Practice Questions

Q84.The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted, 𝑎 and 𝑏 are respectively mean and variance of remaining 6 observation, then 𝑎+ 3 𝑏- 5 is equal to ________

Q84.The sum of all those terms, of the arithmetic progression 3, 8, 13, . . . , 373, which are not divisible by 3, is equal to ________. JEE Main 2023 (10 Apr Shift 1) JEE Main Previous Year Paper

Q84.Let an ellipse with centre (1, 0) and latus rectum of length 21 have its major axis along x-axis. If its minor axis subtends an angle 60∘ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to _______.

Q84.The 4th term of GP is 500 and its common ratio is 𝑚∈𝑁. Let 𝑆𝑛 denote the sum of the first 𝑛 terms of 𝑚, 𝑚 is ______ this GP. If 𝑆6 > 𝑆5 + 1 and 𝑆7 < 𝑆6 + 12, then the number of possible values of

Q84.The remainder when 19200 + 23200 is divided by 49, is _____ .

Q84.Let 𝛼> 0, be the smallest number such that the expansion of 𝑥 3 + 2 has a term 𝛽𝑥-𝛼, 𝛽∈𝑁. Then 𝛼 is 𝑥3 equal to _____ .

Q85.The coefficient of 𝑥7 in 1 - 𝑥+ 2𝑥310 is __________ .

Q85.If 𝑓𝑥= 𝑥2 + 𝑔'1𝑥+ 𝑔"2 and 𝑔𝑥= 𝑓1𝑥2 + 𝑥𝑓'𝑥+ 𝑓"𝑥, then the value of 𝑓4 - 𝑔4 is equal to _____ .

Q85.The mean of the coefficients of 𝑥, 𝑥2, … … , 𝑥7 in the binomial expression of ( 2 + 𝑥) 9 is _________

Q85.If the domain of the function 𝑓𝑥= sec-1 is [𝛼, 𝛽) ∪( 𝛾, 𝛿], then 3𝛼+ 10𝛽+ 𝛾+ 21𝛿 is equal to 5𝑥+ 3 __________ is the largest, = 4AB. If the area of ∆CAB is 2√3 - 3 unit2, when θ2

Q85.Let 𝐴= 1, 2, 3, 4, . . . . . . . . . . 10 and 𝐵= 0, 1, 2, 3, 4 . The number of elements in the relation 𝑅= (𝑎, 𝑏) ∈𝐴× 𝐴: 2𝑎- 𝑏2 + 3𝑎- 𝑏∈𝐵 is __________ .

Q86.Let the plane x + 3y −2z + 6 = 0 meet the co-ordinate axes at the points A, B, C . If the orthocenter of the triangle ABC is (α, β, 76 ), then 98(α + β)2 is equal to __________.

Q86.Let A = {1, 2, 3, 4} and R be a relation on the set A × A defined by R = {((a, b), (c, d)) : 2a + 3b = 4c + 5d} . Then the number of elements in R is _________. α, β > 0 , then α2 + β2 is dx , |x| <

Q86.Let →a,→b,→cbe three vectors such that →a = √31, 4 →b = →c = 2 and 2(→a →b) → 2 2π →a×→c , then is equal to _____ . between b and →cis → 3 b ) ( →a⋅

Q86.Let 𝑓1𝑥= 3𝑥+ 2 𝑥∈𝑅- - 3 For 𝑛≥2, define 𝑓𝑛𝑥= 𝑓1𝑜𝑓𝑛- 1𝑥. If 𝑓5𝑥= 𝑎𝑥+ 𝑏 gcd𝑎, 𝑏= 1, then 𝑎+ 𝑏 is 2𝑥+ 3, 2. 𝑏𝑥+ 𝑎, equal to ________

Q86.Let →a = 6ˆi + 9ˆj + 12ˆk, b = αˆi + 11ˆj −2ˆk and →cbe vectors such that →a×→c=→a× b If →a⋅→c= −12, and →c⋅(ˆi −2ˆj + ˆk) = 5 then →c⋅(ˆi + ˆj + ˆk) is equal to _______

Q86.Let a tangent to the curve 9𝑥2 + 16𝑦2 = 144 intersect the coordinate axes at the points 𝐴 and 𝐵. Then, the minimum length of the line segment 𝐴𝐵 is ______

Q86.If the variance of the frequency distribution 𝑥𝑖 2 3 4 5 6 7 8 Frequency 𝑓i 3 6 16 𝛼 9 5 6 is 3, then 𝛼 is equal to

Q86.The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper

Q86.Let →a, b and →cbe three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D −−−→ → → → → → → be →a− b +→c, λ→a−3 b + 4→c, −→a+ 2 b −3→cand 2→a−4 b + 6→crespectively. If AB , AC and AD are coplanar, then λ is : JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper

Q86.Let →a = 3ˆi +ˆj −ˆk and →c= 2ˆi −3ˆj + 3ˆk. If b is a vector such that →a = b ×→c and b = 50, then → 2 72 − b +→c is equal to __________.

Q86.Let 𝐻𝑛: 𝑥2 𝑦2 1, 𝑛∈ℕ. Let 𝑘 be the smallest even value of 𝑛 such that the eccentricity of 𝐻𝑘 is a 1 + 𝑛- 3 + 𝑛= rational number. If 𝑙 is the length of the latus rectum of 𝐻𝑘, then 21𝑙 is equal to

Q87. lim 48 𝑥 𝑡3 is equal to 𝑥→0 𝑥4 ∫0 𝑡6 + 1𝑑𝑡

Q87.The number of ordered triplets of the truth values of 𝑝, 𝑞 and 𝑟 such that the truth value of the statement 𝑝∨𝑞∧𝑝∨𝑟⇒𝑞∨𝑟 is True, is equal to Q88. 0 1 2 Let 𝐴= 𝑎0 3 , where 𝑎, 𝑐∈𝑅. If 𝐴3 = 𝐴 and the positive value of 𝑎 belongs to the interval ( 𝑛- 1, 𝑛], 1 𝑐 0 where 𝑛∈ℕ, then 𝑛 is equal to ____. 2

Q87.Let the equation of the plane P containing the line x + 10 = 8−y2 = z be ax + by + 3z = 2(a + b) and the distance of the plane P from the point (1, 27, 7) be c . Then a2 + b2 + c2 is equal to