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`underset{x->2}{lim} (root 3(60+x^2)-4)/(sin(x - 2))`

20 soldiers are standing in a row and their captain want to send 7 out of them for a mission. In how many ways can captain select them such that at least one soldier next to him is also selected.

Let matrix B = `[[4,1],[-9,-2]]`, then which of the following will not be an element of matrix `B^100`-

Let A=` [[3,0,5,6,-2],[-2,-5,0,1,y],[5,2,x,8,0],[0,-3,2,3,-5],[-4,-7,-2,-1,-9]]` is `5xx5` Square matrix.

Each row and column of matrix A has a value assigned to it. Every element is the sum of its row and column values. For example – 9 is the sum of the value assigned to 5^th row and 5^th column. Then the value of x + y is-

A line L passing through (1, 1) intersect lines `L_ 1 : 12x + 5y = 13` and `L_2 : 12x + 5y = 65` at A and B respectively. If AB = 5, then line L can be –

Three positive numbers from an increasing GP. If the first term is doubled and second term is trebled, the new numbers are in AP. Then the common ratio of G.P. is-

The common tangent of Parabola `y^2 = 4x` and Hyperbola `x^2/4 – y^2/3 =1` touches them at P and Q respectively, the Q can be-

The integral `int (1+2x^2+1/x)e^(x^2-1/x)` dx is equal to-

(where C is integeration constant)

If `[bar a +bar b + 2bar c bar b – bar c bar a + 2bar c] =lambda [bar a bar b bar c ]`, then `lambda` is equal to-

The image of line `(x – 2)/1=(y – 2)/2=z/3` in the plane `2x + y + z = 5` is the line-

The contrapositive of If Kapil is rich then he is honest is-

The sum of the solutions in `x in (0,4pi)` of the equation `7 sin x/3(sin((pi+x)/3))sin ((2pi+x)/3)=1` is-

`tan [pi/4+1/2 cos^-1(5/7)]+ cot [pi/4+1/2 cos^-1(5/7)]` is equal to-

A relation `R_1` is defined on the set R of real numbers as follows: `(x,y)in R_1 <=>x^3=x^2y, `Then relation `R_1` is-

`int e^(x/2) sec 2x(1+4 tan 2x)dx` is equals-

Consider at three dimensional figure represented by `xyz^2=2`, then its minimum distance from origin is-

AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP=3AB. If C is the mid point of AB and CB subtends an angle `beta` at P. then the value of `tan beta` is-

Let `A(z_1), B(z_2), C(z_3)` are three points on Argand plane such that `|z_1|=|z_2|=|z_3| =4`. The image of `P((-z_2z_3)/z_1)` about the line BC is-

In a set of 2n observations, half of them are equal to `alpha` and the remaining half are equal to `-alpha`. If the standard deviation of all the observations is 2, then `|alpha|` is equal to-

Let f(x) be a continuous function such that `int_-3^3f(x)dx=0` and `int_0^3f(x)dx=3`. then the area bounded by y=f(x), x-axis, x=-3 and x=3 is equal to-

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