What are the factors of 2450?
The factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350,... View Article
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If m is the A.M. of two distinct real numbers l and n (l, n>1) and G1, G2 and G3 are three Geometric Means between l and n then find the value of G1^4+ 2G2^4+ G3^4
Given, m is arithmetic mean of l and m Then, m= \(\begin{array}{l}\frac{l+n}{2}\end{array} \) ⇒ 2m = l + n Now,... View Article
What is the value of 10 to the power -6?
By the law of exponents, a−m = \(\begin{array}{l}\frac{1}{a^{m}}\end{array} \) Therefore, 10−6 = \(\begin{array}{l}\frac{1}{10^{6}}\end{array} \) = 0.000001
If a = -12 and b= 4 then find the value of (-a) ÷ (-b)
Given, a = −12 and b = −4 then, (−a) ÷ (−b) = −(−12) ÷ −(−4) = 12 ÷ 4... View Article
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Speed of the train = 60 km/h = 60 × \(\begin{array}{l}\frac{5}{8}\end{array} \) m/sec Time taken to cross the pole =... View Article
Plot the input characteristics of BJT mentioning different regions
Solution: The three different configurations of BJT are: Common Base (CB) Configuration Common Emitter (CE) Configuration Common Collector (CC) Configuration... View Article
Hysteresis loops for two magnetic materials A and B are given below: These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:
a) A for transformer and B for electric generators b) A for electric generators and transformers c) B for electromagnets... View Article
If the perimeter of the equilateral triangle is 180 cm, what will be its area?
Solution: Given perimeter of equilateral triangle = 180 cm All sides of an equilateral triangle are equal in measure. Let... View Article
The equation of a straight line which passes through the point (-3, 5) such that the portion of it between the axes is divided by the point in the ratio 5 : 3 (reckoning from x-axis) will be
(a) x+y-2 = 0 (b) 2x+y+1 = 0 (c x+2y-7 = 0 (d) x-y+8 = 0 Solution: Equation of line... View Article
Integrate e2x.
Solution: We have to find ∫e2x dx. Put u = 2x du = 2 dx => dx = ½ du... View Article
Feet to metre formula
Feet to metre formula is used to convert length in feet to metre. The standard unit for measurement of length... View Article
The area of a circle inscribed in an equilateral triangle is 48π square units. Then the perimeter of the triangle is (in units)
(a) 72√3 (b) 48√3 (c) 72 (d) 36 Solution: Given area of circle = 48π πr2 = 48π => r2=... View Article
Find the equation of the plane containing the lines (x−5)/4=(y−7)/4=(z+3)/−5 and (x−8)/7=(y−4)/1=(z−5)/3
If lines \(\begin{array}{l}\frac{x-x_{1}}{a_{1}}=\frac{y-y_{1}}{b_{1}}=\frac{z-z_{1}}{c_{1}}\end{array} \) and \(\begin{array}{l}\frac{x-x_{2}}{a_{2}}=\frac{y-y_{2}}{b_{2}}=\frac{z-z_{2}}{c_{2}}\end{array} \) lie in same plane then \(\begin{array}{l}\begin{vmatrix}x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ a_{1}& b_{1}... View Article
Let the matrices A and B such that then find the value of A8 – (a) 4B (b) 128B (c)−128B (d)64B
Given, A = \(\begin{array}{l}\begin{bmatrix} i& -i \\ -i& i \\\end{bmatrix}\end{array} \) and B = \(\begin{array}{l}\begin{bmatrix} 1& -1 \\ -1& 1\\\end{bmatrix}\end{array}... View Article
How to convert 128 in binary?
Binary conversion of decimal number 128 We divide the given decimal number with 2 and note down the remainders 128/2... View Article
How many possible 9-digit codes can be formed?
We can use numbers from 0 to 9 to form 9-digit code Case 1:If the code has a repetition of... View Article
Using the extended euclidean algorithm, find the multiplicative inverse of 12 in Z26
According to the Extended Euclidean Algorithm The multiplicative inverse of an integer b in Zn will exist only if GCD(n,b)... View Article
Find the general term for the sequence pattern 2, 6, 12, 20, 30,…
By observing the given sequence we get an idea that the pattern is quadratic We can write each term as... View Article
The mirror image of the curve Arg(z+i/z−1) = pi/4 across the real line x − y = 0
We know, z = x + iy ∴ \(\begin{array}{l}\frac{z+i}{z-1}=\frac{x+iy+1}{x+iy-1}\end{array} \) = \(\begin{array}{l}\frac{[x+i(y+1)][(x-1)-iy]}{[(x-1)+iy][(x-1)-iy]}= \frac{x(x-1)+y(y+1)+i[(x-1)(y+1)-xy]}{(x-1)^{2}+y^{2}} \end{array} \) Let \(\begin{array}{l}X=\frac{x(x-1)+y(y+1)}{(x-1)^{2}+y^{2}}\end{array} \) and \(\begin{array}{l}Y=\frac{(x-1)(y+1)-xy}{(x-1)^{2}+y^{2}}\end{array}... View Article
Convert 1210.26° in degrees minutes and seconds
We will take the decimal part 0.26°= 0.26 × 60’ = 15.6’ =15’ + (0.6 × 60”) = 15’ 36”... View Article
