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WBJEE Maths Test - 9 - Question 1

In the expansion of (1+x)^{(p+q)} the ratio of coefficients of x^{p} and x^{q} is :

Detailed Solution for WBJEE Maths Test - 9 - Question 1

WBJEE Maths Test - 9 - Question 2

WBJEE Maths Test - 9 - Question 3

If 1, ω, ω^{2} are cube roots of unity and a + b + c = 0, then (a + bω + cω^{2})^{3} + (a + bω^{2} + cω)^{3} =

WBJEE Maths Test - 9 - Question 4

If circles x^{2}+y^{2}+2ax+c=0 and x^{2}+y^{2}+2by+c=0 touch each other, then

WBJEE Maths Test - 9 - Question 5

If the coefficient of x^{7} and x^{8} are equal in the expansion of [(2)+(x/3)]^{n} then the value of n is :

WBJEE Maths Test - 9 - Question 6

The locus of the centre of the circle which cuts circles x^{2}+y^{2}+2g₁x+2f₁y+c₁=0 and x^{2}+y^{2}+2g₂x+2f₂y+c₂=0 orthogonally, is

WBJEE Maths Test - 9 - Question 7

If the imaginary part of [(2z+1)/(iz+1)] is -2, then the locus of z in complex plane represent.

WBJEE Maths Test - 9 - Question 11

Given 2x-y+2z=2, x-2y+z=-4, x+y+λz=4, then the value of λ such that the given system of equation has no solution, is :

Detailed Solution for WBJEE Maths Test - 9 - Question 12

Detailed Solution for WBJEE Maths Test - 9 - Question 13

WBJEE Maths Test - 9 - Question 14

The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is

WBJEE Maths Test - 9 - Question 15

The differential equation corresponding to the family of curves y=c(x-c)^{2}, where c is a constant, is :

WBJEE Maths Test - 9 - Question 18

The latus rectum of an ellipse is 1/3 of the major axis. It's eccentricity is

WBJEE Maths Test - 9 - Question 19

In an ellipse the distance between its foci is 6 and its minor axis is 8. Then its eccentricity is

WBJEE Maths Test - 9 - Question 21

Equation of the tangent to the hyperbola 2x^{2} - 3y^{2} = 6 which is parallel to the line y = 3x + 4 is

Detailed Solution for WBJEE Maths Test - 9 - Question 21

WBJEE Maths Test - 9 - Question 29

The length of the latus rectum of the parabola y^{2} + 8x − 2y + 17 = 0 is

WBJEE Maths Test - 9 - Question 30

The number of ways in which 5 boys and 3 girls be seated in a row so that each girl is between two boys is

Detailed Solution for WBJEE Maths Test - 9 - Question 30

WBJEE Maths Test - 9 - Question 31

In an examination there are three objective questions and in each question there are 4 options. The number of ways in which any candidate may not give correct answers to all questions is

WBJEE Maths Test - 9 - Question 32

The number of 3 digit odd numbers, that can be formed by using the digits 1, 2, 3, 4, 5, 6 when the repetition is allowed is

WBJEE Maths Test - 9 - Question 33

A problem in EAMCET examination is given to 3 students *A, B* and *C* whose chances of solving it are respectively. The probability that the problem will be solved is

WBJEE Maths Test - 9 - Question 34

A person puts three cards addressed to three different people in three envelopes with three different addresses without looking. What is the probability that the cards go into their respective envelopes

Detailed Solution for WBJEE Maths Test - 9 - Question 34

WBJEE Maths Test - 9 - Question 35

A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in first two times is

Detailed Solution for WBJEE Maths Test - 9 - Question 37

WBJEE Maths Test - 9 - Question 38

If the cube roots of unity are 1, ω, ω^{2} then the roots of the equation(x - 1)^{3} + 8 = 0, are

WBJEE Maths Test - 9 - Question 39

If a, b and c are real numbers such that a^{2} + b^{2} + c^{2} = 1, then ab + bc + ca lies in the interval

WBJEE Maths Test - 9 - Question 40

The absiccae of the points of the curve y = x^{3} in the interval [-2, 2], when the slope of the tangent can be obtained by mean value theorem for the interval [-2, 2] are

