NTA JEE Main 26th February 2021 Shift 2

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NTA JEE Main 26th February 2021 Shift 2 - Question 3

A scooter accelerates from rest for time $$t_1$$ at constant rate $$a_1$$ and then retards at constant rate $$a_2$$ for time $$t_2$$ and comes to rest. The correct value of $$\frac{t_1}{t_2}$$ will be:

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NTA JEE Main 26th February 2021 Shift 2 - Question 4

The trajectory of a projectile in a vertical plane is $$y = \alpha x - \beta x^2$$, where $$\alpha$$ and $$\beta$$ are constants and $$x$$ & $$y$$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $$\theta$$ and the maximum height attained $$H$$ are respectively given by

NTA JEE Main 26th February 2021 Shift 2 - Question 5

An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field 200 $$\frac{N}{C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.
[g = 9.8 m $$s^{-2}$$; $$\sin 30^{\circ} =\frac{1}{2}$$; $$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$$] 

NTA JEE Main 26th February 2021 Shift 2 - Question 6

Two masses $$A$$ and $$B$$, each of mass $$M$$ are fixed together by a massless spring. A force acts on the mass $$B$$ as shown in figure. If the mass $$A$$ starts moving away from mass $$B$$ with acceleration $$a$$, then the acceleration of mass $$B$$ will be:

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NTA JEE Main 26th February 2021 Shift 2 - Question 7

A cord is wound round the circumference of wheel of radius $$r$$. The axis of the wheel is horizontal and the moment of inertia about it is $$I$$. A weight $$mg$$ is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be

NTA JEE Main 26th February 2021 Shift 2 - Question 8

The length of metallic wire is $$l_1$$ when tension in it is $$T_1$$. It is $$l_2$$ when the tension is $$T_2$$. The original length of the wire will be:

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NTA JEE Main 26th February 2021 Shift 2 - Question 10

Given below are two statements:
Statement I: A second's pendulum has a time period of 1 second.
Statement II: It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below

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NTA JEE Main 26th February 2021 Shift 2 - Question 13

Given below are two statements
Statement I: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.
Statement II: If $$R$$ is the radius of a solid metallic sphere and $$Q$$ be the total charge on it. The electric field at any point on the spherical surface of radius $$r (< R)$$ is zero but the electric flux passing through this closed spherical surface of radius $$r$$ is not.
In the light of the above statements, choose the correct answer from the options given below:

NTA JEE Main 26th February 2021 Shift 2 - Question 14

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km h$$^{-1}$$ in a horizontal direction. The total intensity of earth's field at that part is $$2.5 \times 10^{-4}$$ Wb m$$^{-2}$$ and the angle of dip is 60°. The emf induced between the tips of the plane wings will be

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NTA JEE Main 26th February 2021 Shift 2 - Question 16

Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R: Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:

NTA JEE Main 26th February 2021 Shift 2 - Question 17

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ respectively. Then choose the correct relation for these vectors.

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NTA JEE Main 26th February 2021 Shift 2 - Question 19

A radioactive sample is undergoing $$\alpha$$ decay. At any time $$t_1$$, its activity is $$A$$ and another time $$t_2$$, the activity is $$\frac{A}{5}$$. What is the average life time for the sample?

NTA JEE Main 26th February 2021 Shift 2 - Question 21

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of $$OA : AB$$ will be $$x : 5$$. The value of $$x$$ is ______

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NTA JEE Main 26th February 2021 Shift 2 - Question 22

1 mole of rigid diatomic gas performs a work of $$\frac{Q}{5}$$ when heat $$Q$$ is supplied to it. The molar heat capacity of the gas during this transformation is $$\frac{xR}{8}$$. The value of $$x$$ is
[$$R$$ universal gas constant]

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NTA JEE Main 26th February 2021 Shift 2 - Question 23

The volume $$V$$ of a given mass of monoatomic gas changes with temperature $$T$$ according to the relation $$V = KT^{\frac{2}{3}}$$. The workdone when temperature changes by 90 K will be $$xR$$. The value of $$x$$ is [R universal gas constant]

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NTA JEE Main 26th February 2021 Shift 2 - Question 27

A point source of light S, placed at a distance 60 cm infront of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is ______ cm

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NTA JEE Main 26th February 2021 Shift 2 - Question 28

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $$x : 3$$. The value of $$x$$ is

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NTA JEE Main 26th February 2021 Shift 2 - Question 33

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In $$TlI_3$$, isomorphous to $$CsI_3$$, the metal is present in +1 oxidation state.
Reason R: Tl metal has fourteen f electrons in its electronic configuration.
In the light of the above statements, choose the most appropriate answer from the options given below:

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NTA JEE Main 26th February 2021 Shift 2 - Question 34

Match List-I with List-II.

