mathematics Question Bank - Sarthaks eConnect

Let g(x) = ƒ(x) sin x, where ƒ(x) is a twice differentiable fucntion on `(–oo, oo)` such that ƒ'`(–pi)` = 1. The value of g''(–`pi`) equals :–

The order of the differential equation whose general solution is `y = c_1 cos 2x + c_2 cos^2x + c_3 sin^2 x + c_4` is :–

If f(x) = `int_0^x(e^t+3)dt`, then which of the following is always true `AAx inR` ?

Then ƒ(x) is :–

If z = (3 + 7i)(a + ib), where a, b `hatI` Z – {0}, is purely imaginary, then the minimum value of `|z|^2` is :–

let `C_1 : x^2 + y^2 = (3+2sqrt2)^2` be circle. PA and PB are pair of tangents on `C_1` where P is any point on the direction circle of `C_1`. Then the radius of the smallest circle which touches `C_1` externally and also the two tangents PA and PB is :–

The area bounded by the graph y =|[x – 3]|, x-axis and the lines x = –2 and x = 3 (where [.] stands for the greatest integer function) is:–

The number of integral value(s) of `lamda` for which vectors

`X^2hati-hatj+Xhatk , (lamda-1)hati-2lamdahatj+hatk and hati-hatj+hatk` in the order from righ handed system `AAX inR` is :–

If two curves `c_1` : x = `y^2` and `c_2` : xy = k cut at right angles, then find the value of k.

The variable plane `(2lamda + 1)x + (3 – lamda)`y + z = 4 always passes through the line:–

Statement 1 : If n `in` N then `((n^2)!)/(n!)^n` is a natural number.
Statement 2 : The number of ways in which `n^2` objects can be distributed among n persons equally is `((n^2)!)/(n!)^n`

Consider the following relations R = `{(x, y)/(x, y)` are real numbers and x = wy for some rational number w}

s=`{(m/n,p/q)}`m,n,p,q are integer such that nq`!=`0 and {qm = pm}

Statement 1 : S is the equivalence relation, but R is not an equivalence relation
Statement 2 : R and S both are symmetric

Let p, q are statements and r be the statement "p iff q". Consider the following statements.
Statement 1 : r is equivalent to –`(p harr–q)`
Statement 2 : r is equivalent to (p^~q)v(~p^q)

If `veca,vecb` are two unit vectors such that `veca+(veca xxvecb)=vecc`,where`|vecc|=2`, then the value of `[vecavecbvecc]` is:

Let ABC be a triangle such that cos A=`2/3` and cosB=`3/4`,then

If `m_1, m_2` are the roots of the equation `x^2+(sqrt3+2)x+sqrt3-1=0`then the area of the triangle formed by the lines y = `m_1x, y = m_2x` and y=2 is :

If `alpha,beta` are the roots of quadratic equation

`x^2-(3+2^(sqrt(log_(2^3)))-3^(sqrtlog_(3^2)))x-2(3^(log_(3^2))-2^(log_(2^3)))=0`

then the value of `alpha^2+alpha beta+beta^2` is equal to :

Circles radii 5, 5 and 8 are mutually extremally tangent. If a fourth circle of radius r touches all the three circles externally, then the value of r is numbers.

Let A=`[[-5,-8,-7],[3,5,4],[2,3,3]]` and B=`[[x],[y],[2]]`.If AB is a scalar multiple of B, then the value of x + y is :

If `a_1, a_2, a_3`..... is an arithmetic progression with common difference 1 and `a_1 + a_2 + a_3 + ....+ a_98` = 137 the value of `a_2 + a_4 + a_6 +..... + a_98` is :

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