As you are asking for Kishore Vaigyanik Protsahan Yojana (KVPY) test paper , so on your demand here I am providing same :

1. Let r be a root of the equation x2 + 2x + 6 = 0. The value of (r + 2) (r + 3) (r + 4) (r + 5) is equal to .
(A) 51 (B) –51 (C) –126 (D) 126
2. Let R be the set of all real numbers and let f be a fucntion R to R such that
1 ( ) (1 ) 1
2
fx x f x æ ö + + - = ç ÷
è ø
, for all x R Î . Then 2f(0) + 3f(1) is equal to.
(A) 2 (B) 0 (C) –2 (D) –4
3. The sum of all positive integers n for which
3 3 3
2 2 2
1 2 ..... (2 )
1 2 .....
n
n
+ + +
+ + +
is also an integer is.
(A) 8 (B) 9 (C) 15 (D) Infinite
4. Let x and y be two 2-digit numbers such that y is obtained by reversing the digits of x. Suppose they
also satisfy x2 – y2 = m2 for some positive integer m. The value of x + y + m is.
(A) 88 (B) 112 (C) 144 (D) 154
5. Let p(x) = x2 – 5x + a and q(x) = x2 – 3x + b, where a and b are positive integers. Suppose hof(p(x),q(x)
= x – 1 and k(x) = 1cm (p(x), q(x)). If the coefficient of the highest degree term of k(x) is 1, the sum of
the roots of (x – 1) + k(x) is.
(A) 4 (B) 5 (C) 6 (D) 7
6. In a quadrilateral ABCD, which is not a trapezium, it is known that 60 DAB ABC Ð =Ð = °. Moreover,
CAB CBD Ð = Ð . Then.
(A) AB = BC + CD (B) AB = AD + CD (C) AB = BC +AD (D) AB = AC + AD
7. A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region
inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

Attached Files

Kishore Vaigyanik Protsahan Yojana (KVPY) test paper.pdf (549.6 KB, 73 views)