What Is The State Or Regional Political Party?
The state or regional political party refers to the parties that take care of people living within the respective regions,... View Article
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The Radii Of Two Circles Are 8cm And 6cm Respectively. Find The Radius Of The Circle Having Its Area Equal To The Sum Of The Areas Of The Two Circles.
Let the radius of the required circle is r cm. Therefore, \(\begin{array}{l}\Pi r^{2} = \Pi r^{2}_{1} + \Pi r^{2}_{2}\end{array} \)... View Article
Find the square of 3a – 4b.
The formula used is given below. \(\begin{array}{l}(a-b)^{2}= a^{2}+b^{2}-2 a b \\ (3 a-4 b)^{2} =9 a^{2}+16 b^{2}-2 \times 3 a... View Article
The cost of 5 kg of wheat is Rs. 91.50. What quantity of wheat can be purchased in Rs. 183?
Rs. 91.50 – 5 kgRs. 1 – (5 / 91.5) kgRs. 183 – (5 / 91.5) * 183= 10 kg
If the number x is chosen from the numbers 1, 2, 3 and a number y is selected from the numbers 1, 4, 9 find the probability that xy < 9.
x can be chosen in 3 ways and in accordance with that there are 3 ways of choosing number y,... View Article
How many even numbers are there in the following sequence of numbers, each of which, is followed by an odd number as well as preceded by an even number? 8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9
There are four such even numbers.\(\begin{array}{l}8 \underline{6} 76 \underline{8} 93275342 \underline{2} 35522 \underline{8} 119\end{array} \)
Can two numbers have 12 as their HCF and 512 as their LCM? Justify your answer.
They cannot have 512 as their LCM.The highest common factor is one of the factors of the least common multiple.... View Article
Find the next term of the given series: 17, 27, 37, 56, 66, (………).
17 + 10 = 2727 + 10 = 3737 + 19 = 5656 + 10 = 6666 + 10 =... View Article
What is the square root of 72?
72 = 2 × 2 × 2 × 3 × 3√72 = √(2 × 2 × 2 × 3 ×... View Article
Prove that the points (0, 0), (5, 5) and (- 5, 5) are the vertices of a right isosceles triangle.
Let A (0, 0), B (5, 5) and C (- 5, 5) be the given points.\(\begin{array}{l}A B=\sqrt{(5-0)^{2}+(5-0)^{2}}\\ \Rightarrow A B=\sqrt{25+25}\\... View Article
Find the area of a regular hexagon having side a.
To find the area of a regular hexagon having side a. \(\begin{array}{l}\text { Area of a regular hexagon is }... View Article
How many 5 digit even numbers can be formed using the digits 0, 1, 2, 3, 4, 5.
(i) Without repetition Number of ways = 4 × 4 × 3 × 2 × 2 = 192 ways. Total... View Article
Compare the surds: 7√2 and 5√3.
Take 7 √2 and 5 √3.On squaring,49 * 2 and 25 * 398 and 7598 is bigger than 75.7√2 is... View Article
What is the derivative of cot2 x?
The given function is \(\begin{array}{l}\frac{d}{dx}\left(cot^2x\right)\\ =2\cot \left(x\right)\frac{d}{dx}\left(\cot \left(x\right)\right)\\ =2\cot \left(x\right)\left(-\csc ^2\left(x\right)\right)\\ =-2\csc ^2\left(x\right)\cot \left(x\right)\end{array} \)
What is 12 per cent of 250?
12% of 250= (12 / 100) * 250= 0.12 * 250= 30
The differential equation of all circles with a centre at the origin is
The equation of family of circle with the centre at the origin is x2 + y2 = a2.On differentiating, 2x... View Article
The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides. Let the sides be x cm, y cm, and (37 – x – y) cm.
To find the lengths of the sides. \(\begin{array}{l}\text \ Let \ the \ sides \ be \ x \mathrm{~cm}, \mathrm{y}... View Article
In Δ ABC, if cos A = sin B – cos C then show that it is a right-angled triangle.
To show that the triangle is a right-angled triangle. \(\begin{array}{l}\cos A=\sin B-\cos C\\ \cos A+\cos C=\sin B\\ 2 \cos \left(\frac{\mathrm{A}+\mathrm{C}}{2}\right)... View Article
Three angles that add up to 180° are in the ratio 2 : 3 : 7. Find them.
The ratio of three angles = 2 : 3 : 7Let the first angle be = 2x, second angle =... View Article
Find the derivative of [ln (tan x)]2.
The given function is \(\begin{array}{l}\frac{d}{dx}\left(ln\left(tan\:x\right)\right)^2\\ =2\ln \left(\tan \left(x\right)\right)\frac{d}{dx}\left(\ln \left(\tan \left(x\right)\right)\right)\\ =2\ln \left(\tan \left(x\right)\right)\cdot \:2\csc \left(2x\right)\\ =4\ln \left(\tan \left(x\right)\right)\csc \left(2x\right)\end{array} \)
