Practice Questions

Q59.The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is ___ BM.

Q59.For a chemical reaction A →B , it was found that concentration of B is increased by 0. 2 mol L−1 in 30 min. The average rate of the reaction is ________ ×10−1 mol L−1 h−1 . (in nearest integer)

Q60.The number of compound/s given below which contain/s −COOH group is ___ . (Integer answer) (A) Sulphanilic acid (B) Picric acid (C) Aspirin (D) Ascorbic acid

Q60.A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have _____ peptide linkages.

Q60.Number of bridging CO ligands in [Mn2 (CO)10] is

Q61.If (√3 + + + √3 = 0 1)x + √3 = 0 (2) x2 + (√3 1)x (1) x2 −(√3 = 0 = 0 (4) x2 −(√3 −1)x −√3 (3) x2 + (√3 −1)x −√3

Q62.The probability of selecting integers a ∈[−5, 30] such that x2 + 2 (a + 4) x −5a + 64 > 0 , for all x ∈R, is: (1) 7 (2) 2 36 9 (3) 1 (4) 1 6 4 JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

Q82.For real numbers α and β, consider the following system of linear equations: x + y −z = 2, x + 2y + αz = 1 and 2x −y + z = β. If the system has infinite solutions, then α + β is equal to ______.

Q82.If 𝑆= + + + + … , then 160 𝑆 is equal to . 5 52 53 54

Q83.If the value of 1 + 1 1 1 + + + … . . upto ∞ is 𝑙, then 𝑙2 is equal to 3 32 33 .

Q85.The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1)(1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to −1), for x ≤0 2 (x

Q85.The missing value in the following figure is

Q86.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is 5x8+7x6

Q86.The value of the integral ∫π0 |sin 2x|dx is ________.

Q86.Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (−5, 0). If the locus of the point P is a circle of radius r, then 4r2 (in the nearest integer) is equal to __________.

Q89.If the projection of the vector ˆi + 2ˆj + ˆk on the sum of the two vectors 2ˆi + 4ˆj −5ˆk and −λˆi + 2ˆj + 3ˆk is 1, then λ is equal to _______.

Q90.Suppose the line 𝑥- 2 = 𝑦- 2 = 𝑧+ 2 lies on the plane 𝑥+ 3𝑦- 2𝑧+ 𝛽= 0 . Then ( 𝛼+ 𝛽) is equal to 𝛼 -5 2 . JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper

Q90.A fair coin is tossed n− times such that the probability of getting at least one head is at least 0. 9. Then the minimum value of n is _______. JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

Q6. A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm s−1 . Its kinetic energy is: (1) 8.75 × 10−4 J (2) 8.75 × 10−3 J (3) 6.25 × 10−4 J (4) 1.13 × 10−3 J

Q10.A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104N. When the tension is changed to T, the velocity changed to 2v . The value of T is close to: (1) 2.50 × 104N (2) 5.15 × 103 N (3) 30.5 × 104 N (4) 10.2 × 102 N

Q13.A galvanometer having a coil resistance 100 Ω gives a full scale deflection when a current of 1mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter given full scale deflection for a potential difference of 10V? (1) 10kΩ (2) 8.9 kΩ (3) 7.9 kΩ (4) 9.9 kΩ

Q21.The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be __________

Q21.The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then value of x is

Q23.Nitrogen gas is at 300 °C temperature. The temperature (in K ) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is … … … . (Molar mass of N2 gas 28 g ).

Q24.In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength λ is used. Then the value of λ is (in nm ) __________.