List of top Mathematical Ability Questions on Geometry

Equation of a straight line which makes an angle \(150^\circ\) with the positive direction of X-axis and an intercept \(4\) units on the Y-axis is

The arithmetic mean of \(4^2,\,8^2,\,12^2,\ldots,32^2\) is

The straight line \(5x+3ay+k=0\) with the slope \(\dfrac{10}{9}\) passing through the point \((4,8)\), then \(k=\)

The equation of the line passing through the origin and perpendicular to the line joining the points \(A(4,-3)\) and \(B(6,3)\) is

A line cuts the positive axes \(OX\), \(OY\) in the points \(A\), \(B\) respectively. If the point \(P(3,5)\) divides the line \(AB\) in the ratio \(2:1\) internally, then the equation of the line is

A line passing through the point \(P(2,1)\) meets the coordinate axes in \(A\) and \(B\). If \(P\) divides \(AB\) in the ratio \(4:3\), then the equation of \(AB\) is

The equation of a straight line whose slope is \(\frac13\) and which divides the line joining the points \(A(0,2)\) and \(B(5,-3)\) in the ratio \(4:7\) is

Let \(A(7,2)\), \(B(0,1)\) be any two points. If the distance of \(P(x,5)\) from \(A\) is same as the distance from \(B\), then the value of \(x\) is

ABCD is a quadrilateral with \(A(3,5)\), \(B(5,9)\) and \(C(3,7)\). If the line \(y=3x\) meets the sides \(AB\) and \(BC\) in points \(P\) and \(Q\) respectively, then \(PQ^2=\)

In a triangle \(PQR\), \(PS\) is the angle bisector of \(\angle P\). \(PQ=3\), \(QS=2\) and \(SR=3\), then \(PR=\)

\(P,Q,R\) are points on a circle with centre \(O\) as shown in the figure. If \(\angle PQR=100^\circ\), then \(\angle OPR=\)

\(ABCD\) is a cyclic quadrilateral whose diagonals intersect at \(E\). If \(\angle DBC=70^\circ\), \(\angle BAC=30^\circ\) and \(AB=BC\), then \(\angle ECD=\)

In a trapezium, the two non-parallel sides are of length \(13\) cm each. The distance between the parallel sides is \(12\) cm. If the smaller of the parallel sides is \(11\) cm, then the sum of the lengths of the two diagonals, in cm, is

In the adjacent figure \(PT\) is a tangent drawn from an external point \(P\) touching the circle at \(T\). \(PAB\) is a secant cutting the circle at \(A\) and \(B\). If \(PT=5\) cm and \(PA=4\) cm, then \(AB\) (in cm) is

The line \(L_1\) is parallel to \(L_2\) and line \(L_3\) is parallel to \(L_4\). In the figure, the relation between \(a^\circ\) and \(b^\circ\) is

Find \[ \tan1^\circ \tan2^\circ \tan3^\circ \cdots \tan89^\circ \]

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

If \[ \csc\theta+\cot\theta=5 \] then \[ 11+12\tan\theta= \]

If \[ f(x)=x^2+5x+p \] and \[ g(x)=x^2+3x+q \] have a common factor, then \[ (p-q)^2= \]

If the polynomial \[ ax^4+bx^3+2x^2+4 \] is divisible by \[ x^2-x-2, \] then \(a+b=\)

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?

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

Six times a number when divided by \(8\) leaves remainder \(4\). How many such numbers are there between \(0\) and \(8\)?

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