Generalized Method of Intervals Generalized Method of Intervals for Solving Inequalities: Let . Where k₁, k₂, … kn ϵ Z and a₁, a₂, …., an are fixed real numbers satisfying the condition. a₁ < a₂ < a₃ < … < a n₋₁ < an For solving F(x) > 0 (or) F(x) < 0, consider the Read more about Generalized Method of Intervals[…]
Himachal Pradesh Common Entrance Test (HPCET) 2019 Notification Released The Government of Himachal Pradesh has established the Himachal Pradesh Technical University with the mandate to create excellent competent environment to impart the technical education across the State Eligibility Criteria: Age: Student should complete the age of 17 years on or before 31st December of the Read more about Himachal Pradesh Common Entrance Test (HPCET) 2019 Notification Released[…]
Intensity of Gravitational Field The intensity of the gravitational field of a body at a point in the field is defined as the force experienced by a body of unit mass placed at that point provided the presence of unit mass does not disturb the original gravitational field. It is always directed towards the centre Read more about Intensity of Gravitational Field[…]
Jawaharlal Institute of Postgraduate Medical Education and Research (JIPMER) 2019 Notification Released Jawaharlal Institute of Postgraduate Medical Education and Research, Puducherry (JIPMER) under Government of India since the year 1956, is one of the leading Medical Institutions of India. Spread over a sprawling 195 acres campus in an urban locale of Puducherry (formerly Pondicherry), JIPMER Read more about Jawaharlal Institute of Postgraduate Medical Education and Research (JIPMER) 2019 Notification Released[…]
Telangana State Engineering, Agriculture & Medical Common Entrance Test (TS EAMCET) 2019 Notification Released A Common Entrance Test designated as “Telangana State Engineering, Agriculture & Medical Common Entrance Test” (TS EAMCET 2019) will be conducted by JNT University Hyderabad for the academic year 2019-2020 for admission into the First Year of Professional Courses i.e. B. Read more about Telangana State Engineering, Agriculture & Medical Common Entrance Test (TS EAMCET) 2019 Notification Released[…]
Multinomial Theorem Consider the equation x₁ + x₂ + … + xᵣ = n, where aᵢ ≤ xᵢ ≤ bᵢ; xᵢ ϵ 1; I = 1, 2, …, r. In order to find the number of solutions of the given equation satisfying the given condition. We observe that the number of solutions is the same Read more about Multinomial Theorem[…]
Horizontal Range of the Escaping Liquid Water stands at a depth H in a tank whose sides are vertical. A hole is made in one of the walls at a depth h below the water surface. Let container remains at rest. When the liquid remains emerges out of the hole, it goes along a parabolic Read more about Horizontal Range of the Escaping Liquid[…]
Force of Reaction due to Ejection of Liquid A cylindrical vessel has an opening of cross-sectional area “a” near the bottom. A disc is held against the opening to prevent liquid of density ρ from coming out. If the height of the liquid above opening is h. Let us analyse the force on the disc Read more about Force of Reaction due to Ejection of Liquid[…]
Properties of ⁿC r – III 5.. Proof: L.H.S = . . . . . . . Hence proved . 6. . 7. Maximum value of ⁿCr we can observe that in the list of ⁶C₀, ⁶C₁, ⁶C₂, ⁶C₃, ⁶C₄, ⁶C₅ and ⁶C₆the maximum value is ⁶C₃. Also, in the list of ⁷C₀, ⁷C₁, ⁷C₂, Read more about Properties of ⁿC r – III[…]
Properties of ⁿCr – II 3) ⁿCr + ⁿC(r-1) = (ⁿ⁺1)Cr L.H.S = ⁿ C r + ⁿ C (r -1) . . . . . . . . . Hence L.H.S = R. H. S ⁿCr + ⁿC(r-1) = ⁿ⁺1Cr 4. rⁿCr = n(ⁿ ⁻ ¹) C(r-1) L. H. S = rⁿCr . . Read more about Properties of ⁿCr – II[…]