-
1. All the three roots of equation x3 –- 3x +1 = 0 lie on the interval (A) [–2, 0] (B) [–1, 1] (C) [–2, 2] (D) [–1, 2] 2. If ax2 + bx + c, a, b, c belog to R has no real zeros and if a + b + c < 0 then (A) c > 0 (B ...
-
1. If p, q, r be in H.P. and p and r be different having same sign, then the root of the equation px2 + 2q + r = 0 will be (A) Real (B) Equal (C) Imaginary (D) None of these 2. If the equation (k – 2) x2- – (k –- 4) x- – ...
-
Two mirrors at an angle θº produce 5 images of a point. The number of images produced when θ is decreased to θº – 30º is (A) 9 (B) 10 (C) 11 (D) 12 ...
-
1. If ABCD is cyclic quadrilateral, show that AC . BD = AB . CD + BC . AD 2. In a ΔABC, show that a3 cos (B – C) + b3 cos (C – A) + c3 cos (A – B) = 3 abc ...
-
1. A man observes, that when he moves up a distance c meters on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30º; and when he moves up further a distance c meters the angl ...
-
find the largest interval in which x lies satisfying x^{12}-x^{9}+x^{4}-x+1>0 ...
-
From a conduction ring of radius R which carries a charge Q (uniformly distributed) along its periphery a small length dl is cut off. The electric field at the center due to the remaining part is ? ...
-
1. Find the real values of a so that a2+2a,a2+3a+8,2a+3 are the sides of a triangle. 2. If x=2+21/3+22/3 then the value of x3-6x^2+6x is ? 3. Find the eqn whose roots are two more than the roots of ax^2+bx+c=0 . ...
-
find the max value of (cos\,\, \alpha _{1}) (cos\,\, \alpha _{2}) ...... (cos\,\, \alpha _{n}) under the restrictions 0\leq \alpha _{i}\leq \Pi /2 and (cot\,\, \alpha _{1}) (cot\,\, \alpha _{2}) ...... (cot\,\, \alpha _{n}) = ...
-
If f(x)=\frac{ax}{x+1} , x\neq -1 then for what value of a is f(f(x))=x ? ...
-
If ax+by+c=0 is a tangent to xy=4, then find the sign of a and c . ...
-
What digit is the least frequent between the numbers 1 and 1,000? ...
-
How can you add eight 8's to get the number 1,000? (only use addition) ...
-
A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the s ...
-
Find the sum of all four digit palindromes. ...
-
1. Find the total number of terms in the expansion of (x + y + z + w)n , n ∈ N. 2. Find numerically greatest term in the expansion of (2 + 3x)9, when x = 3/2 ...
-
1. If α,β are the roots of x2+px+q=0 then express α5+β5 in terms of p and q. 2. \left|\left|x-1 \right|-x \right| \leq 4 ...
-
Let z and w be two complex numbers such that \bar{z} +i\bar{w} =0 and arg zw=∩ , then arg z is equal to ? ...
-
1. Sum of the series : 1 + 3x + 5x2 + 7x3 + ......... 2. Sum the series : 1.2.3 + 2.3.4 + 3.4.5. + ......... + to n terms. 3. Sum the series : 12 + (12 + 22) + (12 + 22 + 32) + ........ to n terms. ...
-
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12m/s2. The displacement of the block during the first 0.2 s after the start assuming g = 10 m/s2 is (a) 4 cm (b) 20 ...
-
A cubical block of mass m and edge a slides down a rough inclined plane of inclination with a uniform speed. The torque of the normal force acting on the block about its centre is ? ...
-
5x/2-2x=1 ...
-
two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...
-
two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...
-
two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...
-
two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...
-
\left|x-2 \right|^{log_{2}x^{3}-3log_{x}4} = (x-2)^{3} ...
-
x^{2}+y(x+1)=17 y^{2}+x(y+1)=13 ...
-
If one root of ax^2+bx-2c=0 (a,b,c are real) is imaginary and 8a+2b>c , then a) a>0 and c<0 b)a>0 and c>0 c)a<0,c>0 d)a<0,c<0 ...
-
xy+x+y=23 xz+x+z=41 yz+y+z=27 ...
