List of top Mathematics Questions

If y = a + b(x − 2005) fits the time series data:

x(year):	2003	2004	2005	2006	2007
y (yield in tons):	6	13	17	20	24

Then the value of a + b is :

Given that \(∑p_0q_0\) = 700, \(∑p_0q_1\) = 1450, \(∑p_1q_0\) = 855 and \(∑p_1q_1\) = 1300. Where subscripts 0 and 1 are used for the base year and a current year respectively. The Laspeyer's price index number is:

Which of the following statements are correct?
A. If discount rate > coupon rate, then present value of a bond > face value
B. An annuity in which the periodic payment begins on a fixed date and continues forever is called perpetuity
C. The issuer of bond pays interest at fixed interval at fixed rate of interest to investor is called coupon payment
D. A sinking fund is a fixed payment made by a borrower to a lender at a specific date every month to clear off the loan
E. The issues of bond repays the principle i.e. face value of the bond to the investor at a later date termed as maturity date
Choose the correct answer from the options given below:

The number of all possible matrices of order 2 x 2 with each entry 0 or 1 is:

Hari covers 100m distance in 36 seconds. Ram covers the same distance in 45 seconds. In a 100m race, Hari ahead from Ram is

A mixture contains milk and water in the ratio 8 ∶ x. If 3 liters of water is added in 33 liters of mixture, the ratio of milk and water becomes 2 ∶ 1, then value of x is:

Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :

Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\vec{ a }\), \(\overrightarrow{ CA }=\vec{ b }, \overrightarrow{ AB }=\vec{ c },|\vec{ a }|=6 \sqrt{2},|\vec{ b }|=2 \sqrt{3}\) and \(\vec{ b } \cdot \vec{ c }=12\) Consider the statements :\((S1): |(\vec{ a } \times \vec{ b })+(\vec{ c } \times \vec{ b })|-|\vec{ c }|=6(2 \sqrt{2}-1)\)\((S2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$ If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P (–2, 0) and cuts the y-axis at the point Q, where y is equal to 3. Then the local maximum value of y(x) is :

Let the solution curve of the differential equation $x d y=\left(\sqrt{x^2+y^2}+y\right) d x, x>0$, intersect the line $x =1$ at $y =0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively If $P(X=1)=\frac{4}{243}$, then $P(X=4$ or 5$)$ is equal to :

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)$ is :

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y$-axis at the point $C, D$. Then the area of the quadrilateral $ACBD$ is equal to

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

Consider two GPs $2,2^2, 2^3, \ldots$ and $4,4^2$, $4^3, \ldots$ of 60 and $n$ terms respectively. If the geometric mean of all the $60+ n$ terms is $(2)^{\frac{225}{8}}$, then $\displaystyle\sum_{ k =1}^{ n } k ( n - k )$ is equal to :

Consider the following statements :
Statement 1 : If y = log₁₀x + log_ex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)