JEE(MAIN) Mathematics Mock Test - 3

The product of all roots of is

In determinant radio of the cofactor of -3 and subdeterminant is

The differential equation of the family of lines passing through the origin is

The area bounded by the curve y = x² - 4x, x-axis and line x = 2 is

If f: R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 are

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): f (x)   = log x³ and g (x)   = 3 log x are equal .
Reason(R) : Two functions f and g are said to be equal if their domains, ranges are equal and f (x)   = g (x) ∀ x in the domain .

Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.

A tangent is drawn at the point (3√3 cos θ, sin θ) 0 < θ < (π/2) of an ellipse (x²/27) + (y²/1) = 1 the least value of the sum of the intercepts on the co-ordinate axes by this tangent is attained at θ =

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):
Reason (R): The non zero vectors are always linearly independent

How many numbers between 99 and 1000 can be formed from the digits 2,3,7,0,8,6 so that in each number each digit may occur once only?

The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is

If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is

If the roots of ax² + bx + c = 0 are α,β and roots of Ax² + Bx + C = 0 are α + K, β + K, then B² - 4AC/b² - 4ac is equal to

Let f(x) be a polynominal function of second degree,If f(1) = f(-1) and a,b,c are in A.P., then f'(a),f'(b) and f'(c) are in

The total expenditure incurred by an industry under different heads is best presented as a

If a line in the octant OXYZ and it makes equal angles with the axes, then

If sinα=-3/5, where π<α<(3π/2), then cos(α/2)=

The volume of a parallelopiped whose edges are -12i+αk, 3j-k and 2i+j-15k is 546, then the value of α is

An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder is

If p , x₁ , x₂ , … x_i … and q , y₁ , y₂ , … y_i … are in A.P., with common difference a and b respectively, then the centre of mean position of the points A_i(x_i, y_i) where i = 1, 2, ..., n lies on the line

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): f(x) = |x - 1| + |x - 2| + |x - 3|, where 2 < x < 3 is an identity function.
Reason(R): f : A → f(x) = x is identity function.

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 five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216.
Reason(R) : If sum of any number is divisible by 3, then the number must be divisible by 3.

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 number of non-negative integral solutions of x₁ + x₂ + x₃ + x₄ ≤ 4 (where n is a +ve integer) is ⁿ⁺⁴C₄.
Reason(R): The number of non-negative integral solutions of x₁ + x₂ + .... + x_r = n is equal to ^n+r-1C_r.