WB JEE 2019

Let \(A = \left[ {\matrix{ 3 & 0 & 3 \cr 0 & 3 & 0 \cr 3 & 0 & 3 \cr } } \right]\). Then, the roots of the equation det \((A - \lambda {I_3})\) = 0 (where I3 is the identity matrix of order 3) are

Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix \(A - 3{I_3}\) is

The system of equations\(\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr}\)has infinitely many solutions in R. Then,

A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she ...

There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective col...

A problem in mathematics is given to 4 students whose chances of solving individually are \({{1 \over 2}}\), \({{1 \over 3}}\), \({{1 \over 4}}\) and \({{1 \over 5}}\). The probability that the problem will be solved at least by one student...

If X is a random variable such that \(\sigma\)(X) = 2.6, then \(\sigma\)(1 \(-\) 4X) is equal to

The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be \(\alpha\) and \(\beta\), then tan\(\alpha\) and tan\(\beta\) are

The angles of a triangle are in the ratio 2 : 3 : 7 and the radius of the circumscribed circle is 10 cm. The length of the smallest side is

Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots. Then,

Let x1, x2 be the roots of \({x^2} - 3x + a = 0\) and x3, x4 be the roots of \({x^2} - 12x + b = 0\). If \({x_1} < {x_2} < {x_3} < {x_4}\) and \({x_1},{x_2},{x_3},{x_4}\) are in GP, then ab equals

Let f : X \(\to\) Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)

Let S, T, U be three non-void sets and f : S \(\to\) T, g : T \(\to\) U be so that gof : s \(\to\) U is surjective. Then,

Let the relation \(\rho\) be defined on R as a\(\rho\)b if 1 + ab > 0. Then,

A variable line passes through a fixed point \(({x_1},{y_1})\) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes).

If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by \(-\) d = 0 lies in the 4th quadrant and is equidistant from the two axes, where a, b, c and d are non-zero numbers, then ad : bc equals to

A straight line through the point (3, \(-\)2) is inclined at an angle 60\(^\circ\) to the line \(\sqrt 3 x + y = 1\). If it intersects the X-axis, then its equation will be

A variable line passes through the fixed point \((\alpha ,\beta )\). The locus of the foot of the perpendicular from the origin on the line is

Straight lines x \(-\) y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB = AC. The equation of line AC passing through (2, \(-\)7) is

The direction ratios of the normal to the plane passing through the points (1, 2, \(-\)3), (\(-\)1, \(-\)2, 1) and parallel to \({{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}\) is

The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is

The graphs of the polynomial x2 \(-\) 1 and cos x intersect

If \({e^{\sin x}} - {e^{-\sin x}} - 4 = 0\), then the number of real values of x is

Let \(\widehat \alpha\), \(\widehat \beta\), \(\widehat \gamma\) be three unit vectors such that \(\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )\) where $$\widehat...

The position vectors of the points A, B, C and D are \(3\widehat i - 2\widehat j - \widehat k\), \(2\widehat i - 3\widehat j + 2\widehat k\), \(5\widehat i - \widehat j + 2\widehat k\) and \(4\widehat i - \widehat j - \lambda \widehat k\), ...