List-I (Molecule)List-II (Bond order)
(a) $$Ne_2$$(i) 1
(b) $$N_2$$(ii) 2
(c) $$F_2$$(iii) 0
(d) $$O_2$$(iv) 3

Choose the correct answer from the options given below:
NTA JEE Main 26th February 2021 Shift 2 - Question 35

Calgon is used for water treatment. Which of the following statement is NOT true about Calgon?

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NTA JEE Main 26th February 2021 Shift 2 - Question 39

Match List-I with List-II.

List-IList-II
(a) Sodium Carbonate(i) Deacon
(b) Titanium(ii) Castner-Kellner
(c) Chlorine(iii) van-Arkel
(d) Sodium hydroxide(iv) Solvay

Choose the correct answer from the options given below:
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NTA JEE Main 26th February 2021 Shift 2 - Question 40

Match List-I with List-II.

List-I (Ore)List-II (Metal)
(a) Siderite(i) Cu
(b) Calamine(ii) Ca
(c) Malachite(iii) Fe
(d) Cryolite(iv) Al
(v) Zn

Choose the correct answer from the options given below:
NTA JEE Main 26th February 2021 Shift 2 - Question 41

Match List-I with List-II.

image

Choose the correct answer from the options given below :

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NTA JEE Main 26th February 2021 Shift 2 - Question 47

Ceric ammonium nitrate and $$CHCl_3$$ / alc. KOH are used for the identification of functional groups present in ______ and ______ respectively.

NTA JEE Main 26th February 2021 Shift 2 - Question 48

A. Phenyl methanamine
B. N, N-Dimethylaniline
C. N-Methyl aniline
D. Benzenamine
Choose the correct order of basic nature of the above amines.

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NTA JEE Main 26th February 2021 Shift 2 - Question 49

Match List-I with List-II.

List-IList-II
(a) Sucrose(i) $$\beta$$-D-Galactose and $$\beta$$-D-Glucose
(b) Lactose(ii) $$\alpha$$-D-Glucose and $$\beta$$-D-Fructose
(c) Maltose(iii) $$\alpha$$-D-Glucose and $$\alpha$$-D-Glucose

Choose the correct answer from the options given below:
NTA JEE Main 26th February 2021 Shift 2 - Question 51

The $$NaNO_3$$ weighed out to make 50 mL of an aqueous solution containing 70.0 mg Na$$^+$$ per mL is ______ g.
(Rounded off to the nearest integer) [Given: Atomic weight in g mol$$^{-1}$$ - Na: 23; N: 14; O: 16]

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NTA JEE Main 26th February 2021 Shift 2 - Question 52

A ball weighing 10 g is moving with a velocity of 90 m s$$^{-1}$$. If the uncertainty in its velocity is 5%, then the uncertainty in its position is ______ $$\times 10^{-33}$$ m. (Rounded off to the nearest integer)
[Given: h = $$6.63 \times 10^{-34}$$ Js]

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NTA JEE Main 26th February 2021 Shift 2 - Question 53

The average S - F bond energy in kJ mol$$^{-1}$$ of $$SF_6$$ is ______. (Rounded off to the nearest integer)
[Given: The values of standard enthalpy of formation of $$SF_6(g)$$, $$S(g)$$ and $$F(g)$$ are $$-1100$$, 275 and 80 kJ mol$$^{-1}$$ respectively.]

