Two projectiles are thrown with same initial velocity making an angle of $$45°$$ and $$30°$$ with the horizontal respectively. The ratio of their respective ranges will be
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.
Two projectiles are thrown with same initial velocity making an angle of $$45°$$ and $$30°$$ with the horizontal respectively. The ratio of their respective ranges will be
Login to view the detailed solution.
Two masses $$M_1$$ and $$M_2$$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $$M_2$$ is twice that of $$M_1$$, the acceleration of the system is $$a_1$$. When the mass $$M_2$$ is thrice that of $$M_1$$, the acceleration of the system is $$a_2$$. The ratio $$\dfrac{a_1}{a_2}$$ will be
Login to view the detailed solution.
A ball of mass $$0.15 \text{ kg}$$ hits the wall with its initial speed of $$12 \text{ m s}^{-1}$$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $$100 \text{ N}$$, calculate the time duration of the contact of ball with the wall.
Login to view the detailed solution.
.webp)
A body of mass $$8 \text{ kg}$$ and another of mass $$2 \text{ kg}$$ are moving with equal kinetic energy. The ratio of their respective momenta will be
Login to view the detailed solution.
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be (Take radius of earth $$= 6400 \text{ km}$$ and $$g = 10 \text{ m s}^{-2}$$)
Login to view the detailed solution.
The area of cross section of the rope used to lift a load by a crane is $$2.5 \times 10^{-4} \text{ m}^2$$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be (take $$g = 10 \text{ m s}^{-2}$$)
Login to view the detailed solution.
An ice cube of dimensions $$60 \text{ cm} \times 50 \text{ cm} \times 20 \text{ cm}$$ is placed in an insulation box of wall thickness $$1 \text{ cm}$$. The box keeping the ice cube at $$0°C$$ of temperature is brought to a room of temperature $$40°C$$. The rate of melting of ice is approximately: (Latent heat of fusion of ice is $$3.4 \times 10^5 \text{ J kg}^{-1}$$ and thermal conductivity of insulation wall is $$0.05 \text{ W m}^{-1} °C^{-1}$$)
Login to view the detailed solution.
A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be
Login to view the detailed solution.
A transverse wave is represented by $$y = 2\sin(\omega t - kx) \text{ cm}$$. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be
Login to view the detailed solution.
Two uniformly charged spherical conductors $$A$$ and $$B$$ of radii $$5 \text{ mm}$$ and $$10 \text{ mm}$$ are separated by a distance of $$2 \text{ cm}$$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $$A$$ and $$B$$ will be
Login to view the detailed solution.
A source of potential difference $$V$$ is connected to the combination of two identical capacitors as shown in the figure. When key $$K$$ is closed, the total energy stored across the combination is $$E_1$$. Now key $$K$$ is opened and dielectric of dielectric constant $$5$$ is introduced between the plates of the capacitors. The total energy stored across the combination is now $$E_2$$. The ratio $$\dfrac{E_1}{E_2}$$ will be
Login to view the detailed solution.
A battery of $$6 \text{ V}$$ is connected to the circuit as shown below. The current $$I$$ drawn from the battery is
Login to view the detailed solution.
Two concentric circular loops of radii $$r_1 = 30 \text{ cm}$$ and $$r_2 = 50 \text{ cm}$$ are placed in $$X-Y$$ plane as shown in the figure. A current $$I = 7 \text{ A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately
Login to view the detailed solution.
A velocity selector consists of electric field $$\vec{E} = E\hat{k}$$ and magnetic field $$\vec{B} = B\hat{j}$$ with $$B = 12 \text{ mT}$$. The value $$E$$ required for an electron of energy $$728 \text{ eV}$$ moving along the positive x-axis to pass undeflected is (Given, mass of electron $$= 9.1 \times 10^{-31} \text{ kg}$$)
Login to view the detailed solution.
The oscillating magnetic field in a plane electromagnetic wave is given by $$B_y = 5 \times 10^{-6} \sin[1000\pi(5x - 4 \times 10^8 t)] \text{ T}$$. The amplitude of electric field will be
Login to view the detailed solution.
Light travels in two media $$M_1$$ and $$M_2$$ with speeds $$1.5 \times 10^8 \text{ m s}^{-1}$$ and $$2.0 \times 10^8 \text{ m s}^{-1}$$ respectively. The critical angle between them is
Login to view the detailed solution.
