NTA JEE Main 8th April2023 Shift 1

NTA JEE Main 8th April2023 Shift 1 - Question 1

Report

A cylindrical wire of mass $$(0.4 \pm 0.01)$$ g has length $$(8 \pm 0.04)$$ cm and radius $$(6 \pm 0.03)$$ mm. The maximum error in its density will be

A

3.5%

B

5%

C

1%

D

4%

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 2

Report

Two forces having magnitude A and $$\dfrac{A}{2}$$ are perpendicular to each other. The magnitude of their resultant is:

A

$$\dfrac{\sqrt{5}A}{4}$$

B

$$\dfrac{\sqrt{5}A}{2}$$

C

$$\dfrac{5A}{2}$$

D

$$\dfrac{\sqrt{5}A^2}{2}$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 3

Report

Dimension of $$\dfrac{1}{\mu_0 \varepsilon_0}$$ should be equal to

A

L T$$^{-1}$$

B

T$$^2$$ L$$^{-2}$$

C

L$$^2$$ T$$^{-2}$$

D

T L$$^{-1}$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 4

Report

Two projectiles A and B are thrown with initial velocities of 40 m s$$^{-1}$$ and 60 m s$$^{-1}$$ at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is $$(g = 10$$ m s$$^{-2}$$)

A

4 : 9

B

2 : $$\sqrt{3}$$

C

$$\sqrt{3}$$ : 2

D

1 : 1

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 5

Report

At any instant the velocity of a particle of mass 500 g is $$(2t\hat{i} + 3t^2\hat{j})$$ m s$$^{-1}$$. If the force acting on the particle at $$t = 1$$ s is $$(\hat{i} + x\hat{j})$$ N. Then the value of $$x$$ will be:

A

3

B

4

C

2

D

6

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 6

Report

Given below are two statements:
Statement I: If $$E$$ be the total energy of a satellite moving around the earth, then its potential energy will be $$\dfrac{E}{2}$$.
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $$E$$.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Statement I is correct but Statement II is incorrect

B

Statement I is incorrect but Statement II is correct

C

Both Statement I and Statement II are correct

D

Both Statement I and Statement II are incorrect

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 7

Report

The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

A

200 N

B

Zero

C

100 N

D

300 N

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 8

Report

An aluminium rod with Young's modulus $$Y = 7.0 \times 10^{10}$$ N m$$^{-2}$$ undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit

A

2800

B

11200

C

5600

D

8400

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 9

Report

An air bubble of volume 1 cm$$^3$$ rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is $$1 \times 10^5$$ Pa, the density of water is 1000 kg m$$^{-3}$$ and $$g = 10$$ m s$$^{-2}$$. There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be

A

2 cm$$^3$$

B

3 cm$$^3$$

C

4 cm$$^3$$

D

5 cm$$^3$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 10

Report

Given below are two statements:
Statement I: If heat is added to a system, its temperature must increase.
Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statements, choose the correct answer from the options given below

A

Statement I is true but Statement II is false

B

Both Statement I and Statement II are false

C

Both Statement I and Statement II are true

D

Statement I is false but Statement II is true

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 11

Report

The engine of a train moving with speed 10 m s$$^{-1}$$ towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is: (Neglect air speed. Speed of sound in air = 330 m s$$^{-1}$$)

A

400 Hz

B

200 Hz

C

412 Hz

D

388 Hz

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 12

Report

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the centre O is represented by:

A

B

C

D

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 13

Report

In this figure the resistance of the coil of galvanometer G is 2 $$\Omega$$. The emf of the cell is 4 V. The ratio of potential difference across C$$_1$$ and C$$_2$$ is

A

1

B

$$\dfrac{4}{5}$$

C

$$\dfrac{5}{4}$$

D

$$\dfrac{3}{4}$$

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 14

Report

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

A

to oscillate the coil in magnetic field for longer period of time

B

to bring the coil to rest quickly

C

to produce large deflecting torque on the coil

D

to make the magnetic field radial

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 15

Report

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

A

helical path with the axis perpendicular to the direction of magnetic field B

B

helical path with the axis along magnetic field B

C

circular path

D

straight along the direction of magnetic field B

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 16

Report

In a reflecting telescope, a secondary mirror is used to:

A

reduce the problem of mechanical support

B

make chromatic aberration zero

C

move the eyepiece outside the telescopic tube

D

remove spherical aberration

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 17

Report

Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $$m_p = 1849 m_e$$)

A

1 : 1

B

1 : 1849

C

1 : 43

D

43 : 1

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 18

Report

For a nucleus $$^A_Z X$$ having mass number A and atomic number Z
A. The surface energy per nucleon $$(b_s) = -a_1 A^{2/3}$$.
B. The Coulomb contribution to the binding energy $$b_c = -a_2 \dfrac{Z(Z-1)}{A^{1/3}}$$.
C. The volume energy $$b_v = a_3 A$$
D. Decrease in the binding energy is proportional to surface area.
E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. 

