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If rth and (r + 1)th terms in the expansion of (p + q)ⁿ are equal, then the value of (n + 1)q / r(p+q) is

1) 0 2) 1 3) 1/4 4) 1/2 Solution: (2) 1... View Article

The expression [x + (x³ – 1)^½]⁵ + [x – (x³ – 1)^½]⁵ is a polynomial of degree

1) 5 2) 6 3) 7 4) 8 Solution: (3) 7... View Article

If e^x / 1 -x = B₀ + B₁x + B₂x² +….+ B_nxⁿ + …, then B_n – B_n-1 equals

1) 1/n! 2) 1/(n -1)! 3) 1/n! - (1/(n -1)!) 4) 1 Solution: (1) 1/n!... View Article

The coefficient of x⁴ in [(x / 2) – (3 / x²)]¹⁰ is

1) 405 / 256 2) 504 / 259 3) 450 / 263 4) None of these Solution: (1) 405 / 256... View Article

If the 4th term in the expansion of [ax + (1 / x)]ⁿ is 5 / 2, for all x belongs to R, then the values of a and n are

1) 1 / 2, 6 2) 6, 1/2 3) 2, 6 4) None of these Solution: (1) 1 / 2, 6... View Article

If the 6^th term in the expansion of the binomial [latex]left[sqrt{2^{log left(10-3^{x}right)}}+sqrt[5]{2^{(x-2) log 3}}right]^{m}[/latex] = 21 and known that the binomial coefficient of 2nd, 3rd and 4th terms in the expansion represent respectively the 1st, 3rd and 5th of an AP, then x =

1) 0 2) 1 3) - 2 4) 3 Solution: (1) 0... View Article

The coefficient of three consecutive of (1 + x)ⁿ⁺⁵ are in the ratio 5 : 10 : 14. Then, n is equal to (answer lies between 0 to 9 )

1) 1 2) 3 3) 4 4) 6 Solution: (4) 6... View Article

If (a + bx)^-3 = 1 / 27 + (1 / 3) x + …, then the ordered pair (a, b) equals

1) (3, - 27) 2) (1, 1/3) 3) (3, 9) 4) (3, - 9) Solution: (4) (3, - 9)... View Article

The coefficient of x³ in the infinite series expansion of 2/(1- x) (2 – x), for |x| < 1 is

1) - (1/16) 2) 15/8 3) - (1/8) 4) 15/16 Solution: (2) 15/8... View Article

If the coefficient of x⁸ in (ax² + 1 / bx)¹³ is equal to the coefficient of x^-8 in (ax – 1 / bx²)¹³, then a and b will satisfy the relation

1) ab + 1 = 0 2) ab = 1 3) a = 1 - b 4) a + b = - 1 Solution: (1) ab + 1 = 0... View Article

If 21^st and 22^nd terms in the expansion of (1 + x)⁴⁴ are equal, then x is equal to

1) 8/7 2) 21/22 3) 7/8 4) 23/24 Solution: (3) 7 / 8 In the expansion of (1 + x)44, T21 = T22 Tr+1 / Tr = {[n - r + 1] / (r)} x T22 / T21 =... View Article

The sum of the coefficients in the expansion of (5x – 4y)ⁿ, where n is a positive integer is

1) 0 2) n 3) 1 4) - 1 Solution: (3) 1 The given expansion is (5x - 4y)n. (5x - 4y)n = nC0 (5x)n + nC1 (5x)n-1 (- 4y) + …… + nCn (- 4y)n Put... View Article

Given positive integers r > 1, n > 2 and that the coefficient of (3r)^th and (r + 2)^th terms in the binomial expansion of (1+ x)²ⁿ are equal. Then

1) n = 2r 2) n = 2r + 1 3) n = 3r 4) none of these Solution: (1) n = 2r In the expansion (1 + x)2n, t3r = 2nC3r-1 (x)3r-1 tr+2 = 2nCr+1... View Article

What is an example of a Lazarus Taxon?

The coelacanth is the most well-known example of Lazarus taxon. Register at BYJU’S Biology to explore other fascinating concepts.... View Article

What are examples of hypercarnivores?

Every member of the family Felidae, including domesticated house cats, are hypercarnivores. Even snakes are considered to be hypercarnivores.... View Article

How Do You Know If Your Colon Is Empty Before a Colonoscopy?

The colour of your stool, after bowel prep, must be a yellowish, clear liquid. If there is any cloudiness in your liquid stool, the bowel prep is... View Article

How Do You Sleep With Nausea?

When nauseous, sleep with your upper body elevated. Sleeping with the fan on, or even sitting near an open window can ease nauseousness ... View Article

How Do You Remove Gas from Your Stomach?

Flatus is a condition where gas is present in the stomach as a result of swallowing air. Moreover, gas can also be produced in the intestines by... View Article

How Do You Remember the 7 Levels of Classification?

Remembering long strands of information in an order can be accomplished with the help of mnemonics. This involves associating special or unique... View Article

How Do You Relax for an ECG?

An ECG test requires the patient to be very still. Any movement, even involuntary movements such as shivering can alter the results. Hence, most... View Article