A nucleus of mass $$M$$ at rest splits into two parts having masses $$\dfrac{M'}{3}$$ and $$\dfrac{2M'}{3}$$ ($$M' < M$$). The ratio of de Broglie wavelength of two parts will be
Login to view the detailed solution.
Mass numbers of two nuclei are in the ratio of $$4:3$$. Their nuclear densities will be in the ratio of
Login to view the detailed solution.
The maximum and minimum voltage of an amplitude modulated signal are $$60 \text{ V}$$ and $$20 \text{ V}$$ respectively. The percentage modulation index will be
Login to view the detailed solution.
In a Vernier Caliper 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $$1 \text{ mm}$$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:
Login to view the detailed solution.
If $$\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k} \text{ m}$$ and $$\vec{B} = \hat{i} + 2\hat{j} + 2\hat{k} \text{ m}$$. The magnitude of component of vector $$\vec{A}$$ along vector $$\vec{B}$$ will be ______ m.
Login to view the detailed solution.
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______ m. Given, the length of the rod is $$10\sqrt{3} \text{ m}$$.
Login to view the detailed solution.
A uniform heavy rod of mass $$20 \text{ kg}$$, cross sectional area $$0.4 \text{ m}^2$$ and length $$20 \text{ m}$$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $$x \times 10^{-9} \text{ m}$$. The value of $$x$$ is ______. (Given: Young's modulus $$Y = 2 \times 10^{11} \text{ N m}^{-2}$$ and $$g = 10 \text{ m s}^{-2}$$)
Login to view the detailed solution.
As per given figures, two springs of spring constants $$K$$ and $$2K$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3 \text{ s}$$, then the period of oscillation in figure (b) will be $$\sqrt{x} \text{ s}$$. The value of $$x$$ is ______.
Login to view the detailed solution.
Three point charges of magnitude $$5 \mu C$$, $$0.16 \mu C$$ and $$0.3 \mu C$$ are located at the vertices $$A$$, $$B$$, $$C$$ of a right angled triangle whose sides are $$AB = 3 \text{ cm}$$, $$BC = 3\sqrt{2} \text{ cm}$$ and $$CA = 3 \text{ cm}$$ and point $$A$$ is the right angle corner. Charge at point $$A$$ experiences ______ N of electrostatic force due to the other two charges.
Login to view the detailed solution.
A potentiometer wire of length $$300 \text{ cm}$$ is connected in series with a resistance $$780 \Omega$$ and a standard cell of emf $$4 \text{ V}$$. A constant current flows through potentiometer wire. The length of the null point for cell of emf $$20 \text{ mV}$$ is found to be $$60 \text{ cm}$$. The resistance of the potentiometer wire is ______ $$\Omega$$.
Login to view the detailed solution.
In a coil of resistance $$8 \Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi = \dfrac{2}{3}(9 - t^2)$$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.
Login to view the detailed solution.
In the given figure, the face $$AC$$ of the equilateral prism is immersed in a liquid of refractive index $$n$$. For incident angle $$60°$$ at the side $$AC$$, the refracted light beam just grazes along face $$AC$$. The refractive index of the liquid $$n = \dfrac{\sqrt{x}}{4}$$. The value of $$x$$ is ______. (Given refractive index of glass $$= 1.5$$)
Login to view the detailed solution.
Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
$$_1^2X + _1^2X = _2^4Y$$
The binding energies per nucleon of $$_1^2X$$ and $$_2^4Y$$ are $$1.1 \text{ MeV}$$ and $$7.6 \text{ MeV}$$ respectively. The energy released in this process is ______ MeV.
Login to view the detailed solution.
The typical transfer characteristic of a transistor in CE configuration is shown in figure. A load resistor of $$2 \text{ k}\Omega$$ is connected in the collector branch of the circuit used. The input resistance of the transistor is $$0.50 \text{ k}\Omega$$. The voltage gain of the transistor is ______.
Login to view the detailed solution.
Hemoglobin contains $$0.34\%$$ of iron by mass. The number of Fe atoms in $$3.3 \text{ g}$$ of hemoglobin is (Given: Atomic mass of Fe is $$56u$$, $$N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$$)
Login to view the detailed solution.
The metal that has very low melting point and its periodic position is closer to a metalloid is
Login to view the detailed solution.
Arrange the following in increasing order of their covalent character.
