List of top Mathematics Questions

If \(A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}\), then :

In the equation \(y_i = β_0+β_1.X_1+ε_1, \ β_0\) stands for

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

Match List I with List II :

List I (Method)		List II (Characteristic)
(A)	Mean	(I)	Identify what is most common
(B)	Median	(II)	Based on sound mathematics
(C)	Mode	(III)	Square-root of the variance
(D)	Standard deviation	(IV)	Divides into 2 equal parts

Choose the correct answer from the options given below:

Let \(a,b,c>1,a^3,b^3 \text{ and } c^3\) be in A.P., and \(log_ab, log_ca \text{ and } log_bc\) be in G.P. If the sum of first 20 terms of an A.P., whose first term is \(\frac{a+4b+c}{3}\) and the common difference is \(\frac{a−8b+c}{10}\) is −444, then abc is equal to:

Given below are two statements about a normally distributed data.
Statement I : 95.45% of the occurrences will lie between \(\bar {X}±3σ\).
Statement II : 68.27% of the occurrences will lie between \(\bar {X}±1σ\).
In the light of the above statements, choose the correct answer from the options given below:

For the system of linear equations\(\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta\) which one of the following statements is NOT correct ?

Which one of the following is more useful and effective for a quick visualization of a limited amount of information?

In what ratio must a grocer mix tea leaves costing Rs.600/kg and rs.650/kg. So that by selling the mixture at Rs.682/kg, he gains 10%?

Read the given statements about correlation carefully and identify the correct statements.
A. A positive relation means that the variables vary in the same direction.
B. If two or more variables are related in a statistical way, is sufficient to conclude that a cause and effect relation exists.
C. A negative relation means that the two variables vary in the opposite direction.
D. Pearson's Product-Moment Method is a method used to calculate r.
Choose the correct answer from the options given below:

Ravi invested certain sum on simple interest. He invested two-third of his sum at 7% p.a and the remaining at 8% p.a. In 3 years he earned ₹1320 as interest. Find the sum invested by him (in ₹).

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

Let αx=exp(x^βy^γ) be the solution of the differential equation 2x²ydy−(1−xy²) dx = 0, x>0 , y(2)=\(\sqrt {log_e2}\). Then α+β−γ equals :

Let T₁ and T₂ be two distinct common tangents to the ellipse \(E: \frac{x^2}{6} + \frac{y^2}{3} = 1\) and the parabola \(P: y^2 = 12x\). Suppose that the tangent T₁ touches P and E at the points A₁ and A₂, respectively and the tangent T₂touches P and E at the points A₄and A₃, respectively. Then which of the following statements is(are) true?

x=logp and y=1/p differential equation

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is

Suppose P is the point on the line joining \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?

The portion of the tangent to the curve x\(^{\frac{2}{3}}\)+y\(^{\frac{2}{3}}\)=a\(^{\frac{2}{3}}\), a>0 at any point of it, intercepted between the axes

Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is

The largest natural number \(n\) such that \(3^n\) divides \(66!\) is:

The tangent at point(a cosθ, b sinθ), 0<θ<\(\frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the x-axis at T and y-axis at T₁, Then the value of \(\min_{\,\,\,0<\theta<\frac{\pi}{2}}\)(OT)(OT₁) is

If A= {P,O,L,Y,T,E,C,H,N, I} and B = {E, X, A, M}, then \(A∩B =\)

Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is

The sum of the absolute maximum and minimum values of the function \(f(x)=\left|x^2-5 x+6\right|-3 x+2\)in the interval \([-1,3]\) is equal to :

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?