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<form method="get" id="searchform" action="<?php echo esc_url( home_url( '/' ) ); ?>">
    <label for="s" class="assistive-text"><?php _e( 'Search', 'twentyeleven' ); ?></label>
    <input type="text" class="field" name="s" id="s" placeholder="<?php esc_attr_e( 'Search', 'twentyeleven' ); ?>" />
<input type="hidden" name="cat" id="cat" value="1" />
    <input type="submit" class="submit" name="submit" id="searchsubmit" value="<?php esc_attr_e( 'Search', 'twentyeleven' ); ?>" />
</form>
//if you need more categories than replace value, like: <input type="hidden" name="cat" id="cat" value="1,3,45,123" />