Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at
The complex number \[{{z}_{1}},\] \[{{z}_{2}}\] and \[{{z}_{3}}\] and satisfying \[\frac{{{z}_{1}}-{{z}_{3}}}{{{z}_{2}}-{{z}_{3}}}=\frac{1-i\sqrt{3}}{2},\] are the vertices of a triangle which is
For all complex numbers \[{{z}_{1}},\] \[{{z}_{2}}\] satisfying \[|{{z}_{1}}|\,=12\] and \[|{{z}_{2}}-3|4\,i=5,\] the minimum value of \[|{{z}_{1}}-{{z}_{2}}|\]is
If the angles of a triangle are \[30{}^\circ \] and \[45{}^\circ \] and the included side is \[\left( \sqrt{3}+1 \right)\]cm. Find the area of the triangle.
A straight line through the origin O meets the parallel lines \[4x+2y=9\] and \[2x+y+6=0\] at points P and Q respectively. Then the point O divides the segment PQ in the ratio
Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then
A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select one book is 63, then the value of n is
Out of a total of 600 bolts, 20 % are too large and 10 % are too small. The remaining are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is
Direction: Read the given passage carefully and answer the questions that follow.
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family.
Direction: Read the given passage carefully and answer the questions that follow.
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family.
Direction: Read the given passage carefully and answer the questions that follow.
A, B, C, D, E, F are members of a family. They are engineer, stenographer, doctor, draughtsman, lawyer and judge (not in order). A, the engineer is married to the lady stenographer. The judge is married to the lawyer. F, the draughtsman is the son of B and brother of E. C, the lawyer is the daughter-in-law of D. E is the unmarried doctor. D is the grandmother of F. There are two married couples in the family.
In a group of six women there are four dancers, four vocal musicians, one actress and three violinists. Girija and Vanaja are among the violinists while Jalaja and Shailaja do not know how to play on the violin. Shailaja and Tanuja are among the dancers. Jalaja, Vanaja, Shailaja and Tanuja are all vocal musicians and two of them are also violinists. If Pooja is an actress, who among the following is certainly a dancer and a violinist?
The letters L, M, N, O, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?