{ cm}$$ along load axis and extension axis respectively. If the value of $$M$$ and $$l$$ are $$500 \text{ g}$$ and $$2 \text{ cm}$$ respectively then percentage error of $$Y$$ is :
Login to view the detailed solution.
A clock has $$75 \text{ cm}$$ long second hand and $$60 \text{ cm}$$ minute hand respectively. In 30 minutes duration the tip of second hand will travel $$x$$ distance more than the tip of minute hand. The value of $$x$$ in meter is nearly (Take $$\pi = 3.14$$) :
Login to view the detailed solution.
.webp)
A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of their kinetic energies $$(K_B : K_A)$$ is :
Login to view the detailed solution.
Three bodies A, B and C have equal kinetic energies and their masses are $$400 \text{ g}$$, $$1.2 \text{ kg}$$ and $$1.6 \text{ kg}$$ respectively. The ratio of their linear momenta is :
Login to view the detailed solution.
A player caught a cricket ball of mass $$150 \text{ g}$$ moving at a speed of $$20 \text{ m/s}$$. If the catching process is completed in $$0.1 \text{ s}$$, the magnitude of force exerted by the ball on the hand of the player is:
Login to view the detailed solution.
Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ radii respectively. If angular momentum of $$A$$ is $$L$$ and that of $$B$$ is $$3L$$, the ratio of time period $$\left(\frac{T_A}{T_B}\right)$$ is:
Login to view the detailed solution.
Correct Bernoulli's equation is (symbols have their usual meaning) :
Login to view the detailed solution.
Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:
Login to view the detailed solution.
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27°C)$$. The ratio of specific heat of gases at constant volume respectively is:
Login to view the detailed solution.
Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
Login to view the detailed solution.
In the given circuit, the terminal potential difference of the cell is :
Login to view the detailed solution.
Paramagnetic substances:
A. align themselves along the directions of external magnetic field.
B. attract strongly towards external magnetic field.
C. has susceptibility little more than zero.
D. move from a region of strong magnetic field to weak magnetic field.
Choose the most appropriate answer from the options given below:
Login to view the detailed solution.
A LCR circuit is at resonance for a capacitor $$C$$, inductance $$L$$ and resistance $$R$$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:
Login to view the detailed solution.
Critical angle of incidence for a pair of optical media is $$45°$$. The refractive indices of first and second media are in the ratio:
Login to view the detailed solution.
A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume $$h = 6.63 \times 10^{-34} \text{ J s}$$, $$m_e = 9.0 \times 10^{-31} \text{ kg}$$ and $$m_p = 1836 \; m_e$$)
Login to view the detailed solution.
Average force exerted on a non-reflecting surface at normal incidence is $$2.4 \times 10^{-4} \text{ N}$$. If $$360 \text{ W/cm}^2$$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:
Login to view the detailed solution.
Binding energy of a certain nucleus is $$18 \times 10^8 \text{ J}$$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:
Login to view the detailed solution.
The output Y of following circuit for given inputs is :
Login to view the detailed solution.
The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1 \text{ mm}$$. The main scale reading is $$2 \text{ cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $$8.635 \text{ g}$$, the density of the sphere is:
Login to view the detailed solution.
Three vectors $$\vec{OP}$$, $$\vec{OQ}$$ and $$\vec{OR}$$ each of magnitude $$A$$ are acting as shown in figure. The resultant of the three vectors is $$A\sqrt{x}$$. The value of $$x$$ is ________.
Login to view the detailed solution.
A uniform thin metal plate of mass $$10 \text{ kg}$$ with dimensions is shown in the figure below. The ratio of $$x$$ and $$y$$ coordinates of center of mass of the plate is $$\frac{n}{9}$$. The value of $$n$$ is ________.
Login to view the detailed solution.
A liquid column of height $$0.04 \text{ cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \text{ kg m}^{-3}$$ and surface tension of soap solution is $$0.28 \text{ Nm}^{-1}$$, then diameter of the soap bubble is ______ cm. (if $$g = 10 \text{ m s}^{-2}$$)
Login to view the detailed solution.
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is ________.
Login to view the detailed solution.
An electric field, $$\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \text{ m}^2$$ area having unit vector $$\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is ______ Vm.
Login to view the detailed solution.
Resistance of a wire at $$0°C$$, $$100°C$$ and $$t°C$$ is found to be $$10\Omega$$, $$10.2\Omega$$ and $$10.95\Omega$$ respectively. The temperature $$t$$ in Kelvin scale is ________.
