A circus artist is climbing a $20$ m long rope, which is tightly streached and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^\circ$
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The matrix $A$ has $x$ rows and $(x+5)$ columns and the matrix $B$ has $y$ rows and $(11-y)$ columns. If both the matri…
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If $3^x = 4^{x-1}$, then $x=$
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Five horse are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select…
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Three house are available in a locality. Three persons apply for the houses. Each applies for one house without consult…
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Consider the function $f$ defined by
$f(x)=\begin{cases} x^2-1, & x
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The sum of the expression $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\cdot…
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The probability that $A$ speaks truth is $4/5$ while this probability for $B$ is $3/4$. The probability that they contr…
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Two finite sets $A$ and $B$ are having $m$ and $n$ elements. The total number of subsets of the first set is $56$ more …
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For any two events $A$ and $B$, the probability that atleast one of them occur is $0.6$. If $A$ and $B$ occur simultane…
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The minimum value of $a$, for which the sum of the squares of the roots of the equation $x^2-(a-2)x-(a+1)=0$
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There are n equally spaced points 1,2,...,n marked on the circumference of a circle. If the point 15 is directly opposi…
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Let S={1,2,....,n}. The number of possible pairs of the form (A,B) with $A \subseteq B$ for subsets $A,B$ of $S$ is
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Sum of the roots of the equation $4^x - 3(2^{x+3}) + 128 = 0$ is
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If the sum of the slopes of the lines given by $x^2 - 2cxy - 7y^2 = 0$ is four times their product, then the value of $…
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The system of equationsx + y + 2z = ax + z = b2x + y + 3z = chas a solution if
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Let $f(x) = x^2 - bx + c$, b is an odd positive integer. If f(x)=0 has two prime numbers as roots and b + c = 35, then …
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The vertex of the parabola whose focus is (-1,1) and directrix is 4x + 3y - 24 = 0 is
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The number of points in $(-\infty,\infty)$, for which $x^2 - x\sin x - \cos x = 0$ is
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There are $4$ books on fairy tales, $5$ novels and $3$ plays. In how many ways can they be arranged in the order books …
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Suppose a population $A$ has $100$ observations $101,102,\ldots,200$ and another population $B$ has $100$ observations …
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