(A) $$CaF_2$$
(B) $$CaCl_2$$
(C) $$CaBr_2$$
(D) $$CaI_2$$
Choose the correct answer from the options given below.
Login to view the detailed solution.
Class XII students were asked to prepare one litre of buffer solution of pH $$8.26$$ by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in $$0.2M$$ ammonia solution to make one litre of the buffer is (Given $$pK_b(NH_3) = 4.74$$; Molar mass of $$NH_3 = 17 \text{ g mol}^{-1}$$. Molar mass of $$NH_4Cl = 53.5 \text{ g mol}^{-1}$$)
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: Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium.
Reason R: Phenolphthalein is a weak acid. It doesn't dissociate in basic medium.
In the light of the above statements, choose the most appropriate answer from the options given below
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: LiF is sparingly soluble in water.
Reason R: The ionic radius of $$Li^+$$ ion is smallest among its group members, hence has least hydration enthalpy.
In the light of the above statements, choose the most appropriate answer from the options given below.
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: Boric acid is a weak acid.
Reason R: Boric acid is not able to release $$H^+$$ ion on its own. It receives $$OH^-$$ ion from water and releases $$H^+$$ ion.
In the light of the above statements, choose the most appropriate answer from the options given below.
Login to view the detailed solution.
The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is
Login to view the detailed solution.
Which of the following is not an example of benzenoid compound?
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.
At $$30°C$$, the half life for the decomposition of $$AB_2$$ is $$200 \text{ s}$$ and is independent of the initial concentration of $$AB_2$$. The time required for $$80\%$$ of the $$AB_2$$ to decompose is (Given: $$\log 2 = 0.30$$; $$\log 3 = 0.48$$)
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: Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold.
Reason R: The colour of the colloidal solution depends on the wavelength of light scattered by the dispersed particles.
In the light of the above statements, choose the most appropriate answer from the options given below
Login to view the detailed solution.
The metal that is not extracted from its sulphide ore is
Login to view the detailed solution.
The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are
Login to view the detailed solution.
The metal complex that is diamagnetic is (Atomic number: Fe, 26; Cu, 29)
Login to view the detailed solution.
Consider the above reaction and predict the major product.
Login to view the detailed solution.
Hydrolysis of which compound will give carbolic acid?
Login to view the detailed solution.
The correct sequential order of the reagents for the given reaction is
Login to view the detailed solution.
Vulcanization of rubber is carried out by heating a mixture of
Login to view the detailed solution.
Animal starch is the other name of
Login to view the detailed solution.
Consider an imaginary ion $$_{22}^{48}X^{3-}$$. The nucleus contains '$$a$$' $$\%$$ more neutrons than the number of electrons in the ion. The value of '$$a$$' is ______.
Login to view the detailed solution.
A $$10 \text{ g}$$ mixture of hydrogen and helium is contained in a vessel of capacity $$0.0125 \text{ m}^3$$ at $$6 \text{ bar}$$ and $$27°C$$. The mass of helium in the mixture is ______ g. (Given: $$R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$$)(Atomic masses of H and He are 1u and 4u, respectively)
Login to view the detailed solution.
For the reaction $$H_2F_2(g) \rightarrow H_2(g) + F_2(g)$$
$$\Delta U = -59.6 \text{ kJ mol}^{-1}$$ at $$27°C$$
The enthalpy change for the above reaction is $$-$$ ______ $$\text{kJ mol}^{-1}$$ (nearest integer) (Given: $$R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$$)
Login to view the detailed solution.
$$20 \text{ mL}$$ of $$0.02M$$ hypo solution is used for the titration of $$10 \text{ mL}$$ of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of $$Cu^{2+}$$ is found to be ______ $$\times 10^{-2} M$$ (nearest integer)
Given : $$2Cu^{2+}+4I^{-}\rightarrow Cu_{2}I_{2} + I_{2}I_{2} + 2S_{2}O_{3}^{-2} \rightarrow 2I^{-} + S_{4}O_{6}^{-2}$$
Login to view the detailed solution.
The elevation in boiling point for 1 molal solution of non-volatile solute A is $$3 \text{ K}$$. The depression in freezing point for 2 molal solution of A in the same solvent is $$6 \text{ K}$$. The ratio of $$K_b$$ and $$K_f$$ i.e., $$K_b/K_f$$ is $$1:X$$. The value of $$X$$ is ______.
Login to view the detailed solution.
