NDA questions
2827 published questions with worked solutions.
- If k is a root of x^2-4x+1=0, then what is ^ -1 k+ ^ -1 1k equal to?
- If ^ -1 k+ ^ -1 12= 4 , then what is the value of k?
- Under what condition will the lines m^2x+ny-1=0 and n^2x-my+2=0 be perpendicular?
- If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q) and (0, 0) form an equilateral triangle, then...
- The vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the...
- ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1, 2) and that of D are (-2, 6), then...
- What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x+y=0 and x-y=0?
- A square is inscribed in a circle x^2+y^2+2x+2y+1=0 and its sides are parallel to coordinate axes. Which one of the following is...
- A tangent to the parabola y^2=4x is inclined at an angle 45^ with the positive direction of x-axis. What is the point of contact...
- What is the distance between the two foci of the hyperbola 25x^2-75y^2=225?
- If any point on an ellipse is (3 , 5 ), then what is the eccentricity of the ellipse?
- If a line in 3 dimensions makes angles , and with the positive directions of the coordinate axes, then what is ( + ) ( - ) equal...
- A(1, 2, -1), B(2, 5, -2) and C(4, 4, -3) are three vertices of a rectangle. What is the area of the rectangle?
- ABC is a triangle right-angled at B. If A(k, 1, -1), B(2k, 0, 2) and C(2+2k, k, 1) are the vertices of the triangle, then what is...
- If a line x+1 p = y-1 q = z-2 r where p=2q=3r, makes an angle with the positive direction of y-axis, then what is 2 equal to?
- What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the line whose direction ratios are 3,...
- A line makes angles , and with the positive directions of the coordinate axes. If a=( ^2 ) i+( ^2 ) j+( ^2 ) k and b= i+ j+ k,...
- Consider the following statements in respect of a vector d=( a b) c : I. d is coplanar with a and b. II. d is perpendicular to c....
- The position vectors of three points A, B and C are a, b and c respectively such that 3 a-4 b+ c= 0. What is AB:BC equal to?
- The position vectors of three points A, B and C are a, b and c respectively, where c=( ^2 ) a+( ^2 ) b. What is ( a b)+( b c)+( c...