If log5 a. loga x = 2, then x is equal to 1) 5 2) 125 3) 25 4) none of these Solution: Given log5 a. loga x = 2 => (log a/log 5) (log x/log a) = 2 => (log x/log 5) =... View Article
If logk x. log5 k = logx 5, k ≠ 1, k>0, then x is equal to 1) k 2) 0 3) 5 4) none of these Solution: We know logb a = log a/log b Given logk x. log5 k = logx 5 => (log x/log k). (log... View Article
7 log (16/15) + 5 log(25/24) + 3 log (81/80) is equal to 1) 0 2) 1 3) log 2 4) log 3 Solution: 7 log (16/15) + 5 log(25/24) + 3 log (81/80) = = log [ (16/15)7 .(25/24)5 .(81/80)3] =... View Article
The value of log3 4 log4 5 log5 6 log6 7 log7 8 log8 9 is 1) 1 2) 2 3) 3 4) 4 Solution: We know logb a = log a/log b So log3 4 log4 5 log5 6 log6 7 log7 8 log8 9 = (log 4/log 3) ×... View Article
If log4 2 + log4 4 + log4 x + log4 16 = 6, then x = 1) 64 2) 32 3) 8 4) 4 Solution: Given log4 2 + log4 4 + log4 x + log4 16 = 6 => log4 (2 × 4 × x × 16) = 6... View Article
Which is the correct order for a given number α in increasing order? 1) log2 α, log3 α, loge α,log10 α 2) log10 α, log3 α, loge α,log2 α 3) log10 α, loge... View Article
If loge (a + b)/2 = ½ (loge a + loge b), then the relation between a and b will be 1) a = b/2 2) a = b 3) a = 2b 4) none of these Solution: Given loge (a + b)/2 = ½ (loge a + loge b) = ½ (loge ab) =... View Article
If log7 2 = m, then log49 28 is equal to 1) 2(1+2m) 2) (1+2m)/2 3) 2/(1+2m) 4) 1 + m Solution: Given log7 2 = m log49 28 = = (1/2) log7 28 = (1/2) [log7 (4×7)] = (1/2)... View Article
Logarithm of [latex]32sqrt[5]{4}[/latex] to the base 2√2 is 1) 3.6 2) 5 3) 4 4) none of these Solution: We use the property logb an = n logb a 32×41/5 = 25× 22/5 = 227/5... View Article
For y = loga x to be defined, a must be 1) any positive real number 2) any number 3) any positive real number ≠ 1 4) none of these Solution: For y = loga x to be... View Article
Simpson’s one-third rule is applied to a function for its 1) Expansion 2) Differentiation 3) Numerical integration 4) None of these Solution: Simpson’s one-third rule is applied to a... View Article
Newton-Raphson process has a 1) Linear convergence 2) Quadratic convergence 3) Cubic convergence 4) None of these Solution: Newton-Raphson process has a... View Article
In Z, the set of all integers, the inverse of -7 w.r.t. * defined by a * b = a + b + 7 ,∀a,b ∈ Z is 1) -14 2) 7 3) 14 4) -7 Solution: Consider the identity element k for any element a belongs to Z. a*k = a a + k + 7 = a => k =... View Article
On the set Q of all rational numbers the operation * which is both associative and commutative is given by a * b, is 1) a + b + ab 2) a2 + b2 3) ab + 1 4) 2a + 3b Solution: If a*b = b*a, then the operation is commutative. If (a*b)*c = a*(b*c), then... View Article
For a, b∈R, defined by a*b = a/(a+b), where a + b ≠ 0. If a*b = 5, then the value of b*a is 1) 5 2) -4 3) -5 4) 4 Solution: Given a*b = a/(a+b) a*b = 5 => a/(a+b) = 5 => 5a + 5b = a => 4a = -5b => b = -4a/5... View Article
If the operation ⨁ is defined by a ⨁ b = a2 + b2 for all real numbers a and b, then (2 ⨁ 3) ⨁ 4 is equal to 1) 120 2) 185 3) 175 4) 129 Solution: a ⨁ b = a2 + b2 (2 ⨁ 3) = 22 + 32 = 13 (2 ⨁ 3) ⨁ 4 = 13 ⨁ 4 = 132 + 42 = 185 Hence... View Article
For any two real numbers, an operation * defined by a * b = 1+ ab is 1) neither commutative nor associative 2) commutative but not associative 3) both commutative and associative 4) associative but not... View Article
How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant?1) 2 2) 3 3) 4 4) 5 Answer: 2) 3 Two vectors cannot give a resultant zero. A third vector should be present in a direction opposite to the resultant of the two... View Article
Which of the following is not a vector quantity? 1) Weight 2) Nuclear spin 3) Momentum 4) Potential energy Answer: 4) Potential energy Solution: Weight, nuclear spin and momentum are... View Article
A bullet moving with a speed of 100 ms-1 can just penetrate two planks of equal thickness. Then, the number of such planks penetrated by the same bullet when the speed is doubled will be 1) 6 2) 10 3) 4 4) 8 Answer: 4) 8 Solution: Equation on motion v2 = u2+ 2as, here acceleration is negative Therefore, v2 = u2 -... View Article
