JEE Main Number Theory — practice questions
72 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Number Theory in the app →$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sin(A + B) equals:If tan θ = 1/2 (acute), find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):A set is:Empty set has cardinality:Universal set:Function f: A → B is onto (surjective) if:Power set of {1, 2, 3} has:n(A ∪ B) =De Morgan's law: (A ∪ B)' =Cartesian product A × B has cardinality:A relation from A to B is:Domain of relation:Number of functions from A (|A| = n) to B (|B| = m):Identity function I: A → A is:Inverse of function f exists if and only if f is:Composition of functions (g ∘ f)(x) =If A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, find A ∩ B:Number of subsets of {1, 2, 3, 4, 5} with exactly 3 elements:For 3 sets A, B, C: n(A ∪ B ∪ C) =100 students; 50 like math, 60 like physics, 30 like both. Find students who like neither:Number of one-one functions from {1, 2, 3} to {a, b, c, d, e}:Equivalence relation requires:For sets A, B: A × B = B × A iff:Range of f(x) = sin(x) from R to R:|A| = 5, |B| = 3. Number of relations from A to B:For f: A → B and g: B → C, (g ∘ f)⁻¹ =Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:Equivalence classes of 'congruent mod 3' on Z:Number of one-one and onto (bijective) functions from {1,2,3} to {1,2,3}:For function f(x) = ax + b (a ≠ 0), inverse is:For f: R → R, f(x) = x³, f is:Distributive law: A ∩ (B ∪ C) =Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:Number of equivalence relations on set {a, b, c}:The identity $1 + \tan^2\theta$ equals:The period of the function $ in x$ is:The radian measure of $45^\circ$ is:The value of $ in\dfrac{\pi}{6}$ is:The expansion of $ in(A+B)$ is:The maximum value of $3 in\theta$ is:The value of $\cos 180^\circ$ is:If a set $A$ has $4$ elements, the number of subsets of $A$ is:For sets $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, $A \cup B$ is:De Morgan's law gives $(A \cap B)'$ as:In a class of $30$, $18$ play cricket, $15$ play football, $8$ play both. The number who play at least one spoIf $|A| = 3$ and $|B| = 4$, the number of elements in $A \times B$ is:A relation $R$ from $A$ to $B$ qualifies as a function when:The function $f: \mathbb{R} \to \mathbb{R}, f(x) = x^2$ is:The graph of $f(x) = 1/x$ in $\mathbb{R} - \{0\}$ is:The general solution of $\cos x = 1/2$ is:A fair coin is tossed twice. The probability of getting at least one head is:If $P(A) = 0.5, P(B) = 0.4, P(A \cap B) = 0.2$, then $P(A | B)$ is:Two events $A$ and $B$ are independent if:A binomial random variable $X$ has $n = 10$ trials and success probability $p = 0.3$. Its mean is:A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Bayes' theorem is essentially used to:For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:The 4 conditions required for a binomial distribution (Bernoulli trials) include all the following EXCEPT:For a binomial distribution B(n, p), the MEAN and VARIANCE are:The number of ways to choose 3 books out of 5 (order does NOT matter) is: