In the given figure, D is the mid-point of BC, then the value of cot y0/cot x0 is
(a) 2 (b) 1/4 (c) ⅓ (d) ½ Solution: In ∆ ACD, cot x = AC/CD ..(i) In ∆ACB, cot... View Article
Latest Posts
If the area of the triangle formed by the points (2a, b) (a + b,2b + a) and (2b, 2a) is 2 sq. units, then the area of the triangle whose vertices are (a + b, a – b),(3b-a, b + 3a ), and (3a – b, 3b – a) will be
Solution: Area of triangle = \(\begin{array}{l}\frac{1}{2}\begin{vmatrix}x_{1} &y_{1} & 1 \\ x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1\\\end{vmatrix}\end{array}... View Article
A problem in statistics is given to four students A, B, C, and D. Their chances of solving it are ⅓, ¼, ⅕, and ⅙ respectively. What is the probability that the problem will be solved?
(a) 1/3 (b) 2/3 (c) 4/5 (d) none of these Solution: P(A) = ⅓ P(B) = ¼ P(C) = ⅕... View Article
The equation x2+2(m-1)+m+5 = 0 has equal and real root. Find the value of m.
Solution: Given x2+2(m-1)+m+5 = 0 For positive roots, b2-4ac = 0 => 4(m-1)2 – 4(m+5) = 0 => 4(m-1)2 =... View Article
If 2 is added to the numerator of a fraction, it reduces to (1/2) and if 1 is subtracted from the denominator, it reduces to (⅓). Find the fraction.
Solution: Let x be the numerator and y be the denominator of the fraction. (x+2)/y = ½ ..(i) x/(y-1) =... View Article
The bisector of ∠B and ∠C of triangle ABC intersect each other at the point O. Prove that ∠BOC = 900+ ½ ∠A.
Solution: Consider ∆BOC. ∠1 + ∠2 + ∠BOC = 1800 ..(i) In ∆ABC, ∠A + ∠B + ∠C = 1800... View Article
Find the middle term in the expansion of ((x/3) + 9y)10.
Solution: Here n = 10 Since n is even, middle term = ((n/2) + 1)th term = (10/2) + 1... View Article
If A is a symmetric and B skew-symmetric matrix and A+B is non-singular and C =(A+B)−1(A-B), then prove that (i) CT(A+B)C =A+B (ii) CT (A-B)C = A-B (iii) CTAC = A
Solution: Since A is symmetric, AT= A B is skew-symmetric, BT = -B Given C = (A+B)−1(A-B) Multiply by (A+B)... View Article
Determine the smallest positive value of x (in degrees) for which tan (x + 1000) = tan (x + 500) tan x tan (x – 500).
(a) 300 (b) 450 (c) 600 (d) 750 Solution: Given tan (x + 1000) = tan (x + 500) tan... View Article
46 square equals
Solution: To find the square of a number, multiply the number by the same number. 462 = 46×46 = 2116
One end of a taut string of length 3m along the x-axis is fixed at x=0. The speed of the waves in the string is 100m/s. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)
a) \(\begin{array}{l}y(t)=A\frac{sin(\pi x)}{6}\frac{cos50\pi t}{3}\end{array} \) b) \(\begin{array}{l}y(t)=A\frac{sin(\pi x)}{3}\frac{cos100\pi t}{3}\end{array} \) c) \(\begin{array}{l}y(t)=A\frac{sin(5\pi x)}{6}\frac{cos250\pi t}{3}\end{array} \) d) \(\begin{array}{l}y(t)=A\frac{sin(5\pi x)}{2}cos250\pi t\end{array} \) Answer: d Solution: The... View Article
Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and −ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
(A) The electrostatic field is zero (B) The electrostatic potential is constant (C) The electrostatic field is constant in magnitude... View Article
A ladder is leaned against a smooth wall and allowed to slip on a frictionless floor. Which figure represents the trace of its COM?
Answer: (c) Solution: The center of mass will move downward and will shift horizontally
A coil has an inductance of 0.7H and is joined in series with a resistance of 220 Ω. When an alternating e.m.f. of 220V at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is
a) 5 ampere b) 0.5 ampere c) 0.7 ampere d) 7 ampere Answer: b) 0.5 ampere Solution: XL=ωL=2πfL=220Ω ϕ=tan−1(XL/R)=tan−1(220/220) =45∘ \(\begin{array}{l}I = \frac{E}{\sqrt{R^{2}+X_{L}^{2}}}= \frac{220}{\sqrt{220^{2}+220^{2}}}... View Article
Out of the following material whose elasticity is independent of temperature
a) steel b) copper c) invar steel d) glass Answer: c) invar steel Solutions: Elasticity decreases with temperature for steel, copper... View Article
A 40μF capacitor is connected to a 200V,50Hz ac supply. The RMS value of the current in the circuit is, nearly:
a) 1.7 A b) 2.05 A c) 2.5 A d) 25.1 A Answer: c) 2.5 A Solution: The RMS value of... View Article
Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0×108 ms−1 and in medium, B is 2.5×108 ms−1. The critical angle for which ray of light going from A to B suffers total internal reflection is
a) sin-1 (1/2) b) sin-1 (2/5) c) sin-1 (4/5) d) sin-1 (3/5) Answer: c) sin-1 (4/5) Solution: nA = c/VA = 3 x 108/2 x 108 = 3/2 =... View Article
An electric field of 300 V/m is confined to a circular area 10 cm in diameter. If the field is increasing at the rate of 20V/m-s, the magnitude of the magnetic field at a point 15 cm from the centre of the circle will be
a) 1.85 x 10-15 T b) 1.85 x 10-16 T c) 1.85 x 10-17 T d) 5.55 x 10-18 T Answer: d) 5.55 x 10-18 T Solution: Area of... View Article
What is the terminal potential difference of a cell when short-circuited?
Answer: The terminal potential difference of a cell when its short-circuited is zero.
A long straight metal rod has a very long hole of radius ′a′ drilled parallel to the rod axis as shown in the figure. If the rod carries a current ′I′. Find the magnetic induction on the axis of the hole, where OC=c:
a) μ0Ic/π(b2 – a2) b) μ0Ic/π(b2 – a2) c) μ0I(b2 – a2)/2πc d) μ0Ic/2πb2 Answer: b) μ0Ic/π(b2 – a2) Solution: Current density, J = I/A =... View Article
