The radical axis of three circles, taken in pairs (A) may form a triangle (B) are necessarily concurrent (C) are necessarily parallel (D) are either concurrent or parallel

If a,b,c,depsilon R and f(x)=ax^3+bx^2-cx+d has local extrema at two points of opposite signs and abgt0 then roots of equation ax^2+bx+c=0 (A) are necessarily negative (B) have necessarily negative real parts (C) have necessarily positive real parts (D) are necessarily positive

Read the following statements which are taken as axioms (i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal. (ii) If a transversal intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent ? Justify your answer.

The equation xy+yz=0 represents (A) a pair of straight lines (B) a pair of parallel lines (C) a pair of parallel planes (D) a pair of perpendicular planes

The equation xy=0 in three dimensional space is represented by (A) a plane (B) two planes at righat angles (C) a pair of parallel planes (D) a pair of straighat lines

Assertion: Number of triangles formed by n concurrent lines and a line which is parallel to one of the n concurrent lines is "^(n-1)C_2. Reason: One and only one triangle is formed by three lines out of which 2 are concurrent and third line is not passing through the point of intersection of the concurrent lines and not parallel to any of the concurrent lines. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Three lines 3x+4y+6=0, sqrt(2) x + sqrt(3) y + 2sqrt(2)=0 and 4x+7y+8=0 are (A) sides of triangle (B) concurrent (C) parallel (D) none of these

The planes x=0 and y=0 (A) are parallel (B) are perpendicular to each other (C) interesect in z-axis (D) none of these

Two circles are drawn with sides A B ,A C of a triangle A B C as diameters. The circles intersect at a point D . Prove that D lies on B C .

From the given figure, write (i) all pairs of parallel lines (ii) all pairs of intersecting lines (iii) concurrent lines and point of concurrence (iv) collinear points

State true or false. (a) The altitude of an acute-angled triangle lies outside the triangle. (b) the orthocentre of an obtuse-angled triangle lies outside the triangle. (c) the orthocentre is the point of concurrency of three medians of a triangle. (d) The vertex containing the right angle is also the orthocentre of a right-angled triangle.