Login to view the detailed solution.
An electron with kinetic energy $$5 \text{ eV}$$ enters a region of uniform magnetic field of $$3 \; \mu T$$ perpendicular to its direction. An electric field $$E$$ is applied perpendicular to the direction of velocity and magnetic field. The value of $$E$$, so that electron moves along the same path, is ______ $$\text{NC}^{-1}$$. (Given, mass of electron $$= 9 \times 10^{-31} \text{ kg}$$, electric charge $$= 1.6 \times 10^{-19} \text{ C}$$)
Login to view the detailed solution.
A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \text{ m}^2$$ and resistance $$100\Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$B = 0.5 \text{ T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \text{ s}$$ is ______ $$\times 10^{-8} \text{ J}$$.
Login to view the detailed solution.
A parallel beam of monochromatic light of wavelength $$600 \text{ nm}$$ passes through single slit of $$0.4 \text{ mm}$$ width. Angular divergence corresponding to second order minima would be ______ $$\times 10^{-3} \text{ rad}$$.
Login to view the detailed solution.
In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \text{ m}$$. If target nucleus has atomic number 80, then maximum velocity of $$\alpha$$-particle is ______ $$\times 10^5 \text{ m/s}$$ approximately. $$\left(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI unit, mass of } \alpha \text{ particle} = 6.72 \times 10^{-27} \text{ kg}\right)$$
Login to view the detailed solution.
Combustion of glucose $$(C_6H_{12}O_6)$$ produces $$CO_2$$ and water. The amount of oxygen (in g) required for the complete combustion of $$900 \text{ g}$$ of glucose is : [Molar mass of glucose in $$\text{gmol}^{-1} = 180$$]
Login to view the detailed solution.
Match List I with List II
Choose the correct answer from the options given below:
Match List I with List II
Choose the correct answer from the options given below:
Login to view the detailed solution.
Match List I with List II
Choose the correct answer from the options given below:
Login to view the detailed solution.
Given below are two statements: Statement I: $$N(CH_3)_3$$ and $$P(CH_3)_3$$ can act as ligands to form transition metal complexes. Statement II: As N and P are from same group, the nature of bonding of $$N(CH_3)_3$$ and $$P(CH_3)_3$$ is always same with transition metals. In the light of the above statements, choose the most appropriate answer from the options given below:
Login to view the detailed solution.
For the given hypothetical reactions, the equilibrium constants are as follows: $$X \rightleftharpoons Y; K_1 = 1.0$$, $$Y \rightleftharpoons Z; K_2 = 2.0$$, $$Z \rightleftharpoons W; K_3 = 4.0$$. The equilibrium constant for the reaction $$X \rightleftharpoons W$$ is
Login to view the detailed solution.
Among the following halogens $$F_2, Cl_2, Br_2$$ and $$I_2$$. Which can undergo disproportionation reactions?
Login to view the detailed solution.
Thiosulphate reacts differently with iodine and bromine in the reactions given below: $$2S_2O_3^{2-} + I_2 \rightarrow S_4O_6^{2-} + 2I^-$$, $$S_2O_3^{2-} + 5Br_2 + 5H_2O \rightarrow 2SO_4^{2-} + 4Br^- + 10H^+$$. Which of the following statement justifies the above dual behaviour of thiosulphate?
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: The stability order of +1 oxidation state of Ga, In and Tl is $$Ga < In < Tl$$. Reason R: The inert pair effect stabilizes the lower oxidation state down the group. In the light of the above statements, choose the correct answer from the options given below:
Which of the following are aromatic?
Given below are two statements:
Statement I: IUPAC name of Compound A is 4-chloro-1,3-dinitrobenzene.
Statement II: IUPAC name of Compound B is 4-ethyl-2-methylaniline. In the light of the above statements, choose the most appropriate answer from the options given below:
In the given compound, the number of $$2°$$ carbon atom/s is _______.
Login to view the detailed solution.
Iron (III) catalyses the reaction between iodide and persulphate ions, in which
A. $$Fe^{3+}$$ oxidises the iodide ion
B. $$Fe^{3+}$$ oxidises the persulphate ion
C. $$Fe^{2+}$$ reduces the iodide ion
D. $$Fe^{2+}$$ reduces the persulphate ion.
Choose the most appropriate answer from the options given below:
Login to view the detailed solution.
