NDA questions
2295 published questions with worked solutions.
- The Cartesian product A A has 25 elements among which are found (3, 1), (6, 2), (5, 3). Which of the following statements is/are...
- Consider the following statements in respect of a relation R from a set A to a set B : I. The set B is called codomain of the...
- A circle touches each of the lines x-y=0 and x+y=0 at unit distance from the origin. The centre of the circle may be at
- A line ( )x+( )y= 2 cuts the coordinate axes at points P and Q. Let M be the midpoint of the line segment PQ. What is the...
- The centre and one of the foci (F) of an ellipse are at (0, 0) and (-c, 0) respectively. If P(x, y) is any point on the ellipse...
- A ray of light passing through the point P(1, 2) reflects on the x-axis at point N and the reflected ray passes through the point...
- A line cuts off intercept p on the x-axis and intercept q on the y-axis, where p>q. The sum of the intercepts is 2 and the...
- Let P and Q be the points on the positive x-axis and positive y-axis respectively. A point N(2, 1) divides the line segment PQ in...
- ABCD is a square. The equations of AB, AD and BD are y=0, x=0 and x+y-4=0 respectively. What is the equation of AC?
- ABC is a triangle, where the vertices A and B are fixed points both lying on the x-axis. Let AB=10 cm. The vertex C moves such...
- What is the eccentricity (e) of the parabola 4x^2+y=0?
- The vertices of a triangle are A(2, 0, 0), B(0, 6, 0) and C(0, 0, 4). If AD, BE and CF are the medians of the triangle, then what...
- A line makes angles , and with the positive directions of x-axis, y-axis and z-axis respectively such that + =90^ . Which of the...
- What is the area of the triangle whose vertices are (0, 7, 10), (-1, 6, 6) and (-4, 9, 6)?
- If O is the origin and P is the point (2, -4, 6), then what is the equation of the plane through P and perpendicular to OP?
- The image of the point P(1, 3, 4) with respect to the plane Ax+By+Cz+D=0 is (-3, 5, 2). If A+B+C=2, then what is D equal to?
- Let a , b , c and d be the vectors. Consider the following : I. ( a b ) ( c d ) II. ( a b ) ( c d ) III. ( a b ) ( c d ) IV. ( a...
- The scalar projection of a = i + j -2 k on b =2 i - j - k is 7/3. What is the value of ?
- How much angle does r =( ) i +( ) j + k make with the positive direction of z-axis?
- Let a and b be unit vectors inclined at 30^ . What is the area of the parallelogram whose sides are represented by the vectors a...