($$a_1, a_2$$ and $$a_3$$ are constants)
Choose the most appropriate answer from the options given below:

A

B, C, E only

B

B, C, D only

C

A, B, C, D only

D

B, C only

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 19

Report

For the logic circuit shown, the output waveform at Y is

A

B

C

D

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 20

Report

A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

A

1240 km$$^2$$

B

3942 km$$^2$$

C

4868 km$$^2$$

D

1549 km$$^2$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 21

Report

The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is ______%.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 22

Report

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $$\dfrac{1}{x}$$ MR$$^2$$, where R is the radius and M is the mass of the semicircular ring. The value of x will be ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 23

Report

An air bubble of diameter 6 mm rises steadily through a solution of density 1750 kg m$$^{-3}$$ at the rate of 0.35 cm s$$^{-1}$$. The co-efficient of viscosity of the solution (neglect density of air) is ________ Pas (given, $$g = 10$$ m s$$^{-2}$$).

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 24

Report

An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 m s$$^{-1}$$. The frequency of the second harmonic is ________ Hz.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 25

Report

An electric dipole of dipole moment is $$6.0 \times 10^{-6}$$ C m placed in a uniform electric field of $$1.5 \times 10^3$$ N C$$^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be ______ mJ.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 26

Report

A current of 2 A flows through a wire of cross-sectional area 25.0 mm$$^2$$. The number of free electrons in a cubic meter are $$2.0 \times 10^{28}$$. The drift velocity of the electrons is ______ $$\times 10^{-6}$$ ms$$^{-1}$$
(given, charge on electron = $$1.6 \times 10^{-19}$$ C).

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 27

Report

The magnetic intensity at the centre of a long current carrying solenoid is found to be $$1.6 \times 10^3$$ A m$$^{-1}$$. If the number of turns is 8 per cm, then the current flowing through the solenoid is ______ A.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 28

Report

An oscillating LC circuit consists of a 75 mH inductor and a 1.2 $$\mu$$F capacitor. If the maximum charge to the capacitor is 2.7 $$\mu$$C. The maximum current in the circuit will be ______ mA.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 29

Report

Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ______ cm.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 30

Report

A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is ______ MeV.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 31

Report

The correct order of electronegativity for given elements is

A

P > Br > C > At

B

Br > P > At > C

C

Br > C > At > P

D

C > P > At > Br

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 32

Report

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Butan-1-ol has higher boiling point than ethoxyethane.
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.
In the light of the above statements, choose the correct answer from the options given below :

A

A is true but R is false

B

Both A and R are true and R is the correct explanation of A

C

Both A and R are true but R is not the correct explanation of A

D

A is false but R is true

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 33

Report

$$2IO_3^- + xI^- + 12H^+ \rightarrow 6I_2 + 6H_2$$ What is the value of x?

A

2

B

12

C

10

D

6

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 34

Report

Given below are two statements:
Statement I: Lithium and Magnesium do not form superoxide
Statement II: The ionic radius of Li$$^+$$ is larger than ionic radius of Mg$$^{2+}$$
In the light of the above statements, choose the most appropriate answer from the questions given below:

A

Statement I is incorrect but Statement II is correct

B

Statement I is correct but Statement II is incorrect

C

Both statement I and Statement II are incorrect

D

Both Statement I and Statement II are correct

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 35

Report

What is the purpose of adding gypsum to cement?

A

To facilitate the hydration of cement

B

To slow down the process of setting

C

To give a hard mass

D

To speed up the process of setting

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 36

Report

Match List I with List II
List-I (Species)                           List-2 (Maximum allowed concentration in ppm in drinking water)
A. F$$^-$$                                              I. < 50 ppm
B. SO$$_4^{2-}$$                                         II. < 5 ppm
C. NO$$_3^-$$                                          III. < 2 ppm
D. Zn                                              IV. < 500 ppm
Choose the correct answer from the options given below.

