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Express as power notation 512.

Solution: 512 = 2×2×2×2× 2×2×2×2×2 = 29 Hence 512 can be written as 29.... View Article

One side of an equilateral triangle measures 8 cm. Find its area using Heron’s formula. What is its altitude?

Solution: By heron’s formula, the area of a triangle = √(s(s-a)(s-b)(s-c)) Where s = (a+b+c)/2 Given side = 8 So s =... View Article

Find dy/dx if y = sec^-1[1/(2x² – 1)].

(a) 1/√(1 - x2) (b) -2/√(1 - x2) (c) 1/(1+x2) (d) none of these Solution: Given y = sec-1[1/(2x2 - 1)]. Put x = cos θ... View Article

The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

(A) √2:1 (B) 2√2:1 (C) 3:2 (D) √3:1 Solution: Let x be the smaller side and y be the longer side. The diagonal of the... View Article

Differentiate, tan^-1 (cos x + sin x)/(cos x – sin x) with respect to x.

(a) 1 (b) 0 (c) 1/2 (d) π/4 Solution: Let y = tan-1 (cos x + sin x)/(cos x - sin x) = tan-1 (1 + tan x)/(1 - tan x) = tan-1 (tan... View Article

25 degree celcius is equal to?

(A) 77 Fahrenheit (B) 85 Fahrenheit (C) 100 Fahrenheit (D) 120 Fahrenheit Solution: The formula to convert Celsius to Fahrenheit is given by... View Article

Solve the following equations. 3x – 2(2x-5) = 2(x+3)-8. Also, verify.

Solution: Given 3x - 2(2x-5) = 2(x+3)-8 …(i) 3x - 4x + 10 = 2x + 6 - 8 -x - 2x = -2 - 10 -3x = -12 x = -12/-3 x = 4 Substitute x =... View Article

Find the missing term. 11, 10, __, 100, 1001, 1000, 10001.

(a) 101 (b) 91 (c) 100 (d) 81 Solution: By observing the pattern, we can see that the second number is obtained by subtracting 1 from first... View Article

What is the next number in the sequence 100, 52, 28, 16, 10, __

(a) 5 (b) 6 (c) 7 (d) 8 Solution: Given 100, 52, 28, 16, 10, __ (100)/2 + 2 = 52 (52/2) + 2 = 28 (28/2) + 2 = 16 (16/2) + 2 = 10 (10/2)... View Article

On children’s day sweets were to be equally distributed among 175 students in a school. Actually on that day 35 children were absent and therefore each child got 4 sweet extra. How many sweets were available in all for distribution?

(a) 2750 (b) 2800 (c) 2672 (d) 2675 Solution: Number of children = 175 Let x be the total number of sweets. So the number of sweets per... View Article

PAN stands for

Answer: Permanent Account Number abbreviated as PAN is a unique 10-digit alphanumeric number issued by the Indian Income Tax Department to... View Article

If a cone and a sphere have equal radii and equal volumes, what is the ratio of the diameter of the sphere to the height of the cone?

(A) 1:1 (B) 1:2 (C) 2:1 (D) 3:2 Solution: Given that a cone and a sphere have equal radii and equal volumes. Let r be the radius of cone... View Article

Archives

Express as power notation 512.

One side of an equilateral triangle measures 8 cm. Find its area using Heron’s formula. What is its altitude?

Find dy/dx if y = sec^-1[1/(2x² – 1)].

The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

Differentiate, tan^-1 (cos x + sin x)/(cos x – sin x) with respect to x.

25 degree celcius is equal to?

Solve the following equations. 3x – 2(2x-5) = 2(x+3)-8. Also, verify.

Find the missing term. 11, 10, __, 100, 1001, 1000, 10001.

What is the next number in the sequence 100, 52, 28, 16, 10, __

On children’s day sweets were to be equally distributed among 175 students in a school. Actually on that day 35 children were absent and therefore each child got 4 sweet extra. How many sweets were available in all for distribution?

PAN stands for

If a cone and a sphere have equal radii and equal volumes, what is the ratio of the diameter of the sphere to the height of the cone?

In the given question, select the related number from the given alternatives. 3265 : 4376 : : 4673 : ?

Factorise x⁴ – 625.

If cos (α + β) = 0, then sin (α – β) can be reduced to

A machinery worth Rs.10,500 depreciated by 5% . Find its value after one year.

Select the most appropriate antonym: safe

Find the zeros of the polynomial f(x) = x² – 2 and verify the relationship between its zeros and coefficients.

The point where two rays meet to form an angle is called the

Factorise x²– 12x + 36.

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