Previous year questions with solutions · 2024 – 2026
| Year | Questions | Papers | Avg / paper | Weightage |
|---|---|---|---|---|
| 2026 | 15 | 19 | 0.79 | 3.16% ▼ 21.1% vs last year |
| 2025 | 19 | 19 | 1 | 4.00% ▼ 17.2% vs last year |
| 2024 | 29 | 20 | 1.4 | 4.83% |
From the point (-1, -1), two rays are sent making angles of 45 with the line x+y=0. These rays get reflected from the mirror x+2y=1. If the equations of the reflected rays are ax+by=9 and cx+dy=7, a, b, c, d Z, then the value of ad+bc is .
Let A, B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If PQ= 92 and R is the radius of the circumcircle of PAB, then 2R is equal to .
If P is a point on the circle x2 + y2 = 4, Q is a point on the straight line 5x + y + 2 = 0 and x - y + 1 = 0 is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such points P is .
Let A(4, -2), B(1, 1) and C(9, -3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and AB of the triangle ABC respectively, is .
Let A(6,8), B(10 ,-10 ) and C(-10 ,10 ), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5a-3h+6k+100 2 ) is equal to .
Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2 is equal to .
If the orthocentre of the triangle formed by the lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 and ax + by - 1 = 0, is the centroid of another triangle, whose circumcentre and orthocentre respectively are (3, 4) and (-6, -8), then the value of |a - b| is .
Let a ray of light passing through the point (3, 10) reflects on the line 2x + y = 6 and the reflected ray passes through the point (7, 2). If the equation of the incident ray is ax + by + 1 = 0, then a2 + b2 + 3ab is equal to .
Consider a triangle ABC having the vertices A(1, 2), B( , ) and C( , ) and angles = 6 and = 2 3. If the points B and C lie on the line y = x + 4, then 2 + 2 is equal to .
Let ABC be an isosceles triangle in which A is at (-1,0), A= 2 3,AB=AC and B is on the positive x-axis. If BC=4 3 and the line BC intersects the line y=x+3 at ( , ), then 4 2 is .
Let A(-2,-1), B(1,0), C( , ) and D( , ) be the vertices of a parallelogram ABCD. If the point C lies on 2x-y=5 and the point D lies on 3x-2y=6, then the value of | + + + | is equal to .
If the sum of squares of all real values of , for which the lines 2x-y+3=0, 6x+3y+1=0 and x+2y-2=0 do not form a triangle is p, then the greatest integer less than or equal to p is .