Detailed Solution for WBJEE Maths Test - 9 - Question 40

WBJEE Maths Test - 9 - Question 41

If the sum of the first n terms of a series be 5n^{2} + 2n, then its second term is

WBJEE Maths Test - 9 - Question 42

If the sum of first n terms of an A.P. be 3n^{2} - n and its common difference is 6, then its first term is

WBJEE Maths Test - 9 - Question 43

The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is

WBJEE Maths Test - 9 - Question 44

The sum of integers from 1 to 100 which are divisible by 2 or 5 is

WBJEE Maths Test - 9 - Question 45

If A, B and C are non-empty sets, then (A - B} ∪ (B - A) equals

WBJEE Maths Test - 9 - Question 46

If √3 + i = (a + i b) (c + i d) then tan⁻^{1} (b/a) + tan⁻^{1} (d/c) is equal to

WBJEE Maths Test - 9 - Question 47

The equation of bisectors between the lines 3x+4y-7=0 and 12x+5y+17=0 are

WBJEE Maths Test - 9 - Question 48

The line joining point (3,5) to the intersection point of lines 4x+y-1=0 and 7x-3y-35=0 is at equal distances from points (0,0) and (8,34) is the statement

WBJEE Maths Test - 9 - Question 49

The condition that one root of the equation ax^{2} + bx + c = 0 be reciprocal of other root is___

Detailed Solution for WBJEE Maths Test - 9 - Question 49

WBJEE Maths Test - 9 - Question 51

The locus of the orthocentre of the triangle formed by the lines

(1 + p)x - py + p(1 + p) = 0,

(1 + q)x - qy + q(1 + q) = 0,

and y = 0, where p ≠ q , is

WBJEE Maths Test - 9 - Question 53

If *l* is the length of the intercept made by a common tangent to the circle x^{2} + y^{2} = 16 and the ellipse x^{2}/25 + y^{2}/4 = 1, on the coordinate axes, then 81*l*^{2} + 3 is equal to

WBJEE Maths Test - 9 - Question 55

In a triangle *ABC*, let ∠C = π ∕ 2 . If *r* is the inradius and *R* is the circumradius of the triangle, then *2(r + R)* is equal to

WBJEE Maths Test - 9 - Question 57

The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines of the vector are:

WBJEE Maths Test - 9 - Question 58

How many real solutions does the equation x^{7} + 14x^{5} + 16x^{3} + 30x − 560 = 0 have?

WBJEE Maths Test - 9 - Question 61

Tangents are drawn from the point (- 1, 2) to *y ^{2} = 4x*. The length of these tangents with intercept on line

WBJEE Maths Test - 9 - Question 62

The differential equation (x^{4} − 2xy^{2} + y^{4}) dx − (2x^{2}y − 4xy^{3} + sin y) dy = 0 has its solution as

WBJEE Maths Test - 9 - Question 64

A line is drawn from A( − 2, 0) to intersect the curve y^{2} = 4x in P and Q in the first quadrant such that then slope of the line is always

WBJEE Maths Test - 9 - Question 65

are non-coplanar non-zero vectors and is any vector in space then,

is equal to

*Multiple options can be correct

WBJEE Maths Test - 9 - Question 66

If f(x) = x^{4}(1-x)^{2}, x ∈ [0,1], then which of the following is true?

*Multiple options can be correct

WBJEE Maths Test - 9 - Question 67

If the points where a, b, c are different from 1, lie on the line *lx + my + n* = 0, then:

*Multiple options can be correct

*Multiple options can be correct

WBJEE Maths Test - 9 - Question 69

Let a, b, c, d real numbers. Suppose that all the roots of the equation z^{4} + az^{3} + bz^{2} + cz + d = 0 are complex numbers lying on the circle |z| = 1 in the complex plane. The sum of the reciprocals of the roots is necessarily

*Multiple options can be correct

*Multiple options can be correct

WBJEE Maths Test - 9 - Question 71

If are any two vectors then the vector bisecting the angle between

*Multiple options can be correct

*Multiple options can be correct

WBJEE Maths Test - 9 - Question 73

If a, b, c are non zero real numbers such that 3 (a^{2} + b^{2} + c^{2} + 1) = 2 (a + b + c + ab + bc + ca) , then a, b, c are in

*Multiple options can be correct

*Multiple options can be correct

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