Practice Questions

Q63.The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to (1) 132 (2) 120 (3) 72 (4) 96

Q63.Let x and y be distinct integers where 1 ≤x ≤25 and 1 ≤y ≤25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 , is _____ .

Q63.If the coefficient of 𝑥15 in the expansion of 𝑎𝑥3 + 1 is equal to the coefficient of 𝑥-15 in the expansion of 𝑏𝑥 3 1 15 1 𝑎𝑥 3 - , where 𝑎 and 𝑏 are positive real numbers, then for each such ordered pair 𝑎, 𝑏: 𝑏𝑥3 (1) 𝑎= 𝑏 (2) 𝑎𝑏= 1 (3) 𝑎= 3𝑏 (4) 𝑎𝑏= 3

Q63.The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is (1) 120 (2) 168 (3) 220 (4) 48 13+23+33......upto n terms

Q63.Number of integral solutions to the equation x + y + z = 21 , where x ≥1, y ≥3, z ≥4 , is equal to _____ .

Q63.If the number of words, with or without meaning. which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k then k is equal to (1) 2835 (2) 5670 (3) 1890 (4) 945

Q63.The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is

Q63.If all the six digit numbers x1x2x3x4x5x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in the increasing order, then the sum of the digits in the 72th number is _______.

Q63.Let S = {z ∈C −{i, 2i} z2−3iz−2 ∈R}. JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q63.Let a1, a2, a3, … …. be an A.P. If a7 = 3, the product (a1a4) is minimum and the sum of its first n terms is zero then n! −4an(n+2) is equal to (1) 381 (2) 9 4 (3) 33 (4) 24 4

Q63.The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is (1) 16800 (2) 33600 (3) 18000 (4) 14800

Q63.If 𝑆𝑛= 4 + 11 + 21 + 34 + 50 + … to 𝑛 terms, then 60𝑆29 - 𝑆9 is equal to (1) 223 (2) 226 (3) 220 (4) 227

Q63.The value of ∑𝑟=22 0 22𝐶𝑟· 23𝐶𝑟 is (1) 45𝐶23 (2) 44𝐶23 (3) 45𝐶24 (4) 44𝐶22

Q64.If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of 4√2 + 4 1 is √3 √6: 1, then the third term from the beginning is: (1) 30√2 (2) 30√3 (3) 60√2 (4) 60√3

Q64.Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1 . Then the serial number of 35337 is

Q64.The number of 4 -letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is _____.

Q64.Let a tangent to the curve 𝑦2 = 24𝑥 meet the curve 𝑥𝑦 = 2 at the points 𝐴 and 𝐵. Then the mid- points of such line segments 𝐴𝐵 lie on a parabola with the (1) directrix 4𝑥= 3 (2) directrix 4𝑥= - 3 3 (3) Length of latus rectum (4) Length of latus rectum 2 2 Q65. 1 1 1 1 sin2𝑡 𝑡→01lim sin 2𝑡+ 2 sin 2𝑡+ 3 sin 2𝑡. . . . . . 𝑛 sin 2𝑡 is equal to (1) 𝑛2 + 𝑛 (2) 𝑛 𝑛𝑛+ 1 (3) (4) 𝑛2 2

Q64.The coefficient of 𝑥301 in 1 + 𝑥500 + 𝑥1 + 𝑥499 + 𝑥21 + 𝑥498 + … . . + 𝑥500 is: (1) 501𝐶302 (2) 500𝐶301 (3) 500𝐶300 (4) 501𝐶200 1 1 1

Q64.Let 𝑎1, 𝑎2, 𝑎3, … . be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the + 𝑎4𝑎4 + 𝑎6 is equal to product of its 3rd and 5th terms be 19. Then 6𝑎2 (1) 3 (2) 3√3 (3) 2 (4) 2√2

Q64.The value of 1 1 1 1 1 + + + … . + + is 1!50! 3!48! 5!46! 49!2! 51!1! (1) 250 (2) 250 50! 51! (3) 251 (4) 251 51! 50!

Q64.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 (1) 720 (2) 126(5!)2 (3) 7(360)2 (4) 7(720)2

Q64.The sum to 20 terms of the series 2 ⋅22 −32 + 2 ⋅42 −52 + 2 ⋅62−. . . . . . . . . . . . is equal to __________.

Q64.Let A1 and A2 be two arithmetic means and G1, G2 and G3 be three geometric means of two distinct positive numbers. Then G41 + G42 + G43 + G21G23 is equal to (1) (A1 + A2)2G1G3 (2) 2(A1 + A2)G1G3 (3) (A1 + A2)G21G23 (4) 2(A1 + A2)G21G23

Q64.If n 1⋅3+2⋅5+3⋅7+....upto terms = 95 then the value of n is α is equal to

Q64.The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is _____ .