Mathematics questions
18011 published questions with worked solutions.
- The number of integral values of a for which the equation ^2x- x+a=0 has roots when x (0, /2) is ____.
- The number of roots of the equation (3+ x)^2=4-2 ^8x, x [0,5 ], is ____.Not in JEE Main syllabus
- The number of solutions of the equation ^4x- ^2x x+2 ^2x+ x=0 in 0 x 3 is ____.Not in JEE Main syllabus
- The number of values of p for which the equation ^3x+1+p^3-3p x=0 (p>0) has a root is ____.
- The number of solutions of the equation x 3x + 3x 9x + 9x 27x =0 in the interval (0, 4 ) is ____.Not in JEE Main syllabus
- The value of a for which the system of equations ^2x+ ^2y= 3a 2 and ^2x+ ^2y= a^2 2 has a solution is ____.Not in JEE Main syllabus
- A circle inscribed in a triangle ABC touches the side AB at D such that AD=5 and BD=3. If A=60^ , then the value of [BC/3] (where...Not in JEE syllabus
- In triangle ABC, A B+ B C+ C A=9/4 and a=2. Then the value of 3 , where is the area of the triangle, is ____.Not in JEE syllabus
- In ABC, C=2 A and AC=2BC. Then the value of a^2+b^2+c^2 R^2 (where R is the circum-radius of the triangle) is ____.Not in JEE syllabus
- The sides of triangle ABC satisfy the relations a+b-c=2 and 2ab-c^2=4. Then the square of the area of the triangle is ____.Not in JEE syllabus
- In ABC, if C=3 A, BC=27 and AB=48, then the value of AC/7 is ____.Not in JEE syllabus
- Consider a ABC in which the sides are a=(n+1), b=(n+2), c=n with C=4/3. Then the value of /12 is ____.Not in JEE syllabus
- Two equilateral triangles are constructed from a line segment of length L (the segment is cut into two parts, possibly of zero...
- The area of a right triangle is 6864 square units. If the ratio of its legs is 143:24, then the value of [r/4], where r is the...Not in JEE syllabus
- In ABC the incircle touches the sides BC, CA and AB respectively at D, E and F. If the radius of the incircle is 4 units and BD,...Not in JEE syllabus
- In ABC, if A+ A- 2 B+ B =0, then the value of ( a+b c )^4 is ____.Not in JEE syllabus
- In ABC, AB=52, BC=56, CA=60. Let D be the foot of the altitude from A, and E be the intersection of the internal angle bisector...Not in JEE syllabus
- In ABC, if r=1, R=3 and s=5, then the value of a^2+b^2+c^2 3 is ____.Not in JEE syllabus
- The altitudes from the angular points A, B and C on the opposite sides BC, CA and AB of ABC are 210, 195 and 182 respectively....Not in JEE syllabus
- Suppose , , and are the interior angles of a regular pentagon, hexagon, decagon and dodecagon respectively. Then the value of | ,...