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NTA JEE Main 26th February 2021 Shift 2 - Question 57

When 12.2 g of benzoic acid is dissolved in 100 g of water, the freezing point of solution was found to be $$-0.93$$ °C ($$K_f(H_2O) = 1.86$$ K kg mol$$^{-1}$$). The number (n) of benzoic acid molecules associated (assuming 100% association) is ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 58

Emf of the following cell at 298 K in V is $$x \times 10^{-2}$$
$$Zn|Zn^{2+}(0.1M)||Ag^+(0.01M)|Ag$$
The value of $$x$$ is ______ (Rounded off to the nearest integer)
[Given: $$E^\theta_{Zn^{2+}/Zn} = -0.76$$ V; $$E^\theta_{Ag^+/Ag} = +0.80$$ V; $$\frac{2.303RT}{F} = 0.059$$]

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NTA JEE Main 26th February 2021 Shift 2 - Question 59

If the activation energy of a reaction is 80.9 kJ mol$$^{-1}$$, the fraction of molecules at 700 K, having enough energy to react to form products is $$e^{-x}$$. The value of $$x$$ is (Rounded off to the nearest integer) [Use R = 8.31 J K$$^{-1}$$ mol$$^{-1}$$]

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NTA JEE Main 26th February 2021 Shift 2 - Question 61

A natural number has prime factorization given by $$n = 2^x 3^y 5^z$$, where $$y$$ and $$z$$ are such that $$y + z = 5$$ and $$y^{-1} + z^{-1} = \frac{5}{6}$$, $$y > z$$. Then the number of odd divisors of $$n$$, including 1, is:

NTA JEE Main 26th February 2021 Shift 2 - Question 62

The sum of the series $$\sum_{n=1}^{\infty} \frac{n^2 + 6n + 10}{(2n+1)!}$$ is equal to

NTA JEE Main 26th February 2021 Shift 2 - Question 63

If $$0 < a, b < 1$$, and $$\tan^{-1}a + \tan^{-1}b = \frac{\pi}{4}$$, then the value of $$(a+b) - \left(\frac{a^2 + b^2}{2}\right) + \left(\frac{a^3 + b^3}{3}\right) - \left(\frac{a^4 + b^4}{4}\right) + \ldots$$ is:

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NTA JEE Main 26th February 2021 Shift 2 - Question 65

Let $$A(1, 4)$$ and $$B(1, -5)$$ be two points. Let $$P$$ be a point on the circle $$(x-1)^2 + (y-1)^2 = 1$$, such that $$(PA)^2 + (PB)^2$$ have maximum value, then the points $$P$$, $$A$$ and $$B$$ lie on

NTA JEE Main 26th February 2021 Shift 2 - Question 66

Let $$f(x)$$ be a differentiable function at $$x = a$$ with $$f'(a) = 2$$ and $$f(a) = 4$$. Then $$\lim_{x \to a} \frac{xf(a) - af(x)}{x - a}$$ equals:

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NTA JEE Main 26th February 2021 Shift 2 - Question 67

Let $$F_1(A, B, C) = (A \wedge \sim B) \vee [\sim C \wedge (A \vee B)] \vee \sim A$$ and $$F_2(A, B) = (A \vee B) \vee (B \to \sim A)$$ be two logical expressions. Then:

NTA JEE Main 26th February 2021 Shift 2 - Question 68

Consider the following system of equations:
$$x + 2y - 3z = a$$
$$2x + 6y - 11z = b$$
$$x - 2y + 7z = c$$
where $$a, b$$ and $$c$$ are real constants. Then the system of equations:

NTA JEE Main 26th February 2021 Shift 2 - Question 69

Let $$A = \{1, 2, 3, \ldots, 10\}$$ and $$f : A \to A$$ be defined as
$$f(k) = \begin{cases} k + 1 & \text{if } k \text{ is odd} \\ k & \text{if } k \text{ is even} \end{cases}$$
Then the number of possible functions $$g : A \to A$$ such that $$gof = f$$ is:

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NTA JEE Main 26th February 2021 Shift 2 - Question 70

Let $$f(x) = \sin^{-1}x$$ and $$g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}$$. If $$g(2) = \lim_{x \to 2} g(x)$$, then the domain of the function $$fog$$ is

NTA JEE Main 26th February 2021 Shift 2 - Question 71

Let $$f: R \to R$$ be defined as $$f(x) = \begin{cases} 2\sin\left(-\frac{\pi x}{2}\right), & \text{if } x < -1 \\ |ax^2 + x + b|, & \text{if } -1 \leq x \leq 1 \\ \sin(\pi x), & \text{if } x > 1 \end{cases}$$
If $$f(x)$$ is continuous on $$R$$, then $$a + b$$ equals:

NTA JEE Main 26th February 2021 Shift 2 - Question 72

The triangle of maximum area that can be inscribed in a given circle of radius 'r' is:

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NTA JEE Main 26th February 2021 Shift 2 - Question 75

Let $$A_1$$ be the area of the region bounded by the curves $$y = \sin x$$, $$y = \cos x$$ and $$y$$-axis in the first quadrant. Also, let $$A_2$$ be the area of the region bounded by the curves $$y = \sin x$$, $$y = \cos x$$, $$x$$-axis and $$x = \frac{\pi}{2}$$ in the first quadrant. Then,

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NTA JEE Main 26th February 2021 Shift 2 - Question 76

Let slope of the tangent line to a curve at any point $$P(x, y)$$ be given by $$\frac{xy^2 + y}{x}$$. If the curve intersects the line $$x + 2y = 4$$ at $$x = -2$$, then the value of $$y$$, for which the point $$(3, y)$$ lies on the curve, is:

NTA JEE Main 26th February 2021 Shift 2 - Question 77

If vectors $$\vec{a_1} = x\hat{i} - \hat{j} + \hat{k}$$ and $$\vec{a_2} = \hat{i} + y\hat{j} + z\hat{k}$$ are collinear, then a possible unit vector parallel to the vector $$x\hat{i} + y\hat{j} + z\hat{k}$$ is:

NTA JEE Main 26th February 2021 Shift 2 - Question 78

Let $$L$$ be a line obtained from the intersection of two planes $$x + 2y + z = 6$$ and $$y + 2z = 4$$. If point $$P(\alpha, \beta, \gamma)$$ is the foot of perpendicular from $$(3, 2, 1)$$ on $$L$$, then the value of $$21(\alpha + \beta + \gamma)$$ equals:

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NTA JEE Main 26th February 2021 Shift 2 - Question 81

Let $$\alpha$$ and $$\beta$$ be two real numbers such that $$\alpha + \beta = 1$$ and $$\alpha\beta = -1$$. Let $$p_n = (\alpha)^n + (\beta)^n$$, $$p_{n-1} = 11$$ and $$p_{n+1} = 29$$ for some integer $$n \geq 1$$. Then, the value of $$p_n^2$$ is ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 82

Let $$z$$ be those complex numbers which satisfy $$|z + 5| \leq 4$$ and $$z(1 + i) + \bar{z}(1 - i) \geq -10$$, $$i = \sqrt{-1}$$. If the maximum value of $$|z + 1|^2$$ is $$\alpha + \beta\sqrt{2}$$, then the value of $$(\alpha + \beta)$$ is

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NTA JEE Main 26th February 2021 Shift 2 - Question 86

Let $$X_1, X_2, \ldots, X_{18}$$ be eighteen observations such that $$\sum_{i=1}^{18}(X_i - \alpha) = 36$$ and $$\sum_{i=1}^{18}(X_i - \beta)^2 = 90$$, where $$\alpha$$ and $$\beta$$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of $$|\alpha - \beta|$$ is ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 87

If the matrix $$A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1 \end{bmatrix}$$ satisfies the equation $$A^{20} + \alpha A^{19} + \beta A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ for some real numbers $$\alpha$$ and $$\beta$$, then $$\beta - \alpha$$ is equal to ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 88

Let the normals at all the points on a given curve pass through a fixed point $$(a, b)$$. If the curve passes through $$(3, -3)$$ and $$(4, -2\sqrt{2})$$, given that $$a - 2\sqrt{2}b = 3$$, then $$(a^2 + b^2 + ab)$$ is equal to ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 89

Let $$a$$ be an integer such that all the real roots of the polynomial $$2x^5 + 5x^4 + 10x^3 + 10x^2 + 10x + 10$$ lie in the interval $$(a, a+1)$$. Then, $$|a|$$ is equal to ______.

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NTA JEE Main 26th February 2021 Shift 2 - Question 90

If $$I_{m,n} = \int_0^1 x^{m-1}(1-x)^{n-1}dx$$, for $$m, n \geq 1$$, and $$\int_0^1 \frac{x^{m-1} + x^{n-1}}{(1+x)^{m+n}} dx = \alpha I_{m,n}$$, $$\alpha \in R$$, then $$\alpha$$ equals ______.

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