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21 Oct 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 21st Oct 2021. Important news and views to boost... View Article

The differential coefficient of log tan x is

Solution: Let y = log tan x dy/dx = (1/tan x)sec2x = (cos x / sin x)/cos2x = 1/cos x sin x = 2/sin 2x = 2 cosec 2x... View Article

Show that 3 tan^-1x = tan^-1(3x-x³)/(1-3x²)

Solution: We know that tan-1A + tan-1B = tan-1(A+B)/(1-AB) LHS = 3 tan-1x = tan-1x + tan-1x + tan-1x = tan-1(2x/(1-x2)) + tan-1x =... View Article

Factorise the following expressions. (i) 7x – 42

(i) 7x - 42 (ii) 6p-12q (iii) 7a2 + 14a (iv) -16z + 20z3 (v) 20l2m + 30alm (vi) 5x2y - 15xy2 (vii) 10a2 - 15b2 + 20c2 (viii) -4a2 +... View Article

Fabina borrows Rs. 12500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who pays more interest and by how much?

Solution: Case 1: Fabina - simple interest Principal, P = 12500 Rate of interest, r = 12% Number of years, n = 3 Simple interest, I = Pnr =... View Article

tan² θ − sec² θ is equal to

(a) 1 (b) -1 (c) 0 (d) none of these Solution: tan2 θ − sec2 θ = (sin2 θ/cos2 θ) - (1/cos2 θ) =... View Article

Write additive inverse of 2/8 and 6/5.

Solution: To find the additive inverse of a number, we have to change the sign of the number. When we add a number and its additive inverse, the... View Article

4 men and 6 women can finish work in 8 days while 3 men and 7 women can do that same work in 10 days. In how many days will 10 women do the same work.

Solution: Let work done by 1 man in a day = x Work done by 1 woman in a day = y 4x + 6y = 1/8 3x + 7y = 1/10 Solving above equations, we get... View Article

The mean of 100 items was found to be 64. Later on, it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is

Solution: Mean = sum of observations/number of observations Given mean of 100 items = 64 Sum of observations = 6400 Sum of misread items =... View Article

Two numbers a and b are selected successively without replacement in that order from the integers 1 to 10. The probability that a/b is an integer, is

(a) 17 /45 (b) 1/5 (c) 17/90 (d) 8/45 Solution: Total numbers of elementary events are: 10 ×9 = 90 (numbers are of... View Article

Solve 9x/(7- 6x) = 15

Solution: 9x/(7- 6x) = 15 Cross multiply 9x = 15(7-6x) 9x = 105 - 90 x 99x = 105 x = 105/99 = 35/33 Hence the value of x is 35/33.... View Article

A solid cylinder of radius r and height h is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is:

(a) 4πrh (b) 4πrh + 2πr2 (c) πrh + πr2 (d) none of these. Solution: Here height of cylinder = 2h Radius = r TSA of cylinder... View Article

Archives

21 Oct 2021: The Hindu Analysis

The differential coefficient of log tan x is

Show that 3 tan^-1x = tan^-1(3x-x³)/(1-3x²)

Factorise the following expressions. (i) 7x – 42

Fabina borrows Rs. 12500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who pays more interest and by how much?

tan² θ − sec² θ is equal to

Write additive inverse of 2/8 and 6/5.

4 men and 6 women can finish work in 8 days while 3 men and 7 women can do that same work in 10 days. In how many days will 10 women do the same work.

The mean of 100 items was found to be 64. Later on, it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is

Two numbers a and b are selected successively without replacement in that order from the integers 1 to 10. The probability that a/b is an integer, is

Solve 9x/(7- 6x) = 15

A solid cylinder of radius r and height h is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is:

Solve for 1/(x-1)(x-2) + 1/(x-3)(x-2) = 2/3, x ≠ 1, 2, 3.

Which of the following is a pair of co-primes?

Check which of the following are solutions of an equation x – 2y = 4.

The difference between two positive integers is 30. The ratio of these integers is 2:5. Find the integers.

Period of cos x is

Factorise 1 + 2ab – (a² + b²)

State whether the statement given is true or false. Zero is the smallest rational number.

Find the cube of 21.

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