The number of non-ionisable protons present in the product B obtained from the following reaction is ______
$$C_2H_5OH + PCl_3 \rightarrow C_2H_5Cl + A$$
$$A + PCl_3 \rightarrow B$$
Login to view the detailed solution.
The spin-only magnetic moment value of the compound with strongest oxidizing ability among $$MnF_4$$, $$MnF_3$$ and $$MnF_2$$ is ______ B.M. (nearest integer)
Login to view the detailed solution.
Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is ______.
Login to view the detailed solution.
A $$100 \text{ mL}$$ solution of $$CH_3CH_2MgBr$$ on treatment with methanol produces $$2.24 \text{ mL}$$ of a gas at STP. The weight of gas produced is ______ mg (nearest integer).
Login to view the detailed solution.
How many of the following drugs is/are example(s) of broad spectrum antibiotic? Ofloxacin, Penicillin G, Terpineol, Salvarsan
Login to view the detailed solution.
The minimum value of the sum of the squares of the roots of $$x^2 + (3-a)x = 2(a-1)$$ is
Login to view the detailed solution.
If $$z = x + iy$$ satisfies $$z - 2 = 0$$ and $$z-i - z+5i = 0$$, then
Login to view the detailed solution.
$$\displaystyle\sum_{\substack{i,j=0 \\ i \neq j}}^{n}$$ $$^n C_{i}$$ $$^n C_{j}$$ is equal to
Login to view the detailed solution.
Let the abscissae of the two points $$P$$ and $$Q$$ on a circle be the roots of $$x^2 - 4x - 6 = 0$$ and the ordinates of $$P$$ and $$Q$$ be the roots of $$y^2 + 2y - 7 = 0$$. If $$PQ$$ is a diameter of the circle $$x^2 + y^2 + 2ax + 2by + c = 0$$, then the value of $$a + b - c$$ is
Login to view the detailed solution.
The equation of a common tangent to the parabolas $$y = x^2$$ and $$y = -(x-2)^2$$ is
Login to view the detailed solution.
The acute angle between the pair of tangents drawn to the ellipse $$2x^2 + 3y^2 = 5$$ from the point $$(1, 3)$$ is
Login to view the detailed solution.
If the line $$x - 1 = 0$$ is a directrix of the hyperbola $$kx^2 - y^2 = 6$$, then the hyperbola passes through the point
Login to view the detailed solution.
Let $$\beta = \displaystyle\lim_{x \to 0} \dfrac{\alpha x - (e^{3x} - 1)}{\alpha x(e^{3x} - 1)}$$ for some $$\alpha \in \mathbb{R}$$. Then the value of $$\alpha + \beta$$ is:
Login to view the detailed solution.
Negation of the Boolean expression $$p \leftrightarrow (q \rightarrow p)$$ is
Login to view the detailed solution.
Let $$A = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$$ and $$B = \begin{pmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & -14^2 \\ -15^2 & 16^2 & 17^2 \end{pmatrix}$$, then the value of $$A'BA$$ is
Login to view the detailed solution.
If $$0 < x < \dfrac{1}{\sqrt{2}}$$ and $$\dfrac{\sin^{-1}x}{\alpha} = \dfrac{\cos^{-1}x}{\beta}$$, then a value of $$\sin\dfrac{2\pi\alpha}{\alpha + \beta}$$ is
Login to view the detailed solution.
The value of $$\log_e 2 \cdot \dfrac{d}{dx}(\log_{\cos x} \cosec x)$$ at $$x = \dfrac{\pi}{4}$$ is
Login to view the detailed solution.
Let $$P$$ and $$Q$$ be any points on the curves $$(x-1)^2 + (y+1)^2 = 1$$ and $$y = x^2$$, respectively. The distance between $$P$$ and $$Q$$ is minimum for some value of the abscissa of $$P$$ in the interval
Login to view the detailed solution.
If the maximum value of $$a$$, for which the function $$f_a(x) = \tan^{-1}(2x) - 3ax + 7$$ is non-decreasing in $$\left(-\dfrac{\pi}{6}, \dfrac{\pi}{6}\right)$$, is $$\bar{a}$$, then $$f_{\bar{a}}\left(\dfrac{\pi}{8}\right)$$ is equal to
Login to view the detailed solution.
