AP EAPCET (Engineering) Sequences — practice questions
63 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Sequences in the app →A fair coin is tossed twice. How many outcomes are there in the sample space?A fair six-sided die is rolled once. What is the probability of getting an even number?$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:A **random variable** is best defined as:A **discrete** random variable is one whose possible values:For a continuous random variable $X$, the probability that $X$ equals any specific value is:The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:Find $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α:The arithmetic mean of n values x1, x2, ..., xn is:Median of an odd-length sorted data set is:Probability of a certain event:Probability of rolling a 6 on a fair die:For independent events A and B, P(A and B) equals: