Recent questions tagged maths

Let $10$ vertical poles standing at equal distance on a straight line, subtend the same angle of elevation $\alpha$ at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from O is 'a'; then the distance between two consecutive poles, is :

asked Oct 8, 2015 by meena.p

1 answer

If $\cos \alpha+ \cos \beta= \large\frac{3}{2}$ and $\sin \alpha +\sin \beta=\frac{1}{2}$ and $\theta$ is the airthmetic mean of $\alpha$ and $\beta$ then $\sin 2 \theta+ \cos 2 \theta$ is equal to :

asked Oct 8, 2015 by meena.p

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If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a values greater than or equal to one is :

asked Oct 8, 2015 by meena.p

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If the length of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum are given that it is an isosceles triangle , is :

asked Oct 8, 2015 by meena.p

1 answer

In a parallelogram $ABCD, |\overrightarrow{AB}|=a;|\overrightarrow{AD}|=b $ and $|\overrightarrow{AC}|=c$, then $\overrightarrow{DB}.\overrightarrow{AB}$ has the value :

asked Oct 8, 2015 by meena.p

1 answer

A plane containing the point $(3,2,0)$ and the line $ \large\frac{x-1}{1} =\frac{y-2}{5} =\frac{z-3}{4}$ also contains the point :

asked Oct 8, 2015 by meena.p

1 answer

The shortest distance between the z- axis and the line $x+y+2z-3=0=2x+3y+4z-4$ is

asked Oct 8, 2015 by meena.p

1 answer

Let $PQ$ be a double ordinate of the parabola, $y^2=-4x$ , Where $P$ lies in the second quadrant . If R divides PQ in the ratio $2:1$ then the locus of R is :

asked Oct 8, 2015 by meena.p

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If the distance between the foci of an ellipse is half the length of its latus recturn , then the eccentricity of the ellipse is :

asked Oct 8, 2015 by meena.p

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If a circle passing through the point $(-1,0)$ touches y-axis at $(0,2)$ then the length of the chord of the circle along the x- axis is :

asked Oct 8, 2015 by meena.p

1 answer

If the incentre of an equilateral triangle is $(1,1)$ and the equation of its one side is $3x+4y+3=0$, then the equation of the circumcircle of this triangle is :

asked Oct 8, 2015 by meena.p

1 answer

A straight line L through the point $(3,-1)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt 3 x+y=1$ . If L also intersects the x- axis then the equation of L is :

asked Oct 8, 2015 by meena.p

1 answer

The solution of the differential equation $ydx-(x+2y^2)dy=0$ is $x=f(0)$. If $f(-1)=1$ then $f(1)$ is equal to

asked Oct 7, 2015 by meena.p

1 answer

Let $f:(-1,1) \to R$ be a continuous function . If $\int\limits_0^{\sin x }f(t)dt =\large\frac{\sqrt 3}{2}$$x$ , then $f\bigg(\large\frac{\sqrt 3}{2} \bigg)$ is equal to

asked Oct 7, 2015 by meena.p

1 answer

Let $f: R \to R $ be a function such that $f(2-x)=f(2+x) $ and $f(4-x)=f(4+x) ,$ for all $x \in R$ and $\int \limits_0^2 f(x) dx =5$ Then the values of $\int \limits_{10}^{50} f(x) dx$ is

asked Oct 7, 2015 by meena.p

1 answer

If $\int \large\frac{\log(t+\sqrt{1+t^2})}{\sqrt {1+t^2}}$$dt= \large\frac{1}{2}$$(g(t))^2+C$, Where C is a constant , then $g(2)$ is equal to :

asked Oct 7, 2015 by meena.p

1 answer

From the top of a 64 meters high tower , a stone is thrown upwards vertically with the velocity of $48\;m/s$ The greatest height (in meters) attained by the stone, assuming the value of the gravitational acceleration $ g= 32\;m/s^2$ is :

asked Oct 7, 2015 by meena.p

1 answer

Let k and K be the minimum and the maximum values of the function $f(x)= \large\frac{(1+x)^{0.6}}{1+x^{0.6}}$ in $[0,1]$ respectively , then the ordered pair $(k,K)$ is equal to :

asked Oct 7, 2015 by meena.p

1 answer

The equation of a normal to the curve , $\sin y = x \sin \bigg( \large\frac{\pi}{3}+y\bigg)$ at $x=0$ is

asked Oct 7, 2015 by meena.p

1 answer

Let k be a non-zero real number . If $f(x) = \left\{ \begin{array} {1 1} \large\frac{ (e^x-1)^2 }{\sin(x/k) log(1+x/4)}, & \quad x \neq 0 \\ 12 ,& \quad x=0\\ \end{array} \right. $ is a continuous function, then the value of k is

asked Oct 7, 2015 by meena.p

1 answer

If $ \sum^5_{n=1} \large\frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3}$, then $k$ to equal to :

asked Oct 7, 2015 by meena.p

1 answer

The Sum of the 3rd and the 4th terms of a G.P is 60 and the product of its first three terms is 1000. If the first term of this G.P is positive , then its 7th term is :

asked Oct 6, 2015 by meena.p

1 answer

The term independent of x in the binomial expansion of $ \bigg( 1- \large\frac{1}{x}$$+3x^5\bigg) \bigg(2x^2-\large\frac{1}{x}\bigg)^8$ is

asked Oct 6, 2015 by meena.p

1 answer

If in a regular polygon the number of diagonals is $54$ , then the number of sides of this polygon is :

