Recent questions in Maths

0 votes

3 answers

If the equation \(x^{2}-c x+d=0\) has roots equal to the fourth powers of the roots of \(x^{2}+a x+b=0\), where \(a^{2}>4 b\), then the roots of \(x^{2}-4 b x+2 b^{2}-c=0\) will be

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

The area of the region lying above \(x\)-axis, and included between the circle \(x^{2}+y^{2}=2 a x \&\) the parabola \(y^{2}=a x\), \(a>0\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

2 answers

A particle is in motion along a curve \(12 y=x^{3}\). The rate of change of its ordinate exceeds that of abscissa in

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

1 answer

Let \(I=\int_{0}^{1} \frac{x^{3} \cos 3 x}{2+x^{2}} d x\). Then

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

9 answers

Consider the parabola \(y^{2}=4 x .\) Let \(P\) and \(Q\) be points on the parabola where \(P .(4,-4) \& Q(9,6) .\) Let \(R\) be a point on the arc of the parabola between \(\mathrm{P} \& \mathrm{Q}\). Then the area of \(\triangle \mathrm{PQR}\) is largest when

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

1 answer

The equation \(x \log x=3-x\)

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

1 answer

The normals to the curve \(y=x^{2}-x+1\), drawn at the points with the abscissa \(x_{1}=0, x_{2}=-1\) and \(x_{3}=\frac{5}{2}\)

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

2 answers

Let \(f(x)=\left\{\begin{array}{cl}-2 \sin x, & \text { if } x \leq-\frac{\pi}{2} \\ A \sin x+B, & \text { if }-\frac{\pi}{2}<x<\frac{\pi}{2} . \text { Then } \\ \cos x, & \text { if } x \geq \frac{\pi}{2}\end{array}\right.\)

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

83 answers

Let \(A\) be the centre of the circle \(x^{2}+y^{2}-2 x-4 y-20=0 .\) Let \(B(1,7)\) and \(D(4,-2)\) be two points on the circle such that tangents at \(B\) and \(D\) meet at \(C\). The area of the quadrilateral \(A B C D\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

62 answers

A line cuts the \(x\)-axis at \(A(5,0)\) and the \(y\)-axis at \(B(0,-3)\). Avariable line \(P Q\) is drawn perpendicular to \(A B\) cutting the \(x\)-axis at \(P\) and the \(y\)-axis at \(Q\). If \(A Q\) and \(B P\) meet at \(R\), then the locus of \(R\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

If the polynomial \(f(x)=\left|\begin{array}{ccc}(1+x)^{a} & (2+x)^{b} & 1 \\ 1 & (1+x)^{a} & (2+x)^{b} \\ (2+x)^{b} & 1 & (1+x)^{a}\end{array}\right|\), then the constant term of \(f(x)\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

148 answers

Let \(\rho\) be a relation defined on \(\mathbb{N}\), the set of natural numbers, as \(\rho=\{(x, y) \in \mathbb{N} \times \mathbb{N}: 2 x+y=41\}\) Then

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

The least positive integer \(n\) such that \(\left(\begin{array}{rr}\cos \frac{\pi}{4} & \sin \frac{\pi}{4} \\ -\sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)^{n}\) is an identity matrix of order 2 is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

Let \(z_{1}\) and \(z_{2}\) be complex numbers such that \(z_{1} \neq z_{2}\) and \(\left|z_{1}\right|=\left|z_{2}\right| .\) If \(\operatorname{Re}\left(z_{1}\right)>0\) and \(1 \mathrm{~m}\left(z_{2}\right)<0\), then \(\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

Let \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) be three unit vectors such that \(\vec{\alpha} \cdot \vec{\beta}=\vec{\alpha} \cdot \vec{\gamma}=0\) and the angle between \(\vec{\beta}\) and \(\vec{\gamma}\) is \(30^{\circ}\). Then \(\vec{\alpha}\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

Let \(\vec{\alpha}=\hat{i}+\hat{j}+\hat{k}, \vec{\beta}=\hat{i}-\hat{j}-\hat{k}\) and \(\vec{\gamma}=-\hat{i}+\hat{j}-\hat{k}\) be three vectors. A vector \(\vec{\delta}\), in the plane of \(\vec{\alpha}\) and \(\vec{\beta}\), whose projection on \(\vec{\gamma}\) is \(\frac{1}{\sqrt{3}}\), is given by

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

For \(0 \leq p \leq 1\) and for any positive \(a, b\); let \(I(p)=(a+b)^{p}, J(p)=a^{p}+b^{p}\), then

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

89 answers

A ladder \(20 \mathrm{ft}\) long leans against a vertical wall. The top end slides downwards at the rate of \(2 \mathrm{ft}\) per second. The rate at which the lower end moves on a horizontal floor when it is \(12 \mathrm{ft}\) from the wall is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

0 votes

3 answers

The foot of the perpendicular drawn from the point \((1,8,4)\) on the line joining the points \((0,-11,4)\) and \((2,-3,1)\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

Page:

« prev
1
2
3
4
5
6
7
...
22
next »

Recent questions in Maths

...