A

A-I, B-II, C-III, D-IV

B

A-II, B-I, C-III, D-IV

C

A-IV, B-III, C-II, D-I

D

A-III, B-II, C-I, D-IV

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 37

Report

The reaction occurs in which of the given galvanic cell?
$$\dfrac{1}{2}H_2(g) + AgCl(s) \rightleftharpoons H^+(aq) + Cl^-(aq) + Ag(s)$$

A

Pt |H$$_2$$(g)| HCl(sol$$^n$$) |AgCl(s)| Ag

B

Ag |AgCl(s)| KCl(sol$$^n$$) |AgNO$$_3$$ |Ag

C

Pt |H$$_2$$(g)| HCl(sol$$^n$$) |AgNO$$_3$$(sol$$^n$$) |Ag

D

Pt |H$$_2$$(g)| KCl(sol$$^n$$) |AgCl(s) |Ag

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 38

Report

The water gas on reacting with cobalt as a catalyst forms

A

Methanal

B

Methanoic acid

C

Ethanol

D

Methanol

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 39

Report

Which of the following represents the Freundlich adsorption isotherms?
(A)

(B)

(C)

(D)

Choose the correct answer from the options given below:

A

A, C, D only

B

A, B only

C

B, C, D only

D

A, B, D only

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 40

Report

Which of the following metals can be extracted through alkali leaching technique?

A

Sn

B

Pb

C

Au

D

Cu

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 41

Report

In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti: 22, V: 23, Cr: 24, Mn: 25, Fe: 26)

A

V (IV)

B

Mn (VII)

C

Fe (III)

D

Ti (III)

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 42

Report

Which halogen is known to cause the reaction given below?

A

All halogens

B

Only Bromine

C

Only Iodine

D

Only Chlorine

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 43

Report

Which of the following complex is octahedral, diamagnetic and the most stable?

A

Na$$_3$$[CoCl$$_6$$]

B

[Ni(NH$$_3$$)$$_6$$] Cl$$_2$$

C

K$$_3$$[Co(CN)$$_6$$]

D

[Co(H$$_2$$O)$$_6$$] Cl$$_2$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 44

Report

The correct order of spin only magnetic moments for the following complex ions is

A

[Fe(CN)$$_6$$]$$^{3-}$$ < [CoF$$_6$$]$$^{3-}$$ < [MnBr$$_4$$]$$^{2-}$$ < [Mn(CN)$$_6$$]$$^{3-}$$

B

[CoF$$_6$$]$$^{3-}$$ < [MnBr$$_4$$]$$^{2-}$$ < [Fe(CN)$$_6$$]$$^{3-}$$ < [Mn(CN)$$_6$$]$$^{3-}$$

C

[Fe(CN)$$_6$$]$$^{3-}$$ < [Mn(CN)$$_6$$]$$^{3-}$$ < [CoF$$_6$$]$$^{3-}$$ < [MnBr$$_4$$]$$^{2-}$$

D

[MnBr$$_4$$]$$^{2-}$$ < [CoF$$_6$$]$$^{3-}$$ < [Fe(CN)$$_6$$]$$^{3-}$$ < [Mn(CN)$$_6$$]$$^{3-}$$

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 45

Report

Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D)
A.

B.

C.

D.

A

$$A - Br_{(b)}; B - I_{(a)}; C - Br_{(a)}; D - Br_{(a)}$$

B

$$A - Br_{(b)}; B - I_{(b)}; C - Br_{(b)}; D - Br_{(b)}$$

C

$$A - Br_{(a)}; B - I_{(a)}; C - Br_{(b)}; D - Br_{(a)}$$

D

$$A - Br_{(a)}; B - I_{(a)}; C - Br_{(a)}; D - Br_{(a)}$$

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 46

Report

The major product formed in the following reaction is

CO$$_2$$H + CO$$_2$$Et compound treated with (i) LiBH$$_4$$/EtOH (ii) H$$_3$$O$$^+$$

A

B

C

D

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 47

Report

Match List I with List II:

A

A-III, B-IV, C-I, D-II

B

A-III, B-IV, C-II, D-I

C

A-IV, B-I, C-II, D-III

D

A-II, B-IV, C-I, D-III

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 48

Report

Match List I with List II:

is reacted with reagents in List I to form products in List II

Choose the correct answer from the options given below:

A

A-IV, B-III, C-II, D-I

B

A-III, B-I, C-II, D-IV

C

A-I, B-III, C-IV, D-II

D

A-III, B-I, C-IV, D-II

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 49

Report

Match List I with List II
List I                             List II
A. Saccharin         I. High potency sweetener
B. Aspartame       II. First artificial sweetening agent
C. Alitame             III. Stable at cooking temperature
D. Sucralose         IV. Unstable at cooking temperature
Choose the correct answer from the options given below :

A

A-IV, B-III, C-I, D-II

B

A-II, B-III, C-IV, D-I

C

A-II, B-IV, C-III, D-I

D

A-II, B-IV, C-I, D-III

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 50

Report

Sulphur (S) containing amino acids from the following are:
(a) isoleucine
(b) cysteine
(c) lysine
(d) methionine
(e) glutamic acid

A

b, c, e

B

a, b, c

C

b, d

D

a, d

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 51

Report

0.5 g of an organic compound (X) with 60% carbon will produce ______ $$\times 10^{-1}$$ g of CO$$_2$$ on complete combustion.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 52

Report

The number of following statement/s which is/are incorrect is ______
A) Line emission spectra are used to study the electronic structure
B) The emission spectra of atoms in the gas phase show a continuous spread of wavelength from red to violet.
C) An absorption spectrum is like the photographic negative of an emission spectrum
D) The element helium was discovered in the sun by spectroscopic method

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 53

Report

The number of following factors which affect the percent covalent character of the ionic bond is______
A) Polarising power of cation
B) Extent of distortion of anion
C) Polarisability of the anion
D) Polarising power of anion

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 54

Report

Three bulbs are filled with CH$$_4$$, CO$$_2$$ and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be ______ atm. (Nearest integer).

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 55

Report

When a 60 W electric heater is immersed in a gas for 100 s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5°C. The heat capacity of the given gas is JK$$^{-1}$$ (Nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 56

Report

The titration curve of weak acid vs. strong base with phenolphthalein as indicator is shown below. The $$K_{phenolphthalein} = 4 × 10^{−10}$$
Given: $$log  2 = 0.3$$

The number of following statement/s which is/are correct about phenolphthalein is ______
A. It can be used as an indicator for the titration of weak acid with weak base.
B. It begins to change colour at pH = 8.4
C. It is a weak organic base
D. It is colourless in acidic medium

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 57

Report

Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole of O$$_3$$ per mole of (X) and gives one mole each of ethanal and propanone is ______ g mol$$^{-1}$$ (Molar mass of C: 12 g mol$$^{-1}$$, H: 1 g mol$$^{-1}$$)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 58

Report

The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is ______°C.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 59

Report

The number of given statement/s which is/are correct is______
(A) The stronger the temperature dependence of the rate constant, the higher is the activation energy.
(B) If a reaction has zero activation energy, its rate is independent of temperature.
(C) The stronger the temperature dependence of the rate constant, the smaller is the activation energy.
(D) If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 60

Report

XeF$$_4$$ reacts with SbF$$_5$$ to form [XeF$$_m$$]$$^{n+}$$[SbF$$_y$$]$$^{z-}$$. $$m + n + y + z$$ = ?

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 61

Report

Let $$\alpha, \beta, \gamma$$ be the three roots of the equation $$x^3 + bx + c = 0$$ if $$\beta\gamma = 1 = -\alpha$$ then $$b^3 + 2c^3 - 3\alpha^3 - 6\beta^3 - 8\gamma^3$$ is equal to

A

$$\dfrac{155}{8}$$

B

21

C

$$\dfrac{169}{8}$$

D

19

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 62

Report

If for $$z = \alpha + i\beta$$, $$|z + 2| = z + 4(1+i)$$, then $$\alpha + \beta$$ and $$\alpha\beta$$ are the roots of the equation

A

$$x^2 + 3x - 4 = 0$$

B

$$x^2 + 7x + 12 = 0$$

C

$$x^2 + x - 12 = 0$$

D

$$x^2 + 2x - 3 = 0$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 63

Report

The number of arrangements of the letters of the word 'INDEPENDENCE' in which all the vowels always occur together is

