List of top Mathematical Ability Questions

If \[ \csc\theta+\cot\theta=5 \] then \[ 11+12\tan\theta= \]
If \[ \sec\theta+\tan\theta=a \] then \[ \sin\theta= \]
If the angles of depression of the top and bottom of an 8 meter tall building from the top of a multistoried building are \(30^\circ\) and \(45^\circ\) respectively, then the height (in meters) of that multistoried building is
The sum of first six terms of an arithmetic progression is \(345\) and the difference between the first term and the sixth term is \(55\). Its first term and common difference are respectively
If \[ \frac{x+a}{b+c}+\frac{x+b}{c+a}+\frac{x+c}{a+b}=3 \] and \[ a+b+c=5, \] then \(x=\)
The number of terms in the geometric progression \[ 3,\; \frac32,\; \frac34,\dots \] that are needed to give a sum \[ \frac{3069}{512} \] is
If \[ \frac{4}{x+y}+\frac{2}{x-y}=2 \] and \[ \frac{3}{x+y}+\frac{1}{x-y}=\frac54 \] then \(y:x=\)
If \[ \sin\theta+\cos\theta=\sqrt2 \] then \[ \sin\theta\cos\theta= \]
If the polynomial \[ ax^4+bx^3+2x^2+4 \] is divisible by \[ x^2-x-2, \] then \(a+b=\)
If a polynomial in \(x\) leaves remainders \(-2,19\) respectively when divided by \(x+3\) and \(x-4\), then the remainder it leaves when it is divided by \[ x^2-x-12 \] is
If \[ f(x)=x^2+5x+p \] and \[ g(x)=x^2+3x+q \] have a common factor, then \[ (p-q)^2= \]
If \[ ax^2+bx+c \] is exactly divisible by \((x-1)\) and \((x-2)\) but leaves a remainder \(6\) when divided by \((x+1)\), then \(a+b-c=\)
The present age of father is four times the age of his son. Five years hence the age of father will be three times the age of his son. Then the present age of the son, in years, is
Each of 24 people in a movie shooting group is an actor, a musician or both. If 10 of the people in that group are actors and 19 of the group are musicians, how many of the group are musicians but not actors?
Six times a number when divided by \(8\) leaves remainder \(4\). How many such numbers are there between \(0\) and \(8\)?
A well of diameter \(3\) m is dug \(14\) m deep. The earth taken out of it is spread evenly all around it in the shape of a circular ring of width \(4\) m to form an embankment. The height of that embankment (in m) is
\(N\) denotes the set of all natural numbers. Define, for \(a \in N\) \[ aN=\{ax:x\in N\} \] Then \[ 5N \cap 3N= \]
The product of two numbers \(x,8\) when divided by \(10\) leaves the remainder \(6\). Then what is the least positive integer \(x\)?
The area of four walls of a room whose length and height are \(22\) m and \(6.5\) m respectively is \(442\) sq.m. The area of the floor in sq.m. is
If the area of a rhombus is \(24\text{ cm}^2\) and one of its diagonals is \(8\) cm, then the side of that rhombus (in cm) is
If the frustum of a cone has radii \(18\) cm and \(6\) cm on either of its ends and its slant height is \(13\) cm, then the volume (in cu. cm) of that frustum is
The area of the four walls of a room is \(88\) sq.m. Its height is \(4\) m and its floor space is square shaped. If it costs Rs.120 per sq.m. to tile its floor, the expenditure involved (in rupees) is
A copper rod of diameter \(1\) cm and length \(8\) cm is drawn into a wire of length \(18\) meters of uniform thickness. Then the thickness of that wire (in cm) is
A tank is in the form of a cylinder with circular base of radius \(10\) units and height \(7\) units. A mug in the form of cube of side \(2\) units is used to fill the tank. How many mugs of oil is required to fill the tank?
A copper rod of diameter \(1\) cm and length \(8\) cm is drawn into a wire of length \(18\) meters of uniform thickness. Then the thickness of that wire (in cm) is