In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A) :A relation R on the set of complex number defined by Z_{1} RZ_{2} ⇔ Z_{1} − Z_{2} is real, is an equivalence relation.
Reason(R) :Reflexive and symmetric properties may not imply transitivity.
The limiting point of the system of coaxial circles x^{2}+y^{2}6x6y+4=0, x^{2}+y^{2}2x4y+3=0 is
The are (in square units) of the region bounded by x^{2} = 8 y , x = 4 and xaxis is
The number of tangents drawn from the point (1,2) to x^{2}y^{2}+2x4y+4=0 is
The correct option is Option D.
It is found that the centre of the circle is (1,2)
Hence, no tangents would pass through it.
The conjugate of complex number [(2+5i)/(43i)] is
[(1i)/(1+i)] =
The solution of differential equation
The maximum value of the function f(x)=[(x)/(4+x+x^{2})] at the interval [1,1] will be
sin⁻^{1} (cos(sin⁻^{1} x) + cos⁻^{1} (sin(cos⁻^{1} x) is equal to
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): y = sin (ax + b) is a general solution of y" + a^2y = 0 .
Reason(R) : y = sin (ax + b) is a trigonometric function.
The inverse of the converse of a conditional statement is the _______________.
The inverse will insert NOT into the statement.
The converse will switch the IF and THEN.
The contrapositive does both.
The contrapositive is the inverse of the converse of the conditional statement.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): The domain of the function
Reason (R): The domain of the function
If A is a square matrix such that A^{2} = I, then A⁻^{1} is equal to
Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively
Let A denote the first set and B denote the second set
We have, n(A) = 2^{m} and n(B) = 2^{n}
As per the question, we have
n(A) = 56 + n(B)
⇒ n(A)  n(B) = 56
⇒ 2^{m}  2^{n} = 56
⇒ 2^{n} (2^{m  n}  1)
⇒ 2^{n} (2^{m  n}  1) = 8 x 7
⇒ 2^{n} = 8 = 2^{3} or (2^{m  n}  1) = 7
⇒ n = 3 or 2^{m  n} = 8 = 2^{3} = 2^{6  3}
⇒ n = 3 or m  n = 3
⇒ n = 3 or m = 6
Hence, the required values of m and n are 6 and 3 respectively
The equation of the directrix to the parabola y^{2} − 2x − 6y − 5 = 0 is
A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is
If in a moderately asymmetrical distribution mode and mean of the data are 6λ and 9λ respectively, then median is
The sides of a parallelogram are lx + ny + n = 0, lx + my + n' = 0, mx + ly + n = 0, mx + ly + n' = 0, the angle between its diagonals is
Let f : (–3, 3) → R be a differentiable function with f(0) = – 2 and f'(0) = – 1 and g(x) = (f(3f(x) + 6))^{3 }then g'(0) is equal to.
It is given that events A and B of an experiment are such that P(A / B) = 1 / 4 and P (B / A) = 1/12 and chance of occurence of an event "only A" is 1/12 (where P(x) denote the probability of occurence of event 'x'). Value of 22P(B) equals
At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100  12√x. If the firm employs 25 more workers, then the new level of production of items is:
If the function ƒ(x) = 2 + x^{2} – e^{–x} and g(x) = ƒ^{–1}(x), then the value of equals
g(ƒ(x)) = x ⇒ g'(ƒ(x)). ƒ'(x) = 1
ƒ(x) = 1 ⇒ x = 0
g'(1). ƒ'(0) = 1
ƒ'(x) = 2x + e^{–x}
ƒ'(0) = 1
g'(1) = 1
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