A

16800

B

33600

C

18000

D

14800

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 64

Report

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together is

A

720

B

$$126(5!)^2$$

C

$$7(360)^2$$

D

$$7(720)^2$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 65

Report

Let $$S_K = \dfrac{1+2+\ldots+K}{K}$$ and $$\sum_{j=1}^n S_j^2 = \dfrac{n}{A}(Bn^2 + Cn + D)$$ where $$A, B, C, D \in N$$ and $$A$$ has least value, then

A

$$A + C + D$$ is not divisible by $$D$$

B

$$A + B = 5(D-C)$$

C

$$A + B + C + D$$ is divisible by 5

D

$$A + B$$ is divisible by $$D$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 66

Report

If the coefficients of three consecutive terms in the expansion of $$(1+x)^n$$ are in the ratio 1:5:20 then the coefficient of the fourth term is

A

2436

B

5481

C

1827

D

3654

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 67

Report

Let $$C(\alpha, \beta)$$ be the circumcentre of the triangle formed by the lines $$4x + 3y = 69$$, $$4y - 3x = 17$$, and $$x + 7y = 61$$. Then $$(\alpha - \beta)^2 + \alpha + \beta$$ is equal to

A

18

B

17

C

15

D

16

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 68

Report

Let $$R$$ be the focus of the parabola $$y^2 = 20x$$ and the line $$y = mx + c$$ intersect the parabola at two points P and Q. Let the points G(10, 10) be the centroid of the triangle PQR. If $$c - m = 6$$, then $$PQ^2$$ is

A

296

B

325

C

317

D

346

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 69

Report

$$\lim_{x \to 0} \left(\left(\dfrac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\dfrac{\sin^3(4x)}{(\log_e(2x+1))^5}\right)\right)$$ is equal to

A

15

B

9

C

18

D

24

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 70

Report

Negation of $$(p \to q) \to (q \to p)$$ is

A

$$(\sim p) \lor p$$

B

$$q \wedge (\sim p)$$

C

$$(\sim q) \wedge p$$

D

$$p \lor (\sim q)$$

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 71

Report

Let the number of elements in sets $$A$$ and $$B$$ be five and two respectively. Then the number of subsets of $$A \times B$$ each having at least 3 and at most 6 elements is

A

752

B

782

C

792

D

772

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 72

Report

Let $$\begin{bmatrix} 2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2 \end{bmatrix}$$. If $$|adj(adj(adj(2A)))| = (16)^n$$, then $$n$$ is equal to

A

8

B

10

C

9

D

12

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 73

Report

Let $$P = \begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \\ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$$, $$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$ and $$Q = PAP^T$$. If $$P^TQ^{2007}P = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ then $$2a + b - 3c - 4d$$ is equal to

A

2004

B

2005

C

2007

D

2006

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 74

Report

Let $$f(x) = \dfrac{\sin x + \cos x - \sqrt{2}}{\sin x - \cos x}$$, $$x \in [0, \pi] - \{\dfrac{\pi}{4}\}$$, then $$f\left(\dfrac{7\pi}{12}\right) f''\left(\dfrac{7\pi}{12}\right)$$ is equal to

A

$$\dfrac{2}{9}$$

B

$$\dfrac{-2}{3}$$

C

$$\dfrac{-1}{3\sqrt{3}}$$

D

$$\dfrac{2}{3\sqrt{3}}$$

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 75

Report

Let $$I(x) = \int \dfrac{x+1}{x(1+xe^x)^2} dx$$, $$x > 0$$. If $$\lim_{x \to \infty} I(x) = 0$$ then $$I(1)$$ is equal to

A

$$\dfrac{e+2}{e+1} - \log_e(e+1)$$

B

$$\dfrac{e+1}{e+2} + \log_e(e+1)$$

C

$$\dfrac{e+1}{e+2} - \log_e(e+1)$$

D

$$\dfrac{e+2}{e+1} + \log_e(e+1)$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 76

Report

The area of the region $$\{(x,y): x^2 \le y \le 8-x^2, y \le 7\}$$ is

A

27

B

18

C

20

D

21

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 77

Report

If the points with position vectors $$\alpha\hat{i} + 10\hat{j} + 13\hat{k}$$, $$6\hat{i} + 11\hat{j} + 11\hat{k}$$, $$\dfrac{9}{2}\hat{i} + \beta\hat{j} - 8\hat{k}$$ are collinear, then $$(19\alpha - 6\beta)^2$$ is equal to

A

36

B

25

C

49

D

16

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 78

Report

The shortest distance between the lines $$\dfrac{x-4}{4} = \dfrac{y+2}{5} = \dfrac{z+3}{3}$$ and $$\dfrac{x-1}{3} = \dfrac{y-3}{4} = \dfrac{z-4}{2}$$ is

A

$$6\sqrt{3}$$

B

$$2\sqrt{6}$$

C

$$6\sqrt{2}$$

D

$$3\sqrt{6}$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 79

Report

If the equation of the plane containing the line $$x + 2y + 3z - 4 = 0 = 2x + y - z + 5$$ and perpendicular to the plane $$\vec{r} = (\hat{i} - \hat{j}) + \lambda(\hat{i} + \hat{j} + \hat{k}) + \mu(\hat{i} - 2\hat{j} + 3\hat{k})$$ is $$ax + by + cz = 4$$ then $$(a - b + c)$$ is equal to

A

18

B

22

C

20

D

24

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 80

Report

In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found defective then the probability that it is manufactured by the machine C is

A

$$\dfrac{5}{14}$$

B

$$\dfrac{9}{28}$$

C

$$\dfrac{3}{7}$$

D

$$\dfrac{2}{7}$$

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 81

Report

The largest natural number $$n$$ such that $$3^n$$ divides 66! is ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 82

Report

Let $$[t]$$ denote the greatest integer $$\le t$$. If the constant term in the expansion of $$\left(3x^2 - \dfrac{1}{2x^5}\right)^7$$ is $$\alpha$$ then $$[\alpha]$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 83

Report

Consider a circle $$C_1: x^2 + y^2 - 4x - 2y = \alpha - 5$$. Let its mirror image in the line $$y = 2x + 1$$ be another circle $$C_2: 5x^2 + 5y^2 - 10fx - 10gy + 36 = 0$$. Let $$r$$ be the radius of $$C_2$$. Then $$\alpha + r$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 84

Report

Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8 be 9 and 9.25 respectively. If $$x > y$$, then $$3x - 2y$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 85

Report

Let $$A = \{0, 3, 4, 6, 7, 8, 9, 10\}$$ and $$R$$ be the relation defined on $$A$$ such that $$R\{(x,y) \in A \times A: x-y$$ is odd positive integer or $$x-y = 2\}$$. The minimum number of elements that must be added to the relation $$R$$, so that it is a symmetric relation, is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 86

Report

If $$a_\alpha$$ is the greatest term in the sequence $$a_n = \dfrac{n^3}{n^4 + 147}$$, $$n = 1, 2, 3, \ldots$$, then $$\alpha$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 87

Report

Let $$[t]$$ denote the greatest integer $$\le t$$. Then $$\dfrac{2}{\pi} \int_{\pi/6}^{5\pi/6} (8[\csc x] - 5[\cot x]) dx$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 88

Report

If the solution curve of the differential equation $$(y-2\log_e x)dx + (x\log_e x^2)dy = 0$$, $$x \gt 1$$ passes through the points $$(e, \dfrac{4}{3})$$ and $$(e^4, \alpha)$$, then $$\alpha$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 8th April2023 Shift 1 - Question 89

Report

Let $$\vec{a} = 6\hat{i} + 9\hat{j} + 12\hat{k}$$, $$\vec{b} = \alpha\hat{i} + 11\hat{j} - 2\hat{k}$$ and $$\vec{c}$$ be vectors such that $$\vec{a} \times \vec{c} = \vec{a} \times \vec{b}$$. If $$\vec{a} \cdot \vec{c} = -12$$, and $$\vec{c} \cdot (\hat{i} - 2\hat{j} + \hat{k}) = 5$$ then $$\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k})$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 8th April2023 Shift 1 - Question 90

Report

Let $$\lambda_1, \lambda_2$$ be the values of $$\lambda$$ for which the points $$\left(\dfrac{5}{2}, 1, \lambda\right)$$ and $$(-2, 0, 1)$$ are at equal distance from the plane $$2x + 3y - 6z + 7$$. If $$\lambda_1 > \lambda_2$$ then the distance of the point $$(\lambda_1 - \lambda_2, \lambda_2, \lambda_1)$$ from the line $$\dfrac{x-5}{1} = \dfrac{y-1}{2} = \dfrac{z+7}{2}$$ is ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution