https://blog.perfectrank.in https://validator.w3.org/feed/docs/rss2.html Q120. The probability of winning a game is 0.3. What is the probability of losing it? Q118. If two dice are thrown simultaneously, then the probability of getting a product of 12 is Q119. A coin is tossed repeatedly. The probability of getting exactly 2 heads in 11 tosses if P(4 heads) = Q117. If P(A) = 1/2, P(B) = 1/3, and P(A/B) = 1/4, then P(A’ ∩ B’) equals Q115. Two dice are thrown simultaneously. The probability that they show different faces is Q116. Cards numbered 1-20 are put in a box. If a card is drawn randomly, the probability of getting a prim Q113. If the data is: x-1, x, x+1, x+2, x+3, 3x+1 with median 9, then 3x + 1 equals Q114. If a die is thrown once, the probability that 3 divides the number appearing is Q112. The mean of numbers ax₁, ax₂, …, axₙ, x₁/a, x₂/a, …, xₙ/a in terms of mean x̄ is Q110. Variance is independent of change of Q111. If 1 is added to each of the numbers 1, 2, 3, …, 10, then variance of the new numbers is Q108. The relation between Mode, Median, and Mean is Q109. The mean of the first 10 multiples of 6 is Q106. The order of the differential equation of the family of curves y = a sin(bx + c) is Q107. The sum of all the frequencies in a frequency distribution table is equal to Q105. For the differential equation y(dy/dx) + x³(d²y/dx²) + xy = cos X, the order p and degree q are such Q103. The integrating factor of dy/dx + y sec x = tan x is Q104. The solution of dy/dx – y = 1 with y(0) = 1 is Q100. The area of the region bounded by x² + y² = π² and y = sin x is Q101. The solution of dy/dx = (√(1-x²))(√(1-y²)) is Q102. The solution of x dy – y dx = 0 represents Q99. The area bounded by y = -(x-1) for x ≤ 1 and y = (x-1) for x > 1, and x = -2 and x = 2 is Q97. ∫₀^(π/2) cos x · e^(sin x) dx equals Q98. If f(x) = Peˣ + Qe²ˣ + Re³ˣ, f(0) = 6, f'(ln 3) = 282 and ∫₀^(ln 2) f(x)dx = 11, then R equals Q94. ∫dx/(7 + 5cos x) equals Q95. ∫x·tan⁻¹(x)/(1+x²)^(3/2) dx equals Q96. ∫₀^π eˣ sin x dx equals Q92. If f(x) = x³ + bx² + cx + d and f(0), f(-1) are odd integers while f(1) ≠ odd, then for x > 1 Q93. ∫dx/(x + x log x) equals Q90. A rectangle has perimeter 2k. Its maximum area is Q91. The maximum value of f(x) = x^(1/x) is Q88. If g(x) = f(eˣ)e^(f(x)) and f(0) = f(1) = 0 and f'(1) = 2, then g'(0) equals Q89. If f'(x) = g(x), f”(x) = -f(x) and h(x) = [f(x)]² + [g(x)]², then for all x Q87. If f(x) = cos x and g(x) = log x, then (gof)'(0) equals Q86. If f(x) = (3x³ + log x)/x² + tan x, then f'(x) is Q85. If y = xˣ, then dy/dx at x = 1 equals Q84. If f(x) = √(25 – x²), then lim(x→1) [f(x) – f(1)]/(x – 1) equals Q83. If g(x) = f(|x|) + |f(x)|, where f(x) = {-2 for -3≤x≤0; x-2 for 0<x≤3}, then g'(x) is Q81. Let f(x) = |x| – |x – 1|. Which of the following statements is correct? Q82. If f(x) = |det[cos x, x, 1; 2sinx, x², 2x; tan x, x, 1]|, then lim(x→0) f(x)/x equals Q80. A vector perpendicular to both →a = î – 2ĵ + k̂ and →b = 4î – 4ĵ + 7k̂ is Q79. If the lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are perpendicular, then Q77. The direction cosines of the vector AB = -2î – 4ĵ + 4k̂ are Q78. If |→a| = 2, |→b| = 3 and →a·→b = 4, then |→a – 2→b| equals Q76. Position vectors of A, B, C are 2î + ĵ – k̂, 3î – 2ĵ + k̂ and î + 4ĵ – 3k̂. Then A, B, C form Q74. If →a = î + ĵ + k̂, →b = 2î + 4ĵ – 5k̂, →c = λî + 2ĵ + 3k̂ and the unit vector along (→b + →c) is pe Q75. If →a = î + ĵ and →b = 2î – ĵ, then the angle between →a and →b is Q72. The points A(0,0,0), B(3,0,0), C(0,4,0), D(0,0,5) form a Q73. If |→a| = √3, |→b| = 2 and →a·→b = √6, then the angle between →a and →b is Q71. The point (-2, -3, -4) lies in which octant?