Solving linear equations using matrix is done by two prominent methods namely the Matrix method and Row reduction or Gaussian elimination method. In this article, we will look at solving lin... Read more

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers. In this article we learn the definit... Read more

If \(\vec{a} . \vec{c} =3 , \vec{a} = \hat{i}+ \hat{j}+ \hat{k}, \vec{b} =\hat{j} – \hat{k}, \vec{a} \times \vec{c} =\vec{b}\), Find \([\vec{a} \ \; \vec{b} \;\; \vec{c}]\) Answer \([\... Read more

Solve \(\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{r=0}^{2n-1}\frac{n^2}{n^2+4r^2}\) Answer: [(1/2)] tan-14 – 0 Solution: \(\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{r=0}^{2n-1}\frac{1}... Read more

Q. A wire of length 36 units is cut into two parts which are bent respectively to form a square of side x units and a circle of radius of r units. If the sum of areas of the square and the c... Read more

If \(arg(\frac{z-1}{z+1}) = \frac{\pi}{4}\), then find equation of circle. Answer: √2 Solution: Read more

Q. Sum of infinite terms A, AR, AR2, AR3,…. is 15. If the sum of the square of these terms is 150, then find the sum of AR2, AR4, AR6, ⋯. Answer: ½ Solution: A + AR + AR2 + ⋯ = 15 ⇒A/(... Read more

Q. \(0.4\hat{i}+0.8\hat{j}+c\hat{k}\) represents a unit vector when c is 1) -0.2 2) √0.2 3) √0.8 4) 0 Answer: 2) √0.2 Solution: \(\sqrt{(0.4)^{2}+(0.8)^{2}+c^{2}} = 1\) = 0.16 + 0.64 +c2 = 1... Read more

Q. A particle of mass 2 mg moves with constant speed and is found to pass two points 5.0 m apart in a time interval of 5 ms. Find the kinetic energy of the particle 1) 1 J 2) 2 J 3) 3 J 4) 4... Read more

Q. A spring of force constant 800 Nm-1 has an extension of 5cm. The work done in extending it from 5 cm to 15 cm is 1) 16 J 2) 8 J 3) 32 J 4) 24 J Answer: 2) 8 J Solution: Force constant, k... Read more

Q. A bullet of mass 10 g is fired horizontally with a velocity 1000 ms-1 from a rifle situated at a height 50 m above the ground. If the bullet reaches the ground with a velocity 500 ms-1, t... Read more

Q. A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time, the particle goes up is 1) –0.5 J 2) –1.25 J 3) 1.25 J... Read more

Q. A body moves a distance of 10 m along a straight line under action of 5 N force. If work done is 25 J, then the angle between the force and direction of motion of the body will be 1) 75°... Read more

Q. When a force is applied to a moving body, its motion is retarded. Then, the work done is 1) positive 2) negative 3) zero 4) positive and negative Answer: 2) negative Solution: Work is sai... Read more