Title FIITJEE AITS 2023.pdf ✅

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com FIITJEE ALL INDIA TEST SERIES PART TEST – I JEE (Main)-2023 TEST DATE: 12-11-2022 Time Allotted: 3 Hours Maximum Marks: 300 General Instructions:  The test consists of total 90 questions.  Each subject (PCM) has 30 questions.  This question paper contains Three Parts.  Part-A is Physics, Part-B is Chemistry and Part-C is Mathematics.  Each part has only two sections: Section-A and Section-B.  Section – A : Attempt all questions.  Section – B : Do any five questions out of 10 questions. Section-A (01 – 20, 31 – 50, 61 – 80) contains 60 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong answer. Section-B (21 – 30, 51 – 60, 81 – 90) contains 30 Numerical based questions. The answer to each question is rounded off to the nearest integer value. Each question carries +4 marks for correct answer and –1 mark for wrong answer. Yash Patil TG ~ @bohring_bot TG ~ @bohring_bot < 3
AITS-PT-I-PCM-JEE(Main)/2023 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 2 Physics PART – A SECTION – A (Single Choice Answer Type) This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. In the diagram, the variation of coefficient of friction of the surface is shown. The external force F applied on board is equal to 2Mg. Now the board is gently pulled so it starts moving. The variation of acceleration of board with respect to displacement has been shown. The ratio tan 1: tan 2: tan 3 is smooth smooth F A B C D l l l Coefficient of friction for A to B = 3, B to C = 2, C to D =  1 2 3 a x (A) 3 : 2 : 1 (B) 3 : 4 : 1 (C) 3 : 4 : 5 (D) 1 : 2 : 3 2. In terms of the basic units of mass M, length L, time T and charge Q, the dimensions of magnetic permeability of vacuum 0 are (A) [MLQ2 ] (B) [ML2 T 1Q 2 ] (C) [LTQ1 ] (D) [LT1Q 1 ] 3. A thin massless rod of length 2 has equal point masses m attached at its ends as shown in the figure. The rod is rotating about an axis passing through its centre and making angle  with it. The magnitude of net torque about O is (A) 2 2 2m sin cos     (B) 2 2 2m sin    (C) 2 2 2 2m sin    (D) 2 2 2 2m cos    m    O 4. A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate given by dm 2 kt dt  , where m is the instantaneous mass, t is time and k is a constant. The equation of motion of the rain drop is dv dm m v mg dt dt   If the drop starts falling at t = 0, with zero initall velocity and initial mass m0(m0 = 2 gm, k = 12 gm/s3 and g = 1000 cm/s2 ), the velocity v of the drop after one second is (A) 250 cm/s (B) 500 cm/s (C) 750 cm/s (D) 1000 cm/s Yash Patil TG ~ @bohring_bot TG ~ @bohring_bot < 3

AITS-PT-I-PCM-JEE(Main)/2023 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 4 10. A rod of mass m and length  is hinged at one of its end A as shown in the figure. A force F is applied at a distance ‘x’ from A. The acceleration of centre of mass ‘a’ varies with ‘x’ as F A x (A) x a (B) x a (C) x a (D) x a 11. A smooth rod OP is fixed vertically. A disc of mass m and radius R is rolling without slipping on a rough horizontal surface as shown. Velocity of centre of mass of disc is v0. A rod AB of length L is connected with disc at A, R/2 distance vertically up from centre of disc with pin joint (about which it can rotate freely), other end of the rod is attached to a small smooth ring B, which can move freely over rod OP. At an instant rod AB makes an angle 60° with the vertical. The velocity of ring on the vertical rod at this instant is 60° R A v0 B P O (A) 0 3 3 v 2 (B) 0 3 v 2 (C) 0 v (D) 0 v 2 12. The police is chasing a thief and both move on same straight road. After passing a particular point, their velocity v vary with time t as shown in the figure. When will the police catch the thief? (A) 90 sec (B) 80 sec (C) 60 sec (D) 120 sec 40 v(m/s) 30 t(s) 13. Last mango in the mango tree is located at 30 m horizontal and 40 m vertical from a boy. The speed and angle with horizontal with which the boy should throw a stone so as to hit the last mango? (A) 50 m/s, tan1 (2) (B) 30 m/s, tan1 (3) (C) 30 m/s, tan1 (2) (D) 20 m/s, tan1 (3) 14. A plate bent at right angles along its centre line, is placed onto a horizontal fixed cylinder of radius R as shown. The minimum co-efficient of friction between the cylinder and the plate so that plate does not slip off the cylinder will be (Assume mass of plate and cylinder to be same) (A) 1 2 (B) 2 (C) 2 1 (D) 1 1 2  R Side view Yash Patil TG ~ @bohring_bot TG ~ @bohring_bot < 3