Doubtly
@Doubtly · Joined Feb 2021
- Answers
- 3,792
- Questions
- 4,963
- Upvotes received
- 429
- Determine whether the following system of equations has a unique solution, no solutions or infinitely many solution Answer: infinitely many solutions For a₁x + b₁y = c₁ and a₂x + b₂y = c₂ , compare the ratios of coefficients. Here a₁ = 3, b₁ = -7, c₁ = 5 a... 1
- If sec A+ tan A = p, then find the value of sec A – tan A. Answer: sec A - tan A = 1/p Use the identity sec²A - tan²A = 1 . Factorising the left side: (sec A + tan A)(sec A - tan A) = 1 Given sec A +... 1
- D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm Answer: DE = 3 cm Since DE ∥ BC, triangle ADE is similar to triangle ABC (AA similarity: ∠A is common and corresponding angles ∠ADE = ∠ABC).... 1
- The first three terms of an AP are 3y – 1, 3y +5 and 5y +1 respectively. Then find the value of ‘y’. Answer: y = 5 If a, b, c are in AP, then b - a = c - b , i.e. 2b = a + c . 2(3y + 5) = (3y - 1) + (5y + 1) 6y + 10 = 8y 2y = 10 ⇒ y = 5 Chec... 1
- The mid-point of line segment AB is the point P (0, 4). If the coordinates of B are (-2, 3) then find the coordinates Answer: A = (2, 5) Let A = (x, y) . By the mid-point formula, the mid-point of AB is P = (x + (-2)/2,\ y + 3/2) = (0, 4) Equating coordinate... 1
- For what value of k, are the roots of the quadratic equation kx (x – 2) + 6 = 0 equal? Answer: k = 6 Expand the equation: kx(x-2) + 6 = 0 ⇒ kx² - 2kx + 6 = 0 . Here a = k , b = -2k , c = 6 . Roots are equal when the discriminan... 1
- Without actual division find whether 18/30 will have a terminating decimal expansion or a non-terminating repeating Answer: 18/30 has a terminating decimal expansion. First reduce the fraction to its lowest terms: 18/30 = 3/5 A rational number p/q in lowes... 1
- Does the angle of banking depend on the mass of the vehicle? It does not depends upon mass of the vehicle as it only depends upon:- 1.acceleration due to gravity 2.radius of curvature 3.speed of the ve... 1
- Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center Answer: K = R/√(2) ≈ 0.707 R The moment of inertia of a uniform disc of mass M and radius R about an axis through its centre and perpendicul... 1
- A person swims 100 m in the first 40 s, 80 m in the next 40 s and 45 m in the last 20 s. What is the average speed? formula for velocity is given as; v=x/t therefore, v₁=x₁/t₁=100m/40sec=2.5m/s. v₂=x₂/t₂=80m/40sec=2m/s v₃=x₃/t₃=45m/20sec=2.25m/s Vavg=V1+V2... 2
- A bullet having a mass of 10 g and moving with a speed of 1.5 m/s, penetrates a thick wooden plank of mass 90 g. Answer: 0.15 m/s Use the law of conservation of momentum: total momentum before = total momentum after. Convert masses to kg: bullet m₁ = 10... 1
- An object of mass 16 kg is moving with an acceleration of 3 m/s2 . Calculate the applied force. Answer: Force = 48 N; acceleration of the 24 kg object = 2 m/s² By Newton's second law, F = ma . For the 16 kg object: F = 16\ kg × 3\ m/s²... 1
- An object moves 18 m in the first 3 s, 22 m in the next 3 s and 14 m in the last 3 s. What is its average speed? Average speed = Total \ Distance/Total \ time = 18+22+14/3+3+3=54/9 =6m/s 1
- Take 5 examples from your surroundings and give explanation based on Newtons laws of motion. 1) When a ball is kicked in space, the ball keeps moving in one direction as there is no gravity. The ball stops when it hits an object or p... 2
- Give scientific reasons. d. The velocity of an object at rest is considered to be uniform. Velocity of an object is said to be uniform when its speed and direction does not change. The object at rest has uniform speed of zero all t... 1
- Give scientific reasons. c. It is easier to stop a tennis ball as compared to a cricket ball, when both are travelling Momentum of a body is the product of its mass and velocity i.e. p=mv and the rate of change of momentum of a body is equal to the force appl... 1
- Give scientific reasons. b. Even though the magnitudes of action force and reaction force are equal and their When two bodies interact, the action and reaction forces come into action. Even though their magnitude are same and their direction are oppo... 1
- Give scientific reasons. a. When an object falls freely to the ground, its acceleration is uniform. When an object falls freely to the ground, it is under the effect of a constant force known as force of gravity. No other forces act on it.... 1