JEE Main entrance exam Question Bank Solutions

Negation of the Boolean statement (p ∨ q) ⇒ ((∼r) ∨ p) is equivalent to ______.

Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.

The statement among the following that is a tautology is ______.

Which of the following Boolean expression is a tautology?

The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.

If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8^th terms is ______.

The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.

If n AM's are inserted between 1 and 31 and ratio of 7^th and (n – 1)^th A.M. is 5:9, then n equals ______.

Consider

Statement 1: (p∧∼q) ∧ (∼p ∧ q) is a fallacy.

Statement 2: (p→q) ↔ (∼q→∼p) is a tautology.

The sum of n terms of an AP is 3n² + 5n. The number of term which equals 164 is ______.

If arg(z) < 0, then arg(–z) – arg(z) = ______.

(p ⇒ q) ∩ (q ⇒ r) ⇒ (p ⇒ r) is ______.

If a₁, a₂, a₃, .......... are an A.P. such that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225, then a₁ + a₂ + a₃ + ...... + a₂₃ + a₂₄ is equal to ______.

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.

If 100 times the 100^th term of an A.P. with non zero common difference equals the 50 times its 50^th term, then the 150th term of this A.P. is ______.

The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.

Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If `lim_(x rightarrow 0) ((f(x))/x^2 + 1)` = 3 then f(–1) is equal to ______.

The conditional statement ((p ∧ q) `rightarrow` ((∼p) ∨ r)) v (((∼p) ∨ r) `rightarrow` (p ∧ q)) is ______.

Which of the following Boolean expressions is not a tautology?

If q is false and p ∧ q `leftrightarrow` r is true, then which one of the following statements is a tautology?