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Find the value of cos (sec^-1 x + cosec^-1x), |x| ≥ 1.

(a) 1 (b) 0 (c) -1 (d) 2 Solution: We know that sec-1 x + cosec-1 x = π/2 cos (sec-1 x + cosec-1 x) = cos π/2 = 0 Hence... View Article

Prove that tan²a – tan²b = [cos² b – cos²a]/cos² a cos² b = (sin²a – sin²b)/(cos²a. cos²b)

Solution: LHS = tan2 a - tan2 b = (sin2 a/cos2 a) - (sin2 b/cos2 b) = (cos2 b sin2 a - cos2 a sin2 b)/cos2 a cos2 b = [cos2b (1 - cos2 a) -... View Article

tan 54⁰ can be expressed as

(a) (cos 90 + sin 90)/(cos 90 - sin 90) (b) (cos 90 - sin 90)/(cos 90 + sin 90) (c) (sin 90 - cos 90)/(cos 90 + sin 90) (d) none of these... View Article

Solve x²+ 7x = 7 and give your answer correct to two decimal places.

Solution: x2 + 7x = 7 x2 + 7x - 7 = 0 Using quadratic formula x = [-b±√(b2- 4ac)]/2a = [-7±√(72 + 28)]/2 =... View Article

Solve: ((1200/x) + 2) (x – 10) – 1200 = 60

Solution: ((1200/x) + 2) (x - 10) - 1200 = 60 ((1200/x) + 2) (x - 10) = 1200 + 60 ((1200/x) + 2) (x - 10) = 1260 (1200 + 2x) (x - 10) = 1260x... View Article

The numeral for ninety million ninety thousand ninety is

(a) 9090095 (b) 90090090 (c) 909090 (d)None of these Solution: We know 1 million = 10,00,000 So 90 million = 900,00,000 90 thousand =... View Article

Which expression is equal to (x^-1+y^-1)^-1?

(A) xy (B) x+y (C) xy/(x+y) (D) (x+y)/xy Solution: We know x-1 = 1/x (x-1+y-1)-1 = (1/x + 1/y)-1 = [(x+y)/xy]-1 = xy/(x+y) Hence option... View Article

Which of the following two sets are equal?

(A) A = {1,2} and B = {1} (B) A = {1,2} and B = {1,2,3} (C) A = {1,2,3} and B = {2,1,3} (D) A = {1,2,4} and B = {1,2,3} Solution: when two... View Article

Find the degree measure of 1/4 radian.

Solution: We know π radian = 180 degrees. So 1 radian = 180/π 1/4 radian = (180/π)×1/4 = 45/π = 45 ×7/22 =... View Article

The value of sin² 5⁰ + sin² 10⁰ + sin² 15⁰ + … + sin² 85⁰ + sin² 90⁰ is

(A) 7 (B) 8 (C) 9.5 (D) 10 Solution: We know sin (90-x) = cos x sin2(90-x) = cos2 x Also sin2x + cos2 x = 1 sin2 50 +... View Article

Find the points of the intersection of the medians of a triangle whose vertices are (-1, 0), (5, -2) and (8, 2).

Solution: The points of the intersection of the medians of a triangle is the centroid. Let A(-1, 0), B(5, -2) and C(8, 2) be the vertices of... View Article

Find the value of 95 × 95 using the algebraic identity.

Solution: We know (a-b)2 = a2- 2ab + b2 95 = 100-5 95 × 95 = 952 = (100 - 5)2 = 1002 - 1000 + 52 = 10000 - 1000 + 25 = 9025... View Article

Is 2352 a perfect square? If not, find the smallest number by which 2352 must be multiplied so that the product is a perfect square. Find the square root of the new number.

Answer: Square root of 2352 = 48.497 It is not a perfect square. Let us prime factorise 2352. 2352 =... View Article

Fill in the blank with the most suitable determiner. “Would you like ________ coffee?” my host asked.

(A) some (B) any (C) little (D) much Answer: A determiner denotes whether the noun is referring to a definite or indefinite element of a... View Article

Solve the following equation 13x – 5 = 3/2

Solution: 13x - 5 = 3/2 13x = 3/2 + 5 = (3+10)/2 = 13/2 => x = 1/2... View Article

If 1/5: 1/x = 1/x :1/125 then the value of x is

(a) 15 (b) 20 (c) 25 (d) 35 Solution: ⅕: 1/x = 1/x :1/125 Product of extremes = product of means (⅕) ×(1/125) = (1/x) ×... View Article

05 Nov 2021: The Hindu Analysis

There is no Hindu Analysis for today since there is no edition of 'The Hindu' newspaper.... View Article

A step-down transformer reduces the voltage of a transmission line from 2200 V to 220 V. The power delivered by it is 880 W and its efficiency is 88%. The input current is

1) 4.65 mA 2) 0.045 A 3) 0.45 A 4) 4.65 A Answer:3) 0.45 A Solution: η = 88 % = 88/100 η = output power/input power 88/100 =... View Article

A current of 5 A is flowing at 220 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2200 V and 50% of power is lost, then the current in the secondary will be

1) 2.5 A 2) 5 A 3) 0.25 A 4) 0.5 A Answer: 3) 0.25 A Solution: Output power is half of the input power Ps = 0.5 Pp VsIs = 0.5 VpIp... View Article

A generator at a utility company produces 100 A of current at 4000 V. The voltage is stepped-up to 240000 V by a transformer before it is sent on a high voltage transmission line. The current in the transmission line is

1) 3.67 A 2) 2.67 A 3) 1.67 A 4) 2.40 A Answer: 3) 1.67 A Solution: V1I1 = V2I2 4000 x 100 = 240000 x I2 I2 = (4000 x... View Article