9 সেমি দৈর্ঘ্য এবং প্রস্থ 6 সেমি আয়তক্ষেত্রের সেমিতে একটি দ্বিভুজের দৈর্ঘ্য হল : A. 3sqrt(13) B. ...

The length of a digonal in cm of a rectangle of length 9 cm and width 6 cm is : A. 3sqrt(13) B. pm 3sqrt(13) C. 3sqrt(5) D. pm 3sqrt(5)

If vec a and vec b are any two vectors of magnitudes 2 and 3, respectively,such that |2(vec a xxvec b)|+|3(vec a*vec b)|=k, then the maximum value of k is sqrt(13) b.2sqrt(13) c.6sqrt(13) d.10sqrt(13)

Two circles, each having radius 4, have a common tangent given by 3x+2y-6=0 at (2, 0) . Then their centres are : (A) (2+ 5/sqrt(13), 8/sqrt(13)), (2- 5/sqrt(13) , (-8)/sqrt(13)) (B) (2+ 12/sqrt(13), 8/sqrt(13)) , (2- 12/sqrt(13), (-8)/sqrt(13)) (C) (2, 3), (4, 5) (D) none of these

In a triangle the lengths of the two larger are 10 and 9 respectively.If the angles are in A.P., the , length of the third side can be (A) 5-sqrt(6) (B) 3sqrt(3) (C) 5 (D) 5+sqrt(6)

If in a /_\ ABC, a=6, b=3 and c(A-B)= 4/5 then (A) C=pi/4 (B) A=sin^-1 2/sqrt(5) (C) ar(/_\ ABC)=9 (D) none of these

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be (a) 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

If the function f(x) = x^(3) - 6x^(2) + ax + b satisfies Rolle's theorem in the interval [1,3] and f'[(2sqrt(3)+1)/sqrt(3)]=0 , then a=

Solve the following pair of linear equations by the substitution method. (i) x+y=14 ;x- y=4 (ii) s-t=3; s/3+t/2=6 (iii) 3x-y=3;9x-3y=9 (iv) 0. 2 x+0. 3 y=1. 3 ;0. 4 x+0. 5 y=2. 3 (v) sqrt(2)x+sqrt(3)y=0;sqrt(3)x-sqrt(8)y=0 (vi)3x/2-5y/2=-2;x/3+y/2=13/6

A parallelopiped is formed by planes drawn through the points (1,2,3) and (9,8,5) parallel to the coordinate planes. The length of its diagonal is (A) 2sqrt(14) units (B) 2sqrt(26) units (C) 6sqrt(3) units (D) 2sqrt(21) units