asked Oct 6, 2015 by meena.p

1 answer

If $\begin{vmatrix} x^2+x & x+1 & x-2 \\2x^2+3x-1 & 3x & 3x-3 \\ x^2+2x+3 & 2x-1 & 2x-1 \end{vmatrix}=ax-12$ then 'a' is equal to :

asked Oct 6, 2015 by meena.p

1 answer

If A is a $3 \times 3 $ matrix such that $|5.adj A|=5,$ then $|A|$ is equal to :

asked Oct 6, 2015 by meena.p

1 answer

If the two roots of the equation, $(a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2=0$ are real and distinct , then the set of all values of 'a' is :

asked Oct 6, 2015 by meena.p

1 answer

If z is a non-real complex number, then the minimum value of $ \large\frac{I_mz^5}{(I_mz)^5}$ is :

asked Oct 6, 2015 by meena.p

1 answer

Let $A=\{x_1,x_2....,x_7\}$ and $B= \{y_1,y_2,y_3\}$ be two sets contains seven and three distinct elements respectively. Then the total number of function $f:A \to B$ that are onto , if there exist exactly three elements x in A Such that $f(x)=y_2$ , is equal to :

asked Oct 6, 2015 by meena.p

1 answer

The contrapositive of the statement If it is raining, then I will not come, is :

asked Sep 30, 2015 by meena.p

1 answer

If $f(x)=2 \tan^{-1} x + \sin^{-1} \bigg(\large\frac{2x}{1+x^2}\bigg),$$x >1$ then $f(5) $ is equal to

asked Sep 30, 2015 by meena.p

1 answer

In a $\Delta ABC, \frac{a}{b}$$=2+\sqrt 3$ and $\angle C=60^{\circ}$. Then the ordered pair $\angle A, \angle B) $ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs.54 and per day mean wage of all the workers is Rs.60, then per day mean wage of the night shift workers (in Rs) is :

asked Sep 30, 2015 by meena.p

1 answer

Let X be a set containing 10 elements and $P(X)$ be its power set. If A and B are picked up at random from $P(X)$, with replacement , then the probability that A and B have equal number of elements, is :

asked Sep 30, 2015 by meena.p

1 answer

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt 3 $. If $\overrightarrow{c}=\overrightarrow{a}+2 \overrightarrow{b}+3(\overrightarrow{a} \times \overrightarrow{b})$, then $2 |\overrightarrow{c}|$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

If the shortest distance between the lines $\large\frac{x-1}{\alpha } = \frac{y+1}{-1}= \frac{z}{1} $$, (\alpha \neq -1) $ and $x+y+z+1=0=2x-y+z+3 $ is $ \large\frac{1}{\sqrt 3} $, then a value of $\alpha $ is

asked Sep 30, 2015 by meena.p

1 answer

If the points $(1, 1, \lambda)$ and $(23, 0, 1)$ are equidistant from the plane, $3x+4y-12z+13=0,$ then $\lambda$ satisfies the equation :

asked Sep 30, 2015 by meena.p

1 answer

An ellipse passes through the foci of the hyperbola, $9x^2-4y^2=36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\large\frac{1}{2}$, then which of the following points does not lie on the ellipse ?

asked Sep 30, 2015 by meena.p

1 answer

If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$(for some fixed k) at a point $(\alpha, \beta)$ then $(\alpha, \beta)$ is :

asked Sep 30, 2015 by meena.p

1 answer

If $y+3x=0$ is the equation of a chord of the circle, $ x^2+y^2-30=0$, then the equation of the circle with this chord as diameter is :

asked Sep 30, 2015 by meena.p

1 answer

Let L be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at P. If $L_1$ is the line perpendicular to L and passing through the point $(-2, 1),$ then the point of intersection of L and L1 is :

asked Sep 30, 2015 by meena.p

1 answer

The points $\bigg(0,\large\frac{8}{3}\bigg),$$(1,3)$ and $(82,30)$ :

asked Sep 30, 2015 by meena.p

1 answer

If y(x) is the solution of the differential equation $(x+2) \large\frac{dy}{dx}$$=x^2+4x-9, x \neq -2 $ and $y(0)=0,$ then $y(-4)$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

The area (in square units) of the region bounded by the curves $y+2x^2=0$ and $y+3x^2=1$, is equal to :

asked Sep 30, 2015 by meena.p

1 answer

For $x >0$ , let $f(x)= \int \limits_1^x \large\frac{log t}{1+t}$$dt$. Then $f(x)+f\bigg(\large\frac{1}{x}\bigg)$ is equal to:

asked Sep 30, 2015 by meena.p

1 answer

The integral $\int \large\frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}$ is equal to

asked Sep 29, 2015 by meena.p

1 answer

Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0, h)$ meet the x-axis at points A and B. If the area of $DAPB$ is minimum, then h is equal to :

asked Sep 29, 2015 by meena.p

1 answer

If Rolles theorem holds for the function $f (x)=2x^3+bx^2+cx, x \in [-1, 1],$ at the point $x= \large\frac{1}{2}$, then $2b+c$ equals :

asked Sep 29, 2015 by meena.p

1 answer

The distance, from the origin, of the normal to the curve, $x= 2 \cos t +2 t \sin t; y=2 \sin t- 2t \cos t 2t $ at $t= \large\frac{\pi}{4}$ is :

asked Sep 29, 2015 by meena.p

1 answer

$\lim \limits _{x \to 0} \large\frac{e^{x^2}-\cos x}{\sin ^2 x}$ is equal to

asked Sep 29, 2015 by meena.p

1 answer

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