Number of Complexes with even number of electrons in $$t_{2g}$$ orbitals is - $$[Fe(H_2O)_6]^{2+}$$, $$[Co(H_2O)_6]^{2+}$$, $$[Co(H_2O)_6]^{3+}$$, $$[Cu(H_2O)_6]^{2+}$$, $$[Cr(H_2O)_6]^{2+}$$
Login to view the detailed solution.
An octahedral complex with the formula $$CoCl_3 \cdot nNH_3$$ upon reaction with excess of $$AgNO_3$$ solution gives 2 moles of $$AgCl$$. Consider the oxidation state of $$Co$$ in the complex is '$$x$$'. The value of "$$x + n$$" is ______
Login to view the detailed solution.
Which among the following compounds will undergo fastest $$S_N2$$ reaction.
Login to view the detailed solution.
Identify the major products A and B respectively in the following set of reactions.
Login to view the detailed solution.
Identify the product (P) in the following reaction:
Login to view the detailed solution.
Match List I with List II
Choose the correct answer from the options given below:
The incorrect statement regarding the given structure is
A hypothetical electromagnetic wave is shown below. The frequency of the wave is $$x \times 10^{19}$$ Hz. $$x =$$ ______ (nearest integer)
Login to view the detailed solution.
Number of molecules from the following which are exceptions to octet rule is ______ $$CO_2$$, $$NO_2$$, $$H_2SO_4$$, $$BF_3$$, $$CH_4$$, $$SiF_4$$, $$ClO_2$$, $$PCl_5$$, $$BeF_2$$, $$C_2H_6$$, $$CHCl_3$$, $$CBr_4$$
Login to view the detailed solution.
Consider the figure provided. 1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at $$18°C$$. If the piston is moved to position B, keeping the temperature unchanged, then '$$x$$' L atm work is done in this reversible process. $$x =$$ ______ L atm. (nearest integer) [Given: Absolute temperature $$= °C + 273.15$$, $$R = 0.08206 \text{ L atm mol}^{-1} \text{K}^{-1}$$]
Login to view the detailed solution.
The number of optical isomers in following compound is: ________
A solution containing $$10 \text{ g}$$ of an electrolyte $$AB_2$$ in $$100 \text{ g}$$ of water boils at $$100.52°C$$. The degree of ionization of the electrolyte $$(\alpha)$$ is ______ $$\times 10^{-1}$$. (nearest integer) [Given: Molar mass of $$AB_2 = 200 \text{ g mol}^{-1}$$, $$K_b$$ (molal boiling point elevation const. of water) $$= 0.52 \text{ K kg mol}^{-1}$$, boiling point of water $$= 100°C$$; $$AB_2$$ ionises as $$AB_2 \rightarrow A^{2+} + 2B^-$$]
Login to view the detailed solution.
Consider the following reaction $$A + B \rightarrow C$$. The time taken for A to become $$1/4^{th}$$ of its initial concentration is twice the time taken to become $$1/2$$ of the same. Also, when the change of concentration of $$B$$ is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis. The overall order of the reaction is ________
Login to view the detailed solution.
The 'spin only' magnetic moment value of $$MO_4^{2-}$$ is ______ BM. (Where M is a metal having least metallic radii among $$Sc, Ti, V, Cr, Mn$$ and $$Zn$$). (Given atomic number: $$Sc = 21, Ti = 22, V = 23, Cr = 24, Mn = 25$$ and $$Zn = 30$$)
Login to view the detailed solution.
Major product $$B$$ of the following reaction has ______ $$\pi$$-bond.
Login to view the detailed solution.
If $$279 \text{ g}$$ of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be ______ g. (nearest integer) (consider complete conversion).
Login to view the detailed solution.
Number of amine compounds from the following giving solids which are soluble in NaOH upon reaction with Hinsberg's reagent is ________
The sum of all the solutions of the equation $$(8)^{2x} - 16 \cdot (8)^x + 48 = 0$$ is :
Login to view the detailed solution.
Let $$z$$ be a complex number such that $$|z + 2| = 1$$ and $$\text{Im}\left(\frac{z+1}{z+2}\right) = \frac{1}{5}$$. Then the value of $$|\text{Re}(z + 2)|$$ is
Login to view the detailed solution.
If the set $$R = \{(a, b) : a + 5b = 42, a, b \in \mathbb{N}\}$$ has $$m$$ elements and $$\sum_{n=1}^{m}(1 - i^{n!}) = x + iy$$, where $$i = \sqrt{-1}$$, then the value of $$m + x + y$$ is
Login to view the detailed solution.
If $$\sin x = -\frac{3}{5}$$, where $$\pi < x < \frac{3\pi}{2}$$, then $$80(\tan^2 x - \cos x)$$ is equal to
Login to view the detailed solution.
The equations of two sides AB and AC of a triangle ABC are $$4x + y = 14$$ and $$3x - 2y = 5$$, respectively. The point $$\left(2, -\frac{4}{3}\right)$$ divides the third side BC internally in the ratio $$2 : 1$$. The equation of the side BC is
Login to view the detailed solution.
Let the circles $$C_1 : (x - \alpha)^2 + (y - \beta)^2 = r_1^2$$ and $$C_2 : (x - 8)^2 + \left(y - \frac{15}{2}\right)^2 = r_2^2$$ touch each other externally at the point $$(6, 6)$$. If the point $$(6, 6)$$ divides the line segment joining the centres of the circles $$C_1$$ and $$C_2$$ internally in the ratio $$2 : 1$$, then $$(\alpha + \beta) + 4(r_1^2 + r_2^2)$$ equals
Login to view the detailed solution.
Let $$H : \frac{-x^2}{a^2} + \frac{y^2}{b^2} = 1$$ be the hyperbola, whose eccentricity is $$\sqrt{3}$$ and the length of the latus rectum is $$4\sqrt{3}$$. Suppose the point $$(\alpha, 6), \alpha > 0$$ lies on $$H$$. If $$\beta$$ is the product of the focal distances of the point $$(\alpha, 6)$$, then $$\alpha^2 + \beta$$ is equal to
Login to view the detailed solution.
Let $$A = \begin{bmatrix} 2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b \end{bmatrix}$$. If $$A^3 = 4A^2 - A - 21I$$, where $$I$$ is the identity matrix of order $$3 \times 3$$, then $$2a + 3b$$ is equal to
Login to view the detailed solution.
Let $$[t]$$ be the greatest integer less than or equal to $$t$$. Let $$A$$ be the set of all prime factors of 2310 and $$f : A \rightarrow \mathbb{Z}$$ be the function $$f(x) = \left[\log_2\left(x^2 + \left[\frac{x^3}{5}\right]\right)\right]$$. The number of one-to-one functions from $$A$$ to the range of $$f$$ is
Login to view the detailed solution.
For the function $$f(x) = (\cos x) - x + 1, x \in \mathbb{R}$$, between the following two statements (S1) $$f(x) = 0$$ for only one value of $$x$$ in $$[0, \pi]$$. (S2) $$f(x)$$ is decreasing in $$\left[0, \frac{\pi}{2}\right]$$ and increasing in $$\left[\frac{\pi}{2}, \pi\right]$$.
Login to view the detailed solution.
Let $$f(x) = 4\cos^3 x + 3\sqrt{3}\cos^2 x - 10$$. The number of points of local maxima of $$f$$ in interval $$(0, 2\pi)$$ is
Login to view the detailed solution.
The number of critical points of the function $$f(x) = (x - 2)^{2/3}(2x + 1)$$ is
Login to view the detailed solution.
Let $$I(x) = \int \frac{6}{\sin^2 x (1 - \cot x)^2} dx$$. If $$I(0) = 3$$, then $$I\left(\frac{\pi}{12}\right)$$ is equal to
Login to view the detailed solution.
The value of $$k \in \mathbb{N}$$ for which the integral $$I_n = \int_0^1 (1 - x^k)^n dx, n \in \mathbb{N}$$, satisfies $$147I_{20} = 148I_{21}$$ is
Login to view the detailed solution.
Let $$f(x)$$ be a positive function such that the area bounded by $$y = f(x), y = 0$$ from $$x = 0$$ to $$x = a > 0$$ is $$e^{-a} + 4a^2 + a - 1$$. Then the differential equation, whose general solution is $$y = c_1 f(x) + c_2$$, where $$c_1$$ and $$c_2$$ are arbitrary constants, is
Login to view the detailed solution.
Let $$y = y(x)$$ be the solution of the differential equation $$(1 + y^2)e^{\tan x} dx + \cos^2 x(1 + e^{2\tan x}) dy = 0, y(0) = 1$$. Then $$y\left(\frac{\pi}{4}\right)$$ is equal to
Login to view the detailed solution.
The set of all $$\alpha$$, for which the vectors $$\vec{a} = \alpha t\hat{i} + 6\hat{j} - 3\hat{k}$$ and $$\vec{b} = t\hat{i} - 2\hat{j} - 2\alpha t\hat{k}$$ are inclined at an obtuse angle for all $$t \in \mathbb{R}$$, is
Login to view the detailed solution.
If the shortest distance between the lines $$L_1 : \vec{r} = (2 + \lambda)\hat{i} + (1 - 3\lambda)\hat{j} + (3 + 4\lambda)\hat{k}, \lambda \in \mathbb{R}$$ and $$L_2 : \vec{r} = 2(1 + \mu)\hat{i} + 3(1 + \mu)\hat{j} + (5 + \mu)\hat{k}, \mu \in \mathbb{R}$$ is $$\frac{m}{\sqrt{n}}$$, where $$\gcd(m, n) = 1$$, then the value of $$m + n$$ equals
Login to view the detailed solution.
Let $$P(x, y, z)$$ be a point in the first octant, whose projection in the $$xy$$-plane is the point $$Q$$. Let $$OP = \gamma$$; the angle between $$OQ$$ and the positive $$x$$-axis be $$\theta$$; and the angle between $$OP$$ and the positive $$z$$-axis be $$\phi$$, where $$O$$ is the origin. Then the distance of $$P$$ from the $$x$$-axis is
Login to view the detailed solution.
Let the sum of two positive integers be 24. If the probability, that their product is not less than $$\frac{3}{4}$$ times their greatest possible product, is $$\frac{m}{n}$$, where $$\gcd(m, n) = 1$$, then $$n - m$$ equals
Login to view the detailed solution.
The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to ________
Login to view the detailed solution.
Let the positive integers be written in the form:
If the $$k^{th}$$ row contains exactly $$k$$ numbers for every natural number $$k$$, then the row in which the number 5310 will be, is ________
Login to view the detailed solution.
Let $$\alpha = \sum_{r=0}^{n}(4r^2 + 2r + 1)^nC_r$$ and $$\beta = \left(\sum_{r=0}^{n}\frac{^nC_r}{r+1}\right) + \frac{1}{n+1}$$. If $$140 < \frac{2\alpha}{\beta} < 281$$, then the value of $$n$$ is ________
Login to view the detailed solution.
If the orthocentre of the triangle formed by the lines $$2x + 3y - 1 = 0$$, $$x + 2y - 1 = 0$$ and $$ax + by - 1 = 0$$, is the centroid of another triangle, whose circumcentre and orthocentre respectively are $$(3, 4)$$ and $$(-6, -8)$$, then the value of $$|a - b|$$ is ________
Login to view the detailed solution.
The value of $$\lim_{x \to 0} 2\left(\frac{1 - \cos x\sqrt{\cos 2x}\sqrt[3]{\cos 3x} \cdots \sqrt[10]{\cos 10x}}{x^2}\right)$$ is
Login to view the detailed solution.
Let $$A = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}$$. If the sum of the diagonal elements of $$A^{13}$$ is $$3^n$$, then $$n$$ is equal to ________
Login to view the detailed solution.
If the range of $$f(\theta) = \frac{\sin^4\theta + 3\cos^2\theta}{\sin^4\theta + \cos^2\theta}, \theta \in \mathbb{R}$$ is $$[\alpha, \beta]$$, then the sum of the infinite G.P., whose first term is 64 and the common ratio is $$\frac{\alpha}{\beta}$$, is equal to ________
Login to view the detailed solution.
Let the area of the region enclosed by the curve $$y = \min\{\sin x, \cos x\}$$ and the $$x$$ axis between $$x = -\pi$$ to $$x = \pi$$ be $$A$$. Then $$A^2$$ is equal to ________
Login to view the detailed solution.
Let $$\vec{a} = 9\hat{i} - 13\hat{j} + 25\hat{k}$$, $$\vec{b} = 3\hat{i} + 7\hat{j} - 13\hat{k}$$ and $$\vec{c} = 17\hat{i} - 2\hat{j} + \hat{k}$$ be three given vectors. If $$\vec{r}$$ is a vector such that $$\vec{r} \times \vec{a} = (\vec{b} + \vec{c}) \times \vec{a}$$ and $$\vec{r} \cdot (\vec{b} - \vec{c}) = 0$$, then $$\frac{|593\vec{r} + 67\vec{a}|^2}{(593)^2}$$ is equal to ________
Login to view the detailed solution.
Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $$X$$ and $$Y$$ respectively denote the number of blue and yellow balls. If $$\bar{X}$$ and $$\bar{Y}$$ are the means of $$X$$ and $$Y$$ respectively, then $$7\bar{X} + 4\bar{Y}$$ is equal to ________
Login to view the detailed solution.
Educational materials for JEE preparation
Share