WB JEE 2021

\(\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x - 1} \cr } } \right| = 0\) is true for

The locus of the vertices of the family of parabolas \(6y = 2{a^3}{x^2} + 3{a^2}x - 12a\) is

From a point (d, 0) three normal are drawn to the parabola y2 = x, then

Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each word contains exactly three vowels and two consonants. How many of them have all the vowels together?

What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any question?

Four persons A, B, C and D throw and unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins the game if A begins?

Let \(\alpha\), \(\beta\) be the roots of the equation x2 \(-\) 6x \(-\) 2 = 0 with \(\alpha\) > \(\beta\). If an = \(\alpha\)n \(-\) \(\beta\)n for n \(\ge\) 1, then the value of \({{{a_{10}} - 2{a_8}} \over {2{a_9}}}\) is

Let a, b, c be real numbers, each greater than 1, such that \({2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3\). If the value of b is 9, then the value of 'a' must be

Consider the real valued function h : {0, 1, 2, ...... 100} \(\to\) R such that h(0) = 5, h(100) = 20 and satisfying h(p) = \({1 \over 2}\) {h(p + 1) + h(p \(-\) 1)} for every p = 1, 2 ..... 99. Then the value of h(1) is

The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is

Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while \(\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}}} \right),\log \left( {{{2a} \over {7b}}} \right)\) are in A.P. Then a, b, c are the leng...

Let A, B, C be three non-void subsets of set S. Let (A \(\cap\) C) \(\cup\) (B \(\cap\) C') = \(\phi\) where C' denote the complement of set C in S. Then

Let R be the real line. Let the relations S and T or R be defined by \(S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y\) is an integer}. Then

The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two successes is

If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos\(\theta\), b sin\(\theta\)) and B(a cos\(\theta\), \(-\) b sin\(\theta\)) is

Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular bisector of AB meets the Y-axis at R. The locus of the midpoint P of MR is

A moving line intersects the lines x + y = 0 and x \(-\) y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0), A and B has a constant area C. The locus of the mid-point AB is given by the equation

A ray of light along \(x + \sqrt 3 y = \sqrt 3\) gets reflected upon reaching X-axis, the equation of the reflected ray is

If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is

A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.

The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle \(\alpha\). The equation changes to

A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of \(\Delta\)ABC is (1, r, r2) for some real r. If the plane passes through the point (5, 5, \(-\)12) then r =

The equation 6x + 8x = 10x has

let \(\alpha\), \(\beta\), \(\gamma\) be three non-zero vectors which are pairwise non-collinear. if \(\alpha\) + 3\(\beta\) is collinear with \(\gamma\) and \(\beta\) + 2\(\gamma\) is collinear with \(\alpha\) then \(\alpha\) + 3\(\beta\) ...

If a(\(\alpha\) \(\times\) \(\beta\)) + b(\(\beta\) \(\times\) \(\gamma\)) + c(\(\gamma\) + \(\alpha\)) = 0, where a, b, c are non-zero scalars, then the vectors \(\alpha\), \(\beta\), \(\gamma\) are