List of top Mathematics Questions

The function \(f(x) = x^2 - 2x\) is strictly decreasing in the interval.

Let f be a differentiable function in \((0, \frac{π}{2})\). If \(∫_{cosx} ^1 t^2f(t)dt=sin^3x+cosx\), then \(\frac{1}{\sqrt3}f'(\frac{1}{\sqrt3})\) is equal to

If the solution curve of the differential equation \(((tan−1y)−x)dy=(1+y^2)dx\) passes through the point \((1, 0)\), then the abscissa of the point on the curve whose ordinate is \(tan(1)\), is

The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is

Let y = y(x) be the solution curve of the differential equation 

passing through the point (2, √(1/3)). Then √7 y(8) is

The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 

Let the equation of two diameters of a circle x² + y² – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x² – y² = 3 passing through the center of the circle is equal to _______.

Corner points of the feasible region for an LPP, are (0, 2), (3, 0), (6, 0) and (6, 8). If z = 2x + 3y is the objective function of LPP then max. (z)-min.(z) is equal to:

Below are the stages for Drawing statistical inferences.

1. Sample
2. Population
3. Making Inference
4. Data tabulation
5. Data Analysis
   Choose the correct answer from the options given below:

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: