Unit-8:
(a)Sets, functions and relations
(b)Limits, continuity and derivatives and integration
(c)Equations(linear, quadratic and cubic)
(d)Straight lines and circles
(e)Sequence and series
(f)Mathematical reasoning
(g)Matrices and Determinants
Q1.
Let F:R → R be such that f(x) = 4x then f(x + y) will be
(a) f(x) + f(y) (b) f(x) . f(y) (c) f(x) = f(y)
(d) f(x) ÷ f(y)
Solution.
(b) f(x) . f(y)
Solution
Q2.
If x3 - 2x2y2 + 6x + y = 10, then dy/dx at x = 1 and y = 1 is.
(a) 1/3 (b) 5/4
(c) 5/3 (d) 2/3
Solution.
(c) 5/3
Solution
Q3.
The slope of the tangent to the curve y = √(4 - x2) at the point where the ordinate and the abscissa are equal is
(a) 0 (b) 1 (c) 2 (d) -1
Solution.
(d) -1
Solution
Q4.
Find the simplified value of 8A - (1 + A)3, if A is a square matrix such that A2 = A .
(a) 2A
(b) I + A (c) A (d) A - I
Solution.
(d) A - I
Solution
Q5.
Write the number of all possible matrices of order 2 x 2 with each entry ,0,3,4 .
(a) 34 (b) 31
(c) 32 (d) 33
Solution.
(a) 34
Solution
Q6.
Write (2 x 2) matrix which is both sysmmetric and skew - sysmetric.
(a) Identity matrix (b) null matrix of order 2 x 2
(c) scalar matrix (d) diagonal matrix
Solution.
(b) null matrix of order 2 x 2
Solution
Q7.
Only square matrix have determinants .
(a) True (b) False (c) Can't say
Solution.
(a) True
Solution
Q8.
α and β are the roots of the equation 2x2 + 3x + 7 = 0 , find the value of α/β + β/α is .
(a) 6/7 (b) -19/14 (c) 9/4 (d) -2/3
Solution.
(b) -19/14
Solution
Q9.
Find the equation of a line parallel to the line joining the points (5,3) and (2,9) , which passes through the points .(3,-4)
(a) y + 2x - 2 = 0 (b) y + 2x = 0 (c) y - 4x + 6 = 0 (d) y - 2x - 2 = 0
Solution.
(a) y + 2x - 2 = 0
Solution
Q10.
Find the sum of the series . 5 + 55 + 555 + ------------- upto n terms .
(a) 5/9(10n - 10 - 9n) (b) 5/81
(10n + 1 - 9n ) (c) 5/81 (10n+1 - 10 - 9n) (d) 5/9(10 - 9n)
Solution.
(c) 5/81 (10n+1 - 10 - 9n)
Solution
