The hexadecimal number system uses 16 literals (09, AF). Write down its base value.
The base value of the hexadecimal number system is 16.
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Reena wants to prepare vegetable pulao. She needs 300 grams of rice. If she has to feed 4 people. How much rice is needed if the same pulao is prepared for 7 people?
Rice needed to feed 4 people = 300 gramsRice needed to feed 1 person = 300 / 4 = 75... View Article
Evaluate: ∫[(sin6 x + cos6 x) / (sin2 x cos2 x)] dx.
The integral is evaluated as follows. \(\begin{array}{l}\mathrm{I}=\int \frac{\sin ^{6} \mathrm{x}+\cos ^{6} \mathrm{x}}{\sin ^{2} \mathrm{x} \cos ^{2} \mathrm{x}} \mathrm{dx} \\ =\int... View Article
Three letters are drawn from alphabets of 26 letters without replacement. The probability that letters appear orderly is
Total number of ways 3 letters can be selected 3! = 6One out of 6 ways will be in an... View Article
Let A = (a1, a2) and B = (b1, b2) be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between A and B?(A) √65(B) √74 (C) √83 (D) √97
Let A = (a1, a2) and B = (b1, b2) be two points in the plane with integer coordinates.\(\begin{array}{l}\mathrm{AB}=\sqrt{\left(\mathrm{a}_{1}-\mathrm{b}_{1}\right)^{2}+\left(\mathrm{a}_{2}-\mathrm{b}_{2}\right)^{2}} \\... View Article
The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. Write the arithmetic progression thus formed.
Taxi fare for the first km is 15 Rs and then it increases by 8 Rs for each km.The first... View Article
Find the general solution of the following equation: 2 tan x – cot x + 1 = 0.
The given equation is 2 tan x – cot x + 1 = 0.\(\begin{array}{l}\Rightarrow 2 \tan ^{2} x-1+\tan x=0 \\... View Article
Akash bought vegetables weighing 10 kg. Out of this, 3kg 500g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
Total weight = 10 kgWeight of onions = 3.5 kgWeight of tomatoes = 2.075 kgTotal weight = Weight of onion... View Article
Verify the following and name the property also: 3 / 5 × (- 4 / 7 × – 8 / 9) = (3 / 5 × – 4 / 7) × – 8 / 9.
The given expression is 3 / 5 × (- 4 / 7 × – 8 / 9) = (3 /... View Article
By increasing the speed of a car by 10 km / hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Let the original speed of the car be x km / hr.\(\begin{array}{l}\text { Time }=\frac{72}{x} \mathrm{hr} \\ \text { New... View Article
14.9 ÷ 0.64.
The given expression is 14.9 ÷ 0.64.\(\begin{array}{l}\Rightarrow \frac{14.9}{0.64} \\ \Rightarrow \frac{14.90}{0.64} \\ \Rightarrow \frac{1490}{64} \\ \Rightarrow 23.25\end{array} \)
The distance between Hyderabad and Delhi is 1674.9 km by rail how would you express this in centimetres? Also, express this in the scientific form.
The distance between Hyderabad and Delhi is 1674.9 km.\(\begin{array}{l}1 \mathrm{~km}=10^{3}\\ 1 \mathrm{~m}=10^{2} \mathrm{~cm}\\ 1 \mathrm{~km}=10^{3} \times 10^{2} \mathrm{~cm}\\ =10^{5} \mathrm{~cm}\\... View Article
Compute the area of the curvilinear triangle bounded by the y-axis and the curve, y = tanx and y = (2 / 3) cosx.
The area is computed as follows.For the point of intersection\(\begin{array}{l}\tan (x)=\frac{2}{3} \cos (x)\\ 3 \tan (x)=2 \cos (x) \\ 3... View Article
Sarita’s mother is now four times as old as Sarita. Five years hence, her mother will be three times as old as Sarita will be then. Find their present ages.
Assume the age of Sarita to be S and the age of her mother to be M.M = 45 ………..... View Article
Sana and Fatima participated in an apple race. The race was conducted in 6 parts. In the first part, Sana won by 10 seconds. In the second part, she lost by 1 min, then won by 20 seconds in the third part and lost by 25 seconds in the fourth part, she lost by 37 seconds in the fifth part and won by 12 seconds in the last part. Who won the race finally?
The winning time is a positive integer and the losing time be a negative integer. 1 minute = 60 secondsSana’s... View Article
The plane 2x – 3y + z + 6 = 0 divides the line segment joining (2, 4, 16) and (3, 5, – 4) in the ratio
Assume the line segment joining points P (2, 4, 16) and Q (3, 5, – 4) be divided by 2x... View Article
Evaluate 70x4 ÷ 14x2.
The given expression can be divided as follows.\(\begin{array}{l}70 \mathrm{x}^{4} \div 14 \mathrm{x}^{2}=\frac{2 \times 5 \times 7 \times \mathrm{x} \times \mathrm{x}... View Article
Verify that y2 = 4a (x + a) is a solution of the differential equation y [1 – (dy / dx)2] = 2x (dy / dx).
The given equation is y2 = 4a (x + a).\(\begin{array}{l}\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{y}^{2}=\frac{\mathrm{d}}{\mathrm{dx}} 4 \mathrm{a}(\mathrm{x}+\mathrm{a})\\ 2 y \frac{d y}{d x}=\frac{d}{d x} 4... View Article
The general form of 456 is
456 can be split as, 456 = 400 + 50 + 6456 = (4 × 100) + (5 × 10)... View Article
The equation of the bisector of the angle between two lines 3x – 4y + 12 = 0 and 12x – 5y + 7 = 0, which contain the point (- 1, 4) is
The equation of the bisector of the angle between two lines consisting of the point (α, β) is\(\begin{array}{l}\left.\left.\left[\left(a_{1} x+b_{1} y+c\right)... View Article