The integral $$\displaystyle\int \dfrac{1 - \dfrac{1}{\sqrt{3}}(\cos x - \sin x)}{1 + \dfrac{2}{\sqrt{3}}\sin 2x} dx$$ is equal to
Login to view the detailed solution.
$$\displaystyle\int_0^{20\pi} (|\sin x| + |\cos x|)^2 dx$$ is equal to:
Login to view the detailed solution.
The area bounded by the curves $$y = |x^2 - 1|$$ and $$y = 1$$ is
Login to view the detailed solution.
Let the solution curve $$y = f(x)$$ of the differential equation $$\dfrac{dy}{dx} + \dfrac{xy}{x^2 - 1} = \dfrac{x^4 + 2x}{\sqrt{1-x^2}}$$, $$x \in (-1, 1)$$ pass through the origin. Then $$\displaystyle\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) dx$$ is equal to
Login to view the detailed solution.
A vector $$\vec{a}$$ is parallel to the line of intersection of the plane determined by the vectors $$\hat{i}$$, $$\hat{i} + \hat{j}$$ and the plane determined by the vectors $$\hat{i} - \hat{j}$$, $$\hat{i} + \hat{k}$$. The obtuse angle between $$\vec{a}$$ and the vector $$\vec{b} = \hat{i} - 2\hat{j} + 2\hat{k}$$ is
Login to view the detailed solution.
Let $$X$$ be a binomially distributed random variable with mean $$4$$ and variance $$\dfrac{4}{3}$$. Then $$54 P(X \le 2)$$ is equal to
Login to view the detailed solution.
Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______.
Login to view the detailed solution.
If $$\displaystyle\sum_{k=1}^{10} \dfrac{k}{k^4 + k^2 + 1} = \dfrac{m}{n}$$, where $$m$$ and $$n$$ are co-prime, then $$m + n$$ is equal to ______.
Login to view the detailed solution.
Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ______.
Login to view the detailed solution.
If the sum of solutions of the system of equations $$2\sin^2\theta - \cos 2\theta = 0$$ and $$2\cos^2\theta + 3\sin\theta = 0$$ in the interval $$[0, 2\pi]$$ is $$k\pi$$, then $$k$$ is equal to ______.
Login to view the detailed solution.
The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $$\sigma$$ is the standard deviation of the data after omitting the two wrong observations from the data, then $$38\sigma^2$$ is equal to ______.
Login to view the detailed solution.
Let 𝐴 = {1, 2, 3, 4, 5, 6, 7} and 𝐵 = {3, 6, 7, 9}. Then the number of elements in the set $$C \subseteq A : C \cap B \neq \phi$$ is
Login to view the detailed solution.
The number of matrices $$A=\begin{bmatrix}a & b \\c & d \end{bmatrix}$$, where $$𝑎, 𝑏, 𝑐, d ∈ -1, 0, 1, 2, 3, … … , 10,$$ such that $$A=A^{-1}$$, is______.
Login to view the detailed solution.
Suppose $$𝑦 = 𝑦𝑥$$ be the solution curve to the differential equation $$\frac{dy}{dx}-y=2-e^{-x}$$ such that $$\lim_{x \rightarrow \infty} yx$$ If $$𝑎$$ and $$𝑏$$ are respectively the $$𝑥 -$$ and $$𝑦 -$$ intercept of the tangent to the curve at $$𝑥 = 0$$, then the value of $$𝑎 - 4𝑏$$ is equal to _______.
Login to view the detailed solution.
The largest value of $$𝑎$$, for which the perpendicular distance of the plane containing the lines $$\vec{r} = \hat{i} + \hat{j} + \lambda( \hat{i} + a \hat{j} - \hat{k} )\quad \text{and} \quad \vec{r} = \hat{i} + \hat{j} + \mu (\hat{i} + \hat{j} - a \hat{k})$$ from the point 2, 1, 4 is $$\sqrt{3}$$, is
Login to view the detailed solution.
The plane passing through the line $$L:l 𝑥 - 𝑦 + 3(1 - 𝑙 )𝑧 = 1, 𝑥 + 2𝑦 - 𝑧 = 2$$ and perpendicular to the plane $$3𝑥 + 2𝑦 + 𝑧 = 6$$ is $$3𝑥 - 8𝑦 + 7𝑧 = 4$$. If $$\theta$$ is the acute angle between the line $$𝐿$$ and the 𝑦-axis, then $$415 \cos^{2}\theta $$ is equal to_______.
Login to view the detailed solution.
Educational materials for JEE preparation
Share