JEE Main Practice Test- 27 - JEE MCQ

The equation of the circle passing thro' (1,0) and (0,1) and having smallest possible radius is

If |z² - 1|=|z|² + 1 ,then z lies on

If = a + i b , then a and b are

The differential equation of the family of curves y²=4a (x+a) is

The differential equation obtained by eliminating the arbitrary constants a and b from xy = ae^x + be^−x is

If y=sin((1+x²)/(1-x²)), (dy/dx)=

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x²/a²) + (y²/b²) = 1) are given by

The value of lim is

∼ [ (p ∧ q) → (∼ p ∨ q) ] is

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): If M is a n x n matrix with rank n - 1, then M can be made non-singular by changing one element.
Reason(R): An n x n matrix with rank n - 1 has a non-vanishing minor of order n - 1.

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): Solution of  
Reason(R): xdx + ydy =

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):If A and B are two independent events such that
Reason(R):  

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): If
Reason(R): We know that

If I₃ is the identity matrix of order 3, then I₃⁻¹ is

If α , β are the roots of the quadratic equation x² − (a − 2) x − (a + 1)   = 0 , where a is a variable, then the least value of α² + β² is

If the parabola y²=4ax passes thro' the point (1,-2), then the tangent at this point is

If ²⁰C_n+2 = ⁿC₁₆, then n =

If log(a + c), log(c - a), log (a - 2b + c) are in A.P., then

If f (x) = {2x - 3, x ≤ 2} {x, x < 2} then f (1) is equal to

If the range of a randon variable X is {0, 1, 2, 3, 4 ...} with   , then a =

The ratio in which the line joining the points (a,b,c) and (-a,-c,-b) is divided by the xy-plane is

ix(axi)+jx